144 results on '"stochastic optimal control"'
Search Results
2. Optimal consumption, investment and life-insurance purchase under a stochastically fluctuating economy.
- Author
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Mousa, A. S., Pinheiro, D., Pinheiro, S., and Pinto, A. A.
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STOCHASTIC differential equations , *NONLINEAR differential equations , *STOCHASTIC control theory , *DYNAMIC programming , *UTILITY functions , *STOCHASTIC processes - Abstract
We study the optimal consumption, investment and lifeinsurance purchase and selection strategies for a wage-earner with an uncertain lifetime with access to a financial market comprised of one risk-free security and one risky-asset whose prices evolve according to linear diffusions modulated by a continuous-time stochastic process determined by an additional diffusive nonlinear stochastic differential equation. The process modulating the linear diffusions may be regarded as an indicator describing the state of the economy in a given instant of time. Additionally, we allow the Brownian motions driving each of these equations to be correlated. The lifeinsurance market under consideration herein consists of a fixed number of providers offering pairwise distinct contracts. We use dynamic programming techniques to characterize the solutions to the problem described above for a general family of utility functions, studying the case of discounted constant relative risk aversion utilities with more detail. [ABSTRACT FROM AUTHOR]
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- 2024
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3. An exit contract optimization problem.
- Author
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He, Xihao, Tan, Xiaolu, and Zou, Jun
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STOCHASTIC control theory , *STOCHASTIC processes , *CONTRACTS , *CONTRACT theory - Abstract
We study an exit contract design problem, where one provides a universal exit contract to multiple heterogeneous agents, with which each agent chooses an optimal (exit) stopping time. The problem consists in optimizing the universal exit contract w.r.t. some criterion depending on the contract as well as the agents' exit times. Under a technical monotonicity condition, and by using Bank-El Karoui's representation of stochastic processes, we are able to transform the initial contract optimization problem into an optimal control problem. The latter is also equivalent to an optimal multiple stopping problem and the existence of the optimal contract is proved. We next show that the problem in the continuous-time setting can be approximated by a sequence of discrete-time ones, which would induce a natural numerical approximation method. We finally discuss the optimization problem over the class of all Markovian and/or continuous exit contracts. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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4. An optimal control problem for the maintenance of a machine.
- Author
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Lefebvre, Mario and Pazhoheshfar, Peiman
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STOCHASTIC control theory , *DYNAMIC programming , *STOCHASTIC processes , *INTEGRAL equations , *RANDOM variables - Abstract
A controlled discrete-time stochastic process is proposed as a model for the state of a machine. In the proposed model, normal and random wear of the machine are considered. The random wear of the machine during a time unit can be either a discrete or a continuous random variable. The objective is to find a control policy that maximises the profits generated by the machine over its useful lifetime. In this problem, the optimiser must decide whether to do or not to do the maintenance work on the machine at each time unit. The significance of the paper is that the final time in the optimal control problem is a random variable denoting the first time the machine must be replaced. To obtain the optimal control, one can try to solve the dynamic programming equation, which reduces to a difference or an integral equation, satisfied by the value function. Finally, particular cases are solved exactly, or approximately, and explicitly to demonstrate and validate the proposed model. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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5. Time-symmetric optimal stochastic control problems in space-time domains.
- Author
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Cruzeiro, Ana Bela, Oliveira, Carlos, and Zambrini, Jean-Claude
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STOCHASTIC control theory , *SPACETIME , *STOCHASTIC processes - Abstract
We present a pair of adjoint optimal control problems characterizing a class of time-symmetric stochastic processes defined on random time intervals. The associated PDEs are of free-boundary type. The particularity of our approach is that it involves two adjoint optimal stopping times adapted to a pair of filtrations, the traditional increasing one and another, decreasing. They are the keys of the time symmetry of the construction, which can be regarded as a generalization of 'Schrödinger's problem' (1931–1932) to space-time domains. The relation with the notion of 'Hidden diffusions' is also described. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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6. A Stochastic Switched Optimal Control Approach to Formation Mission Design for Commercial Aircraft.
- Author
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Cerezo-Magana, Maria, Olivares, Alberto, and Staffetti, Ernesto
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STOCHASTIC control theory , *COMMERCIAL art , *TRADE missions , *RANDOM numbers , *STOCHASTIC analysis , *ORTHOGONAL polynomials , *POLYNOMIAL chaos - Abstract
This article studies the formation mission design problem for commercial aircraft in the presence of uncertainties. Specifically, it considers uncertainties in the departure times of the aircraft and in the fuel burn savings for the trailing aircraft. Given several commercial flights, the problem consists in arranging them in formation or solo flights and finding the trajectories that minimize the expected value of the DOC of the flights. The formation mission design problem is formulated as an optimal control problem of a stochastic switched dynamical system and solved using nonintrusive gPC-based stochastic collocation. The stochastic collocation method converts the SSOCP into an augmented deterministic switched optimal control problem. With this approach, a small number of sample points of the random parameters are used to jointly solve particular instances of the switched optimal control problem. The obtained solutions are then expressed as orthogonal polynomial expansions in terms of the random parameters using these sample points. This technique allows statistical and global sensitivity analysis of the stochastic solutions to be conducted at a low computational cost. The aim of this article is to establish if, in the presence of uncertainties, a formation mission is beneficial with respect to solo flight in terms of the expected value of the direct operating costs. Several numerical experiments have been conducted in which uncertainties on the departure times and on the fuel saving during formation flight have been considered. The obtained results demonstrate that benefits can be achieved even in the presence of these uncertainties. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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7. THE MOST LIKELY EVOLUTION OF DIFFUSING AND VANISHING PARTICLES: SCHRÖDINGER BRIDGES WITH UNBALANCED MARGINALS.
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YONGXIN CHEN, GEORGIOU, TRYPHON T., and PAVON, MICHELE
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STOCHASTIC processes , *PHYSICAL sciences , *TRANSPORT equation , *MARGINAL distributions , *STOCHASTIC control theory , *NEUTRON transport theory - Abstract
Stochastic flows of an advective-diffusive nature are ubiquitous in biology and the physical sciences. Of particular interest is the problem of reconciling observed marginal distributions with a given prior posed by Schrödinger in 1932 and known as the Schrödinger Bridge Problem (SBP). It turns out that Schrödinger's problem can be viewed as both a modeling problem and a control problem. Due to their fundamental significance, the SBP and its deterministic (zero-noise limit) counterpart of Optimal Mass Transport (OMT) have recently received interest within a broad spectrum of disciplines, including physics, stochastic control, computer science, probability theory, and geometry. Yet, while the mathematics and applications of the SBP/OMT have been developing at a considerable pace, accounting for marginals of unequal mass has received scant attention; the problem of interpolating between "unbalanced" marginals has been approached by introducing source/sink terms into the transport equations, in an ad hoc manner, chiefly driven by applications in image registration. Nevertheless, losses are inherent in many physical processes, and thereby models that account for lossy transport may also need to be reconciled with observed marginals following Schrödinger's dictum; that is, it is necessary to adjust the probability of trajectories of particles, including those that do not make it to the terminal observation point, so that the updated law represents the most likely way that particles may have been transported, or have vanished, at some intermediate point. Thus, the purpose of this work is to develop such a natural generalization of the SBP for stochastic evolution with losses, whereupon particles are "killed" (jump into a coffin/extinction state) according to a probabilistic law, and thereby mass is gradually lost along their stochastically driven flow. Through a suitable embedding we turn the problem into an SBP for stochastic processes that combine diffusive and jump characteristics. Then, following a large-deviations formalism in the style of Schrödinger, given a prior law that allows for losses, we ask for the most probable evolution of particles along with the most likely killing rate as the particles transition between the specified marginals. Our approach differs sharply from previous work involving a Feynman-Kac multiplicative reweighing of the reference measure: The latter, as we argue, is far from Schrödinger's quest. An iterative scheme, generalizing the celebrated Fortet-IPF-Sinkhorn algorithm, permits us to compute the new drift and the new killing rate of the path-space solution measure. We finally formulate and solve a related fluid-dynamic control problem for the flow of one-time marginals where both the drift and the new killing rate play the role of control variables. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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8. Decentralized Learning for Optimality in Stochastic Dynamic Teams and Games With Local Control and Global State Information.
