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A novel optimal control problem is considered for multiple input multiple output (MIMO) stochastic systems with mixed parameter drift, external disturbance and observation noise. The proposed controller can not only track and identify the drift parameters in finite time but, furthermore, drive the system to move towards the desired trajectory. However, there is a conflict between control and estimation, which makes the analytic solution unattainable in most situations. A dual control algorithm based on weight factor and innovation is, therefore, proposed. First, the innovation is added to the control goal by the appropriate weight and the Kalman filter is introduced to estimate and track the transformed drift parameters. The weight factor is used to adjust the degree of drift parameter estimation in order to achieve a balance between control and estimation. Then, the optimal control is derived by solving the modified optimization problem. In this strategy, the analytic solution of the control law can be obtained. The control law obtained in this paper is optimal because the estimation of drift parameters is integrated into the objective function rather than the suboptimal control law, which includes two parts of control and estimation in other studies. The proposed algorithm can achieve the best compromise between optimization and estatimation. Finally, the effectiveness of the algorithm is verified by numerical experiments in two different cases.

We study turn-based stochastic zero-sum games with lexicographic preferences over objectives. Stochastic games are standard models in control, verification, and synthesis of stochastic reactive systems that exhibit both randomness as well as controllable and adversarial non-determinism. Lexicographic order allows one to consider multiple objectives with a strict preference order. To the best of our knowledge, stochastic games with lexicographic objectives have not been studied before. For a mixture of reachability and safety objectives, we show that deterministic lexicographically optimal strategies exist and memory is only required to remember the already satisfied and violated objectives. For a constant number of objectives, we show that the relevant decision problem is in NP ∩ coNP , matching the current known bound for single objectives; and in general the decision problem is PSPACE -hard and can be solved in NEXPTIME ∩ coNEXPTIME . We present an algorithm that computes the lexicographically optimal strategies via a reduction to the computation of optimal strategies in a sequence of single-objectives games. For omega-regular objectives, we restrict our analysis to one-player games, also known as Markov decision processes. We show that lexicographically optimal strategies exist and need either randomization or finite memory. We present an algorithm that solves the relevant decision problem in polynomial time. We have implemented our algorithms and report experimental results on various case studies. [ABSTRACT FROM AUTHOR]

In order to further improve the accurate detection signal, reduce interference between signals, this paper designs a new type of signal detection algorithm for satellite communication systems, using stochastic resonance technology improve the signal-to-noise ratio of the input signal, the signal by using energy detection, double threshold, accurate judgment. The first step in the conventional energy of double threshold detection, the second step into the energy detection method based on stochastic resonance detection process. The experimental results show that this algorithm under the condition of low SNR signals effectively detect, promoted the whole satellite communication system performance. [ABSTRACT FROM AUTHOR]

In order to solve continuous stochastic Lyapunov equations, a novel implicit iterative algorithm is presented by means of successive over relaxation (SOR) iteration in this article. Throughout this method, three tuning parameters are added for the improvement of the convergence rate. It is shown that this algorithm is monotonically bounded, and the convergence condition is also given and extended. Applying the latest updated estimates, this algorithm can attain a better convergence performance compared with other existing iterative algorithms when choosing appropriate tuning parameters. Finally, a numerical example is provided to illustrate the feasibility and priority of this approach. [ABSTRACT FROM AUTHOR]