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Yongacoglu, Bora, Arslan, Gurdal, and Yuksel, Serdar
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STOCHASTIC control theory , *SPACE trajectories , *TEAMS - Abstract
Stochastic dynamic teams and games are rich models for decentralized systems and challenging testing grounds for multiagent learning. Previous work that guaranteed team optimality assumed stateless dynamics, or an explicit coordination mechanism, or joint-control sharing. In this article, we present an algorithm with guarantees of convergence to team optimal policies in teams and common interest games. The algorithm is a two-timescale method that uses a variant of Q-learning on the finer timescale to perform policy evaluation while exploring the policy space on the coarser timescale. Agents following this algorithm are “independent learners”: they use only local controls, local cost realizations, and global state information, without access to controls of other agents. The results presented here are the first, to the best of our knowledge, to give formal guarantees of convergence to team optimality using independent learners in stochastic dynamic teams and common interest games. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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9. Stochastic Linear Quadratic Optimal Control Problem: A Reinforcement Learning Method.
- Author
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Li, Na, Li, Xun, Peng, Jing, and Xu, Zuo Quan
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REINFORCEMENT learning , *DYNAMIC programming , *ONLINE algorithms , *RICCATI equation , *STOCHASTIC control theory - Abstract
This article adopts a reinforcement learning (RL) method to solve infinite horizon continuous-time stochastic linear quadratic problems, where the drift and diffusion terms in the dynamics may depend on both the state and control. Based on the Bellman’s dynamic programming principle, we presented an online RL algorithm to attain optimal control with partial system information. This algorithm computes the optimal control, rather than estimates the system coefficients, and solves the related Riccati equation. It only requires local trajectory information, which significantly simplifies the calculation process. We shed light on our theoretical findings using two numerical examples. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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10. On Forward–Backward Stochastic Differential Equations in a Domination-Monotonicity Framework.
- Author
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Yu, Zhiyong
- Subjects
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STOCHASTIC differential equations , *CONTINUATION methods , *RANDOM variables , *STOCHASTIC systems , *HAMILTONIAN systems , *STOCHASTIC processes - Abstract
In this paper, inspired by various stochastic linear-quadratic (LQ, for short) problems, we develop the method of continuation to study nonlinear forward–backward stochastic differential equations (FBSDEs, for short) in a kind of domination-monotonicity frameworks. The coupling of FBSDEs is in a general form, i.e., it not only appears in integral terms and terminal terms, but also in initial terms. By virtue of introducing various matrices, matrix-valued random variables and matrix-valued stochastic processes, we present the domination-monotonicity framework carefully and rigorously. A unique solvability result and a pair of estimates for coupled FBSDEs are obtained (see Theorem 3.5 in the case of simple domination-monotonicity conditions and Theorem 5.2 in the case of multi-level self-similar domination-monotonicity structures). As applications of theoretical results, the related stochastic Hamiltonian systems of several LQ problems are discussed. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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11. Application of the Free Energy Principle to Estimation and Control.
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vandelaar, Thijs, Ozcelikkale, Ayca, and Wymeersch, Henk
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STOCHASTIC control theory , *COST control , *PREDICTIVE control systems , *PROBABILITY density function , *STOCHASTIC processes , *BINDING energy - Abstract
Based on a generative model (GM) and beliefs over hidden states, the free energy principle (FEP) enables an agent to sense and act by minimizing a free energy bound on Bayesian surprise, i.e., the negative logarithm of the marginal likelihood. Inclusion of desired states in the form of prior beliefs in the GM leads to active inference (ActInf). In this work, we aim to reveal connections between ActInf and stochastic optimal control. We reveal that, in contrast to standard cost and constraint-based solutions, ActInf gives rise to a minimization problem that includes both an information-theoretic surprise term and a model-predictive control cost term. We further show under which conditions both methodologies yield the same solution for estimation and control. For a case with linear Gaussian dynamics and a quadratic cost, we illustrate the performance of ActInf under varying system parameters and compare to classical solutions for estimation and control. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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12. Stochastic Optimization of Microgrids With Hybrid Energy Storage Systems for Grid Flexibility Services Considering Energy Forecast Uncertainties.
- Author
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Garcia-Torres, Felix, Bordons, Carlos, Tobajas, Javier, Real-Calvo, Rafael, Santiago, Isabel, and Grieu, Stephane
- Subjects
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GRID energy storage , *ENERGY storage , *POWER resources , *STOCHASTIC control theory , *QUADRATIC programming - Abstract
This paper presents a stochastic framework for the optimization of microgrids that has the functionality of providing flexibility services to System Operators (SOs) considering uncertainties in the energy forecast. The methodology is developed with the aim of being applied to complex microgrids composed of different distributed energy resources and hybrid energy storage systems (ESS). The associated optimization problem is operated in two stages: the first one performs a stochastic optimization of the microgrid in order to reserve an up/down regulation capacity with which to deal with the energy forecast uncertainties of the microgrid. The different microgrid devices are optimized by considering their operational costs in order to achieve their optimal operation in the Day-Ahead Market (DM). The second stage is used to re-schedule the initial planning according to the signal request and an economic offer from the SO. The control problem is developed using Stochastic Model Predictive Control (SMPC) techniques and Mixed-Integer Quadratic Programming (MIQP), owing to the presence of logic, integer, mixed and probabilistic variables. The simulation results show that the proposed methodology reduces the risk of undergoing up/down-penalty deviations in the Regulation Service Market (RM), also being able to provide flexibility services to the SOs, despite being subject to uncertainties in the energy forecast carried out for the microgrid. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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13. Robust Controller Design for Stochastic Nonlinear Systems via Convex Optimization.
- Author
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Tsukamoto, Hiroyasu and Chung, Soon-Jo
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NONLINEAR systems , *STOCHASTIC systems , *NONLINEAR equations , *STOCHASTIC control theory , *STOCHASTIC analysis , *PID controllers , *STATE feedback (Feedback control systems) - Abstract
This article presents ConVex optimization-based Stochastic steady-state Tracking Error Minimization (CV-STEM), a new state feedback control framework for a class of Itô stochastic nonlinear systems and Lagrangian systems. Its innovation lies in computing the control input by an optimal contraction metric, which greedily minimizes an upper bound of the steady-state mean squared tracking error of the system trajectories. Although the problem of minimizing the bound is nonconvex, its equivalent convex formulation is proposed utilizing SDC parameterizations of the nonlinear system equation. It is shown using stochastic incremental contraction analysis that the CV-STEM provides a sufficient guarantee for exponential boundedness of the error for all time with ${\bf \mathcal {L}_2}$ -robustness properties. For the sake of its sampling-based implementation, we present discrete-time stochastic contraction analysis with respect to a state- and time-dependent metric along with its explicit connection to continuous-time cases. We validate the superiority of the CV-STEM to PID, $\mathcal {H}_\infty$ , and baseline nonlinear controllers for spacecraft attitude control and synchronization problems. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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14. Incentives to Manipulate Demand Response Baselines With Uncertain Event Schedules.
- Author
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Ellman, Douglas and Xiao, Yuanzhang
- Abstract
We study baseline-based demand response (DR) programs. In such programs, customers get rebates based on how much they reduce electricity consumption during DR events relative to a “baseline,” where this baseline is determined by their consumption during previous non-event days. Customers, or automated controls working on their behalf, can achieve higher DR payments by decreasing consumption during DR events (desired behavior), and by increasing consumption during non-event times (baseline manipulation). Importantly, the customers have imperfect knowledge of when future demand response events will occur. To understand customers’ incentives for baseline manipulation, we present a novel multi-stage stochastic dynamic programming model that optimizes customer actions for maximum expected rewards under uncertain event schedules. Analytical results for special cases show fundamental drivers of customer incentives. Simulation results reveal incentives to manipulate baselines and impacts to program performance for a realistic baseline-based demand response program, and how program and customer parameters affect incentives. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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15. Application of stochastic differential games and real option theory in environmental economics
- Author
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Wang, Wen-Kai and Ewald, Christian-Oliver
- Subjects
333 ,Differential games ,Real options ,Stochastic optimal control ,Public goods ,Fisheries ,Maximum sustainable yields ,Cox-Ross-Ingersoll process ,Environmental economics ,HD75.5W26 ,Environmental economics--Mathematical model ,Real options (Finance)--Mathematical models ,Differential games ,Stochastic processes ,Fisheries--Economic aspects--Mathematical models - Abstract
This thesis presents several problems based on papers written jointly by the author and Dr. Christian-Oliver Ewald. Firstly, the author extends the model presented by Fershtman and Nitzan (1991), which studies a deterministic differential public good game. Two types of volatility are considered. In the first case the volatility of the diffusion term is dependent on the current level of public good, while in the second case the volatility is dependent on the current rate of public good provision by the agents. The result in the latter case is qualitatively different from the first one. These results are discussed in detail, along with numerical examples. Secondly, two existing lines of research in game theoretic studies of fisheries are combined and extended. The first line of research is the inclusion of the aspect of predation and the consideration of multi-species fisheries within classical game theoretic fishery models. The second line of research includes continuous time and uncertainty. This thesis considers a two species fishery game and compares the results of this with several cases. Thirdly, a model of a fishery is developed in which the dynamic of the unharvested fish population is given by the stochastic logistic growth equation and it is assumed that the fishery harvests the fish population following a constant effort strategy. Explicit formulas for optimal fishing effort are derived in problems considered and the effects of uncertainty, risk aversion and mean reversion speed on fishing efforts are investigated. Fourthly, a Dixit and Pindyck type irreversible investment problem in continuous time is solved, using the assumption that the project value follows a Cox-Ingersoll- Ross process. This solution differs from the two classical cases of geometric Brownian motion and geometric mean reversion and these differences are examined. The aim is to find the optimal stopping time, which can be applied to the problem of extracting resources.
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- 2009
16. Stochastic Optimal Control of a Descriptor System.
- Author
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Vlasenko, L. A., Rutkas, A. G., Semenets, V. V., and Chikrii, A. A.
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DIFFERENTIAL-algebraic equations , *STOCHASTIC control theory , *DIFFERENTIAL evolution , *WHITE noise , *DESCRIPTOR systems , *MATRIX pencils , *RADIO engineering , *STOCHASTIC differential equations , *STOCHASTIC processes - Abstract
We study the optimal control problem for a descriptor system whose evolution is described by Ito's differential-algebraic equation. The quadratic cost functional is considered. The main constraint is that the characteristic matrix pencil corresponding to the equation is regular. We establish the conditions for the existence and uniqueness of the optimal control and the corresponding optimal state. The results are illustrated on an example of a descriptor system that describes transient states in a radio engineering filter with random perturbations in the form of white noise. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
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17. Event- and Deadline-Driven Control of a Self-Localizing Robot With Vision-Induced Delays.
- Author
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van Horssen, Eelco P., van Hooijdonk, Jeroen A. A., Antunes, Duarte, and Heemels, W. P. M. H.
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ROBOT control systems , *LOCALIZATION (Mathematics) , *STOCHASTIC control theory , *RANDOM variables , *ROBOT vision , *IMAGE processing , *INFORMATION storage & retrieval systems - Abstract
Control based on vision data is a growing field of research and it is widespread in industry. The amount of data in each image and the processing needed to obtain control-relevant information from this data lead to significant delays with a large variability in the control loops. This often causes performance deterioration since in many cases the delay variability is not explicitly addressed in the control design. In this paper, we approach this problem by applying the ideas of recently developed model-based control design methods, which are tailored to address stochastic delays directly, to the motion control of an omnidirectional robot with a vision-based self-localization algorithm. The completion time or delay of the Random Sample Consensus (RANSAC) based localization algorithm is identified as a stochastic random variable with significant variability, illustrating the practical difficulties with data processing. Our main aim is to show that the novel deadline-driven and event-driven control designs significantly outperform a traditional periodic control implementation for a stochastic optimal control performance index. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
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18. Joint hybrid repair and remanufacturing systems and supply control.
- Author
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Berthaut, F., Gharbi, A., and Pellerin, R.