This article investigates the parameter identification problems of the stochastic systems described by the input‐nonlinear output‐error (IN‐OE) model. This IN‐OE model consists of two submodels, one is an input nonlinear model and the other is a linear output‐error model. The difficulty in the parameter identification of the IN‐OE model is that the information vector contains the unknown variables, which are the noise‐free (true) outputs of the system, the approach taken here is to replace the unknown terms with the outputs of the auxiliary model. Based on the over‐parameterization model and the hierarchical identification principle, an over‐parameterization auxiliary model hierarchical gradient‐based iterative algorithm and an over‐parameterization auxiliary model hierarchical least‐squares‐based iterative algorithm are proposed to estimate the unknown parameters of the IN‐OE systems. Finally, two numerical simulation examples are given to demonstrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This article researches the interval‐driven variable convergence rate robust stability/stabilization of uncertain impulsive stochastic systems. First, a new conception of variable convergence rate stability for uncertain impulsive stochastic systems is presented in conjunction with the idea of generalized pole configurations. Also, a new criterion for variable convergence rate robust stability/stabilization of uncertain impulsive stochastic systems is given, which can reflect and regulate the convergence rate of the system state. In addition, a new algorithm is designed by means of an interval‐driven stabilization method. This algorithm, combined with the variable convergence rate criterion, achieves accurate control of the convergence rate of the state at the operational level. Double instances are proposed to verify the superiority of the method. [ABSTRACT FROM AUTHOR]

We develop an algorithm for the equivariant divergence formula of the unstable perturbation of unstable transfer operators, by progressively computing 2u many bounded vectors or covectors on one orbit, where u is the unstable dimension. Combining this with the nonintrusive adjoint shadowing algorithm, we obtain the fast adjoint response algorithm for the linear responses on physical measures of discrete-time uniformly hyperbolic systems. The cost is independent of the number of parameters. We demonstrate our algorithm on a 21-dimensional chaotic system, a system with stochastic noise, and systems with discontinuities. Unlike previous methods, our algorithms are not cursed by dimensionality or the sensitive dependence on initial conditions. [ABSTRACT FROM AUTHOR]

This paper considers the parameter estimation problem for bilinear stochastic systems with autoregressive moving average (ARMA) noise using the stochastic gradientmethod. First, the identification model is derived by eliminating the state variables. Based on the obtained identification model, a multi-innovation generalized extended stochastic gradient (MI-GESG) algorithm is proposed using the multi-innovation identification theory. Furthermore, to enhance the parameter estimation accuracy, a maximum likelihood based MI-GESG (ML-MI-GESG) algorithm is developed by using the maximum likelihood identification principle. Finally, an illustrative simulation example is provided to testify the proposed algorithms. The simulation results show the effectiveness of the proposed algorithms for identifying bilinear systems. [ABSTRACT FROM AUTHOR]

Solving Convex Discrete Optimization via Simulation via Stochastic Search Algorithms Many decision-making problems in operations research and management science require the optimization of large-scale complex stochastic systems with high-dimensional discrete decision variables. For a number of applications, the objective function exhibits convexity in the discrete decision variables, or the problem can be transformed into a convex one. In "Gradient-Based Algorithms for Convex Discrete Optimization via Simulation," Zhang, Zheng, and Lavaei propose provably efficient simulation–optimization algorithms for general convex optimization via simulation problems with high-dimensional discrete decision space. By utilizing the convex structure, the developed algorithms demonstrate a polynomial dependence on the dimension and scale of the decision space. In addition, information-theoretic lower bounds are derived to show the limit of algorithm design. In the case when possibly biased gradient estimators are available, they propose simulation–optimization algorithms to achieve optimality guarantees with a reduced dependence on the dimension. We propose new sequential simulation–optimization algorithms for general convex optimization via simulation problems with high-dimensional discrete decision space. The performance of each choice of discrete decision variables is evaluated via stochastic simulation replications. If an upper bound on the overall level of uncertainties is known, our proposed simulation–optimization algorithms utilize the discrete convex structure and are guaranteed with high probability to find a solution that is close to the best within any given user-specified precision level. The proposed algorithms work for any general convex problem, and the efficiency is demonstrated by proven upper bounds on simulation costs. The upper bounds demonstrate a polynomial dependence on the dimension and scale of the decision space. For some discrete optimization via simulation problems, a gradient estimator may be available at low costs along with a single simulation replication. By integrating gradient estimators, which are possibly biased, we