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REMANUFACTURING ,STOCHASTIC processes ,INVENTORY control ,INDUSTRIAL equipment maintenance & repair ,BUSINESS logistics ,INVENTORY management systems ,ECONOMICS - Abstract
The control of a stochastic manufacturing system that executes capital asset repairs and remanufacturing in an integrated system is examined. The remanufacturing resources respond to planned returns of worn-out equipment at the end of their expected life and unplanned returns triggered by major equipment failures. Remanufacturing operations for planned demand can be executed at different rates and costs corresponding to different replacement and repair modes. The replacement components inventory is provided by an upstream supply with random lead times. The objective is to determine a control policy for both the supply and remanufacturing activities that minimises the average repair/replacement, acquisition and inventory/shortage total cost over an infinite horizon. We propose a suboptimal joint remanufacturing and supply control policy, composed of a multi-hedging point policy (MHPP) for the remanufacturing stage and an (s, Q) policy for the replacement parts supply. The MHPP is based on two inventory thresholds that trigger the use of predefined remanufacturing modes. Control policy parameters are obtained combining analytical modelling, simulation experiments and response surface methodology. The effects of the distribution, mean and variability of the lead time are tested and a sensitivity analysis of cost parameters is conducted to validate the proposed control policy. We also show that our policy leads to a significant cost reduction as compared to a combination of a hedging point policy (HPP) and an (s, Q) policy. [ABSTRACT FROM AUTHOR]
- Published
- 2010
- Full Text
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19. Collective Stochastic Discrete Choice Problems: A Min-LQG Dynamic Game Formulation.
- Author
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Salhab, Rabih, Malhame, Roland P., and Le Ny, Jerome
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MEAN field theory , *EQUILIBRIUM , *RECREATIONAL mathematics , *NASH equilibrium , *STOCHASTIC control theory , *SOCIAL choice , *DISCRETE choice models - Abstract
We consider a class of dynamic collective choice models with social interactions, whereby a large number of nonuniform agents have to individually settle on one of multiple discrete alternative choices, with the relevance of their would-be choices continuously impacted by noise and the unfolding group behavior. This class of problems is modeled here as a so-called min-LQG game, i.e., a linear quadratic Gaussian dynamic and noncooperative game, with an additional combinatorial aspect in that it includes a final choice-related minimization in its terminal cost. The presence of this minimization term is key to enforcing some specific discrete choice by each individual agent. The theory of mean field games is invoked to generate a class of decentralized agent feedback control strategies, which are then shown to converge to an exact Nash equilibrium of the game as the number of players increases to infinity. A key building block in our approach is an explicit solution to the problem of computing the best response of a generic agent to some arbitrarily posited smooth mean field trajectory. Ultimately, an agent is shown to face a continuously revised discrete choice problem, where greedy choices dictated by current conditions must be constantly balanced against the risk of the future process noise upsetting the wisdom of such decisions. We show that any Nash equilibrium of the game is defined by an a priori computable probability matrix, which describes the distribution of the players’ choices over the alternatives. The results are illustrated through simulations. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
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20. The LQG homing problem for a Wiener process with random infinitesimal parameters.
- Author
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LEFEBVRE, MARIO and MOUTASSIM, ABDERRAZAK
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WIENER processes ,STOCHASTIC processes ,STOCHASTIC control theory ,OPTIMAL control theory ,DIFFERENTIAL equations ,BROWNIAN motion - Abstract
The problem of optimally controlling a Wiener process until it leaves an interval (a; b) for the first time is considered in the case when the infinitesimal parameters of the process are random. When a = ∞, the exact optimal control is derived by solving the appropriate system of differential equations, whereas a very precise approximate solution in the form of a polynomial is obtained in the two-barrier case. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
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21. Stochastic Optimization of Braking Energy Storage and Ventilation in a Subway Station.
- Author
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Rigaut, Tristan, Carpentier, Pierre, Chancelier, Jean Philippe, De Lara, Michel, and Waeytens, Julien
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ENERGY consumption , *SUBWAYS , *HEATING & ventilation of subways , *STOCHASTIC analysis , *ENERGY management - Abstract
In the Paris subway system, stations represent about one-third of the overall energy consumption. Within stations, ventilation is among the top consuming devices; it is operated at maximum airflow all day long, for air quality reasons. In this paper, we present a concept of energy system that displays comparable air quality while consuming much less energy. The system comprises a battery that makes it possible to recover the trains braking energy, arriving under the form of erratic and strong peaks. We propose an energy management system that, at short time scale, controls energy flows and ventilation airflow. By using proper optimization algorithms, we manage to match supply with demand, while minimizing energy daily costs. For this purpose, we have designed algorithms that take into account the braking variability. They are based on the so-called stochastic dynamic programming (SDP) mathematical framework. We fairly compare SDP-based algorithms with the widespread model predictive control (MPC) ones. First, both SDP and MPC yield energy/money operating savings of the order of one-third, compared to the current management without battery. Second, depending on the specific design, we observe that SDP outperforms MPC by a few percent, with an easier online numerical implementation. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
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22. The average cost of Markov chains subject to total variation distance uncertainty.
- Author
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Malikopoulos, A.A., Charalambous, C.D., and Tzortzis, I.
- Subjects
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MARKOV processes , *STOCHASTIC processes , *MATHEMATICAL models , *ALGORITHMS , *NUMERICAL analysis - Abstract
Abstract This paper addresses the problem of controlling a Markov chain so as to minimize the long-run expected average cost per unit time when the invariant distribution is unknown but we know it belongs to a given uncertain set. The mathematical model used to describe this set is the total variation distance uncertainty. We show that the equilibrium control policy, which yields higher probability to the states with low cost and lower probability to the states with the high cost, is an optimal control policy that minimizes the average cost. Recognition of such a policy may be of value in practical situations with constraints consistent to those studied here when the invariant distribution is uncertain and deriving online an optimal control policy is required. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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23. Neural approximations in discounted infinite-horizon stochastic optimal control problems.
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Gnecco, Giorgio and Sanguineti, Marcello
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STOCHASTIC processes , *OPTIMAL control theory , *CLOSED loop systems , *ARTIFICIAL neural networks , *MATHEMATICAL optimization - Abstract
Neural approximations of the optimal stationary closed-loop control strategies for discounted infinite-horizon stochastic optimal control problems are investigated. It is shown that for a family of such problems, the minimal number of network parameters needed to achieve a desired accuracy of the approximate solution does not grow exponentially with the number of state variables. In such a way, neural-network approximation mitigates the so-called “curse of dimensionality”. The obtained theoretical results point out the potentialities of neural-network based approximation in the framework of sequential decision problems with continuous state, control, and disturbance spaces. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
24. Considering Uncertainty in Optimal Robot Control Through High-Order Cost Statistics.
- Author
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Medina, Jose R. and Hirche, Sandra
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ROBOT control systems , *ROBOTICS , *STOCHASTIC control theory , *SENSORIMOTOR cortex , *NEUROSCIENTISTS , *CUMULANTS - Abstract
As the application of probabilistic models in robotic applications increases, a systematic robot control approach considering the effects of uncertainty becomes indispensable. Inspired by human sensorimotor findings, in this paper, we study the stochastic optimal control problem with high-order cost statistics in order to synthesize uncertainty-dependent actions in robotic scenarios with multiple uncertainty sources. We present locally optimal risk-sensitive and cost-cumulant solutions for settings with nonlinear dynamics, multiple additive uncertainty sources, and nonquadratic costs. The influence of each uncertainty source on the cost can be individually parameterized offering additional flexibility in the control design. We further analyze the case in which the static uncertain parameters are involved. The simulations of several linear and nonlinear settings with nonquadratic costs and an experiment on a real robotic platform validate our approach and illustrate its peculiarities. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
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25. Stochastic optimal control for sampled‐data system under stochastic sampling.
- Author
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Sun, Haoyuan, Chen, Jie, and Sun, Jian
- Abstract
In this study, the problem of designing a stochastic optimal controller for sampled‐data systems whose sampling interval is subjected to a certain probability distribution is addressed. To design the controller, the Kronecker product operation and the Vandermonde matrix were introduced. A design method of the stochastic optimal controller is proposed. It is shown that the controller guarantee that the closed‐loop system has exponentially mean square stability. Finally, the simulation results illustrate the effectiveness and practicability of the proposed method. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
26. Finite-horizon covariance control for discrete-time stochastic linear systems subject to input constraints.
- Author
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Bakolas, Efstathios
- Subjects
- *
OPTIMAL control theory , *STOCHASTIC processes , *DISCRETE-time systems , *NONLINEAR programming , *CONVEX domains , *ANALYSIS of covariance - Abstract
This work deals with a finite-horizon covariance control problem for discrete-time, stochastic linear systems with complete state information subject to input constraints. First, we present the main steps for the transcription of the covariance control problem, which is originally formulated as a stochastic optimal control problem, into a deterministic nonlinear program (NLP) with a convex performance index and with both convex and non-convex constraints. In particular, the convex constraints in this nonlinear program are induced by the input constraints of the stochastic optimal control problem, whereas the non-convex constraints are induced by the requirement that the terminal state covariance be equal to a prescribed positive definite matrix. Subsequently, we associate this nonlinear program, via a simple convex relaxation technique, with a (convex) semi-definite program, which can be solved numerically by means of modern computational tools of convex optimization. Although, in general, the endpoints of a representative sample of closed-loop trajectories generated by the control policy that corresponds to the solution of the relaxed convex program are not expected to follow exactly the goal terminal Gaussian distribution, they are more likely to be concentrated near the mean of this distribution than if they were drawn from the latter, which is a desirable feature in practice. Numerical simulations that illustrate the key ideas of this work are also presented. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
27. Two Approaches to Stochastic Optimal Control Problems with a Final-Time Expectation Constraint.
- Author
-
Pfeiffer, Laurent
- Subjects
- *
STOCHASTIC processes , *OPTIMAL control theory , *PROBLEM solving , *LAGRANGE equations , *DISCRETE-time systems - Abstract
In this article, we study and compare two approaches to solving stochastic optimal control problems with an expectation constraint on the final state. The case of a probability constraint is included in this framework. The first approach is based on a dynamic programming principle and the second one uses Lagrange relaxation. In this article, we focus on discrete-time problems, but the two discussed approaches can be applied to discretized continuous-time problems. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
28. Approximately Optimal Teaching of Approximately Optimal Learners.
- Author
-
Whitehill, Jacob and Movellan, Javier
- Abstract
We propose a method of generating teaching policies for use in intelligent tutoring systems (ITS) for concept learning tasks , e.g., teaching students the meanings of words by showing images that exemplify their meanings à la Rosetta Stone and Duo Lingo. The approach is grounded in control theory and capitalizes on recent work by , that frames the “teaching” problem as that of finding approximately optimal teaching policies for approximately optimal learners (AOTAOL). Our work expands on , in several ways: (1) We develop a novel student model in which the teacher's actions can partially eliminate hypotheses about the curriculum. (2) With our student model, inference can be conducted analytically rather than numerically, thus allowing computationally efficient planning to optimize learning. (3) We develop a reinforcement learning-based hierarchical control technique that allows the teaching policy to search through deeper learning trajectories. We demonstrate our approach in a novel ITS for foreign language learning similar to Rosetta Stone and show that the automatically generated AOTAOL teaching policy performs favorably compared to two hand-crafted teaching policies. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
29. Constrained minimum variance control for discrete-time stochastic linear systems.
- Author
-
Bakolas, E.
- Subjects
- *
DISCRETE time filters , *LINEAR systems , *STOCHASTIC processes , *AUTOMATIC control systems , *TIME delay systems - Abstract
We propose a computational scheme for the solution of the so-called minimum variance control problem for discrete-time stochastic linear systems subject to an explicit constraint on the 2-norm of the input (random) sequence. In our approach, we utilize a state space framework in which the minimum variance control problem is interpreted as a finite-horizon stochastic optimal control problem with incomplete state information. We show that if the set of admissible control policies for the stochastic optimal control problem consists exclusively of sequences of causal (non-anticipative) control laws that can be expressed as linear combinations of all the past and present outputs of the system together with its past inputs, then the stochastic optimal control problem can be reduced to a deterministic, finite-dimensional optimization problem. Subsequently, we show that the latter optimization problem can be associated with an equivalent convex program and in particular, a quadratically constrained quadratic program (QCQP), by means of a bilinear transformation. Finally, we present numerical simulations that illustrate the key ideas of this work. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
30. Risk-Sensitive Linear Control for Systems With Stochastic Parameters.
- Author
-
Ito, Yuji, Fujimoto, Kenji, Tadokoro, Yukihiro, and Yoshimura, Takayoshi
- Subjects
- *
DIFFERENTIAL equations , *NUMERICAL analysis , *T cells , *NANOPARTICLES , *CRYSTAL structure - Abstract
A novel risk-sensitive (RS) control law is proposed for linear systems with stochastic system parameters. RS control laws are efficient means of handling risk in various failures in control caused by stochastic disturbances. However, stochastic parameters invoke problems, resulting controllers may become nonlinear in the state variable and incompatible with linear systems, cannot be obtained in an exact sense, and are defined only on a bounded state region. To solve these problems, this paper presents a risk-sensitive linear (RSL) control method. The important idea is that a standard RS-type cost function is converted to an expectation of a weighted cost function such that the resulting optimal controller is linear in the state. The weight is designed such that the weighted cost function preserves the characteristics of the original RS control. The designed weight allows one to derive the proposed RSL controller whose exact solution is obtained as a linear feedback law for all states. Furthermore, the RSL control law over an infinite horizon guarantees stochastic stability of the feedback system with the control law. The effectiveness of the proposed RSL control law is demonstrated by a numerical simulation. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
31. Model Predictive Control for Stochastic Max-Plus Linear Systems With Chance Constraints.
- Author
-
Xu, Jia, van den Boom, Ton, and De Schutter, Bart
- Subjects
- *
PREDICTIVE control systems , *STOCHASTIC systems , *MONTE Carlo method , *RANDOM variables , *DISCRETE systems - Abstract
The topic of this paper is model predictive control (MPC) for max-plus linear systems with stochastic uncertainties the distribution of which is supposed to be known. We consider linear constraints on the inputs and the outputs. Due to the uncertainties, these linear constraints are formulated as probabilistic or chance constraints, i.e., the constraints are required to be satisfied with a predefined probability level. The proposed chance constraints can be equivalently rewritten into a max-affine (i.e., the maximum of affine terms) form if the linear constraints are monotonically nondecreasing as a function of the outputs. Based on the resulting max-affine form, two methods are developed for solving the chance-constrained MPC problem for stochastic max-plus linear systems. Method 1 uses Boole's inequality to convert the multivariate chance constraint into univariate chance constraints for which the probability can be computed more efficiently. Method 2 employs Chebyshev's inequality and transforms the chance constraint into linear constraints on the inputs. The simulation results for a production system example show that the two proposed methods are faster than the Monte Carlo simulation method and yield lower closed-loop costs than the nominal MPC method. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
32. Stochastic finite-time partial stability, partial-state stabilization, and finite-time optimal feedback control.
- Author
-
Rajpurohit, Tanmay and Haddad, Wassim
- Subjects
- *
STOCHASTIC processes , *DYNAMICAL systems , *LYAPUNOV functions , *DIFFERENTIAL inequalities , *HAMILTON-Jacobi-Bellman equation - Abstract
In many practical applications, stability with respect to part of the system's states is often necessary with finite-time convergence to the equilibrium state of interest. Finite-time partial stability involves dynamical systems whose part of the trajectory converges to an equilibrium state in finite time. In this paper, we address finite-time partial stability in probability and uniform finite-time partial stability in probability for nonlinear stochastic dynamical systems. Specifically, we provide Lyapunov conditions involving a Lyapunov function that is positive definite and decrescent with respect to part of the system state and satisfies a differential inequality involving fractional powers for guaranteeing finite-time partial stability in probability. In addition, we show that finite-time partial stability in probability leads to uniqueness of solutions in forward time and we establish necessary and sufficient conditions for almost sure continuity of the settling-time operator of the nonlinear stochastic dynamical system. Finally, we develop a unified framework to address the problem of optimal nonlinear analysis and feedback control design for finite-time partial stochastic stability and finite-time, partial-state stochastic stabilization. Finite-time partial stability in probability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function that is positive definite and decrescent with respect to part of the system state and can clearly be seen to be the solution to the steady-state form of the stochastic Hamilton-Jacobi-Bellman equation guaranteeing both finite-time, partial-state stability and optimality. The overall framework provides the foundation for extending stochastic optimal linear-quadratic controller synthesis to nonlinear-nonquadratic optimal finite-time, partial-state stochastic stabilization. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
33. FIRST ORDER BSPDEs IN HIGHER DIMENSION FOR OPTIMAL CONTROL PROBLEMS.
- Author
-
DOKUCHAEV, NIKOLAI
- Subjects
- *
FIRST-order logic , *OPTIMAL control theory , *STOCHASTIC partial differential equations , *PROBLEM solving , *STOCHASTIC processes - Abstract
This paper studies the first order backward stochastic partial differential equations suggested earlier for a case of multidimensional state domain with a boundary. These equations represent analogues of Hamilton--Jacobi--Bellman equations and allow one to construct the value function for stochastic optimal control problems with unspecified dynamics where the underlying processes do not necessarily satisfy stochastic differential equations of a known kind with a given structure. The problems considered arise in financial modeling. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
34. Wind time series modeling and stochastic optimal control for a grid-connected permanent magnet wind turbine generator.
- Author
-
Charalampidis, Alexandros C., Chaniotis, Antonios E., and Kladas, Antonios G.
- Subjects
STOCHASTIC analysis ,OPTIMAL control theory ,WIND turbines ,PARAMETERS (Statistics) ,SIMULATION methods & models - Abstract
In this paper, the control system of a permanent-magnet synchronous machine wind turbine generator connected to the grid is studied. A set of wind speed time series is used to model the rapidly changing wind speed component as a stochastic process. Several control laws, including the nonlinear stochastic optimal controller, are developed, and their efficiency is examined comparatively and under various conditions. Also, the effect of parameter uncertainty to the system efficiency is shown through simulations. The results show that the system efficiency increase obtained by the use of sophisticated control techniques, although not dramatic, is not negligible. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
35. Optimal control of stochastic FitzHugh–Nagumo equation.
- Author
-
Barbu, Viorel, Cordoni, Francesco, and Persio, Luca Di
- Subjects
- *
OPTIMAL control theory , *STOCHASTIC processes , *EXISTENCE theorems , *UNIQUENESS (Mathematics) , *RANDOM noise theory , *VARIATIONAL principles - Abstract
This paper is concerned with the existence and uniqueness of solution for the optimal control problem governed by the stochastic FitzHugh–Nagumo equation driven by a Gaussian noise. First-order conditions of optimality are also obtained. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
36. Analysis on Energy Efficient Switching of Machine Tool With Stochastic Arrivals and Buffer Information.
- Author
-
Frigerio, Nicla and Matta, Andrea
- Subjects
- *
ENERGY consumption , *MACHINE tools , *STOCHASTIC analysis , *INFORMATION theory , *BUFFER storage (Computer science) - Abstract
One of the measures for saving energy is the implementation of control strategies that reduce energy consumption during the machine idle periods. This paper proposes a framework that integrates different control policies for switching the machine off when the production is not critical, and on when the part flow has to be resumed. A general policy is formalized by modeling explicitly the power consumed in each system state. With this policy, the service can be resumed according to time threshold and when N parts have accumulated in the buffer. The behavior of the control strategy under different scenarios is numerically evaluated. Numerical results are based on data acquired with dedicated experimental measurements on a real machining center. A comparison with the common practice in manufacturing and with control policies that do not consider buffer information is also reported. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
37. Exact and approximate solutions to LQG homing problems in one and two dimensions.
- Author
-
Lefebvre, Mario and Zitouni, Foued
- Subjects
STOCHASTIC control theory ,CONTROL theory (Engineering) ,STOCHASTIC processes ,OPTIMAL control theory ,CALCULUS of variations ,LAGRANGE equations - Abstract
Stochastic optimal control problems in which two-dimensional diffusion processes are controlled until they enter a given set are solved explicitly. When symmetry can be used, exact solutions are obtained. The same arguments are valid for one-dimensional processes. In the general case, it is shown how to obtain good approximate solutions. Various examples are presented. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
38. Modeling and Control of Stochastic Systems With Poorly Known Dynamics.
- Author
-
do Val, Joao B. R. and Souto, Rafael F.
- Subjects
- *
DIFFUSION processes , *STOCHASTIC control theory , *STOCHASTIC systems , *UNCERTAIN systems , *OPTIMAL control theory - Abstract
This paper is concerned with controlling poorly known systems, for which only a simplified and rough model is available for control design. There are many systems that cannot be reasonably probed for the sake of identification, yet they are important for areas such as economy, populations, or medicine. The ideas are developed around an alternative way to account for the bare modeling in a stochastic-based setting, and to heighten the control features for such a modified model. The mathematical framework for the optimal control reveals important features such as the raising of a precautionary feedback policy of “keep the action unchanged” (inaction for short), on a certain state-space region. This feature is not seen in the robust approach, but has been pointed out and permeates part of the economics literature. The control problem relies on the viscosity solution for the Hamilton–Jacobi–Bellman equation, and the value of the problem is shown to be convex. When specialized to the quadratic problem with discounted cost, the exact solution inside the inaction region is given by a Lyapunov type of equation, and asymptotically, for large state values, by a Riccati-like equation. This scenario bridges to the stochastic stability analysis for the controlled model. The single control input is developed in full, part analytically, part numerically, for the scalar case, and an approximation is tested for the multidimensional case. The advantage of the precautionary policy is substantial in some situations. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
39. Semidefinite Programming Approach to Gaussian Sequential Rate-Distortion Trade-Offs.
- Author
-
Tanaka, Takashi, Kim, Kwang-Ki K., Parrilo, Pablo A., and Mitter, Sanjoy K.
- Subjects
- *
SEMIDEFINITE programming , *MARKOV processes , *MATHEMATICAL programming , *ESTIMATION theory , *STOCHASTIC processes - Abstract
Sequential rate-distortion (SRD) theory provides a framework for studying the fundamental trade-off between data-rate and data-quality in real-time communication systems. In this paper, we consider the SRD problem for multi-dimensional time-varying Gauss-Markov processes under mean-square distortion criteria. We first revisit the sensor-estimator separation principle, which asserts that considered SRD problem is equivalent to a joint sensor and estimator design problem in which data-rate of the sensor output is minimized while the estimator's performance satisfies the distortion criteria. We then show that the optimal joint design can be performed by semidefinite programming. A semidefinite representation of the corresponding SRD function is obtained. Implications of the obtained result in the context of zero-delay source coding theory and applications to networked control theory are also discussed. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
40. Neural Network-Based Solutions for Stochastic Optimal Control Using Path Integrals.
- Author
-
Rajagopal, Karthikeyan, Balakrishnan, Sivasubramanya Nadar, and Busemeyer, Jerome R.
- Subjects
- *
ARTIFICIAL neural networks , *STOCHASTIC systems , *PATH integrals - Abstract
In this paper, an offline approximate dynamic programming approach using neural networks is proposed for solving a class of finite horizon stochastic optimal control problems. There are two approaches available in the literature, one based on stochastic maximum principle (SMP) formalism and the other based on solving the stochastic Hamilton–Jacobi–Bellman (HJB) equation. However, in the presence of noise, the SMP formalism becomes complex and results in having to solve a couple of backward stochastic differential equations. Hence, current solution methodologies typically ignore the noise effect. On the other hand, the inclusion of noise in the HJB framework is very straightforward. Furthermore, the stochastic HJB equation of a control-affine nonlinear stochastic system with a quadratic control cost function and an arbitrary state cost function can be formulated as a path integral (PI) problem. However, due to curse of dimensionality, it might not be possible to utilize the PI formulation for obtaining comprehensive solutions over the entire operating domain. A neural network structure called the adaptive critic design paradigm is used to effectively handle this difficulty. In this paper, a novel adaptive critic approach using the PI formulation is proposed for solving stochastic optimal control problems. The potential of the algorithm is demonstrated through simulation results from a couple of benchmark problems. [ABSTRACT FROM PUBLISHER]
- Published
- 2017
- Full Text
- View/download PDF
41. AN OPTIMAL FEEDBACK CONTROL-STRATEGY PAIR FOR ZERO-SUM LINEAR-QUADRATIC STOCHASTIC DIFFERENTIAL GAME: THE RICCATI EQUATION APPROACH.
- Author
-
ZHIYONG YU
- Subjects
- *
ZERO sum games , *DIFFERENTIAL games , *STOCHASTIC processes , *FEEDBACK control systems , *CLOSED loop systems , *RICCATI equation - Abstract
In this paper, we study a two-person zero-sum linear-quadratic stochastic differential game problem. From a new viewpoint, we construct an optimal feedback control-strategy pair for the game in a closed-loop form based on the solution of a Riccati equation. A key part of our analysis involves proving the global solvability of this Riccati equation, which is interesting in its own right. Moreover, we demonstrate an indefinite phenomenon arising from the linear-quadratic game. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
42. Uncertainty-Anticipating Stochastic Optimal Feedback Control of Autonomous Vehicle Models
- Author
-
Anderson, Ross
- Subjects
Applied mathematics ,Robotics ,dubins vehicle ,nonlinear control ,path-integral control ,self-triggered control ,stochastic optimal control ,stochastic processes - Abstract
Control of autonomous vehicle teams has emerged as a key topic in the control and robotics communities, owing to a growing range of applications that can benefit from the increased functionality provided by multiple vehicles. However, the mathematical analysis of the vehicle control problems is complicated by their nonholonomic and kinodynamic constraints, and, due to environmental uncertainties and information flow constraints, the vehicles operate with heightened uncertainty about the team's future motion. In this dissertation, we are motivated by autonomous vehicle control problems that highlight these uncertainties, with in particular attention paid to the uncertainty in the future motion of a secondary agent. Focusing on the Dubins vehicle and unicycle model, we propose a stochastic modeling and optimal feedback control approach that anticipates the uncertainty inherent to the systems. We first consider the application of a Dubins vehicle that should maintain a nominal distance from a target with an unknown future trajectory, such as a tagged animal or vehicle. Stochasticity is introduced in the problem by assuming that the target's motion can be modeled as a Wiener process, and the possibility for the loss of target observations is modeled using stochastic transitions between discrete states. An optimal control policy that is consistent with the stochastic kinematics is computed and is shown to perform well both in the case of a Brownian target and for natural, smooth target motion. We also characterize the resulting optimal feedback control laws in comparison to their deterministic counterparts for the case of a Dubins vehicle in a stochastically varying wind. Turning to the case of multiple vehicles, we develop a method using a Kalman smoothing algorithm for multiple vehicles to enhance an underlying analytic feedback control. The vehicles achieve a formation optimally and in a manner that is robust to uncertainty. To deal with a key implementation issue of these controllers on autonomous vehicle systems, we propose a self-triggering scheme for stochastic control systems, whereby the time points at which the control loop should be closed are computed from predictions of the process in a way that ensures stability.
- Published
- 2014
43. Necessary condition for optimal control of fully coupled forward-backward stochastic system with random jumps.
- Author
-
Jingtao, Shi and Zhen, Wu
- Abstract
One kind of fully coupled forward-backward stochastic control system with random jumps is considered here. Necessary condition of Pontraygin's type maximum principle for the optimal control is derived. The control domain is not assumed to be convex and the control variable appears neither in the diffusion nor the jump coefficient of the forward equation. A linear quadratic stochastic optimal control problem is discussed as an illustrate example. [ABSTRACT FROM PUBLISHER]
- Published
- 2012
44. MODELING MEDICAL TREATMENT USING MARKOV DECISION PROCESSES.
- Author
-
Schaefer, Andrew J., Bailey, Matthew D., Shechter, Steven M., and Roberts, Mark S.
- Subjects
MEDICAL care ,MARKOV processes ,DECISION making ,STOCHASTIC processes ,OPERATIONS research - Abstract
Medical treatment decisions are often sequential and uncertain. Markov decision processes (MDPs) are an appropriate technique for modeling and solving such stochastic and dynamic decisions. This chapter gives an overview of MDP models and solution techniques. We describe MDP modeling in the context of medical treatment and discuss when MDPs are an appropriate technique. We review selected successful applications of MDPs to treatment decisions in the literature. We conclude with a discussion of the challenges and opportunities for applying MDPs to medical treatment decisions. [ABSTRACT FROM AUTHOR]
- Published
- 2004
45. Optimal Control With Noisy Time.
- Author
-
Lamperski, Andrew and Cowan, Noah J.
- Subjects
- *
OPTIMAL control theory , *STOCHASTIC systems , *LEVY processes , *RICCATI equation , *FEEDBACK control systems - Abstract
This paper examines stochastic optimal control problems in which the state is perfectly known, but the controller's measure of time is a stochastic process derived from a strictly increasing Lévy process. We provide dynamic programming results for continuous-time finite-horizon control and specialize these results to solve a noisy-time variant of the linear quadratic regulator problem and a portfolio optimization problem with random trade activity rates. For the linear quadratic case, the optimal controller is linear and can be computed from a generalization of the classical Riccati differential equation. [ABSTRACT FROM PUBLISHER]
- Published
- 2016
- Full Text
- View/download PDF
46. A Flexible Stochastic Optimization Method for Wind Power Balancing With PHEVs.
- Author
-
Leterme, Willem, Ruelens, Frederik, Claessens, Bert, and Belmans, Ronnie
- Abstract
This paper proposes a flexible optimization method, based on state of the art algorithms, for the smart control of plug-in hybrid electric vehicles (PHEVs) to balance wind power production. The problem is approached from the perspective of a balance responsible party (BRP) with a large share of wind power in its portfolio. The BRP uses controllable PHEVs to minimize the imbalance of its portfolio resulting from wind power forecast errors. A Markov Decision Process (MDP) formulation in combination with dynamic programming is used to solve the multistage stochastic problem. The main difficulty for applying MDPs to this problem is to efficiently include time interdependence of the wind power forecast error. In the presented approach, the probability distribution and time interdependence of the forecast error are represented by a scenario tree. Because of the MDP formulation, the algorithm is adaptable to deal with different transition models and constraints. This feature enables to use the algorithm in a dynamic environment such as the future smart grid. To demonstrate this, a generic charging model for PHEVs is used in the BRP wind balancing case. The flexibility of the algorithm is shown by investigating the solution for different degrees of complexity in the charging model. [ABSTRACT FROM PUBLISHER]
- Published
- 2014
- Full Text
- View/download PDF
47. Suboptimal event-triggered control for networked control systems.
- Author
-
Molin, A. and Hirche, S.
- Subjects
AUTOMATIC control systems ,STOCHASTIC processes ,MATHEMATICAL optimization ,STOCHASTIC systems ,MATHEMATICS - Abstract
The advent of networked control systems urges the digital control design to incorporate communication constraints efficiently. In order to accommodate this requirement, this article studies the joint design of controller and event-trigger for linear stochastic systems in the presence of a resource-limited communication channel which exhibits packet dropouts and time-delay. The event-trigger situated at the sensor decides at every sampling instance, whether to send information over the communication channel to the controller. The design approach is formulated as a stochastic average-cost optimization problem, where the communication constraints are reflected as an additional cost penalty of the average transmission rate. Different conditions on the communication model are given where the joint optimal design can be split into a separate control and event-trigger design. Based on these results, two suboptimal design approaches are developed. By using drift criteria, stability guarantees of the closed-loop system for both approaches are derived in terms of bounded moment stability. Numerical simulations illustrate the efficacy of the event-triggered approach compared with optimal time-triggered controllers. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
48. Probabilistic Aircraft Midair Conflict Resolution Using Stochastic Optimal Control.
- Author
-
Liu, Weiyi and Hwang, Inseok
- Abstract
This paper studies the problem of aircraft midair conflict resolution, which is a key technology to enable the coordinated and decentralized air traffic control envisioned in the Next Generation Air Transportation System (NextGen). The method proposed in this paper is based on stochastic optimal control, which is able to incorporate uncertainties in both aircraft and wind dynamics. The proposed numerical algorithm uses a Markov chain (MC) to approximate the continuous-time aircraft and wind dynamics, then the optimal control law is derived based on the MC. The proposed algorithm is able to resolve the conflicts between aircraft and moving convective weather regions. For conflict resolution between pairs of aircraft, a decomposition technique is proposed to reduce the computational complexity of the numerical algorithm. Simulations show that the proposed algorithm provides robustness against uncertainties in the system and is suitable for real applications. [ABSTRACT FROM PUBLISHER]
- Published
- 2014
- Full Text
- View/download PDF
49. Stochastic minimax optimal control strategy for uncertain quasi-Hamiltonian systems using stochastic maximum principle.
- Author
-
Hu, R., Ying, Z., and Zhu, W.
- Subjects
- *
STOCHASTIC processes , *OPTIMAL control theory , *UNCERTAINTY (Information theory) , *HAMILTONIAN systems , *GAME theory , *PARAMETER estimation , *MAXIMUM principles (Mathematics) - Abstract
A stochastic minimax optimal control strategy for uncertain quasi-Hamiltonian systems is proposed based on the stochastic averaging method, stochastic maximum principle and stochastic differential game theory. First, the partially completed averaged Itô stochastic differential equations are derived from a given system by using the stochastic averaging method for quasi-Hamiltonian systems with uncertain parameters. Then, the stochastic Hamiltonian system for minimax optimal control with a given performance index is established based on the stochastic maximum principle. The worst disturbances are determined by minimizing the Hamiltonian function, and the worst-case optimal controls are obtained by maximizing the minimal Hamiltonian function. The differential equation for adjoint process as a function of system energy is derived from the adjoint equation by using the Itô differential rule. Finally, two examples of controlled uncertain quasi-Hamiltonian systems are worked out to illustrate the application and effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
50. Control and dynamics of a SDOF system with piecewise linear stiffness and combined external excitations.
- Author
-
Yurchenko, D., Iwankiewicz, R., and Alevras, P.
- Subjects
- *
STIFFNESS (Engineering) , *PIECEWISE linear approximation , *DYNAMIC programming , *DRY friction , *STOCHASTIC processes , *NUMERICAL analysis - Abstract
Abstract: The paper considers a problem of stochastic control and dynamics of a single-degree-of-freedom system with piecewise linear stiffness subjected to combined periodic and white noise external excitations. To minimize the system response energy a bounded in magnitude control force is applied to the systems. The stochastic optimal control problem is handled through the dynamic programming approach. Based on the solution to the Hamilton–Jacobi–Bellman equation it is proposed to use the dry friction control law in the non-resonant case. In the resonant case the stochastic averaging procedure has been used to derive stochastic differential equations for system response amplitude and phase. The joint PDF of response amplitude and phase is derived analytically and numerically using the Path Integration approach. [Copyright &y& Elsevier]
- Published
- 2014
- Full Text
- View/download PDF
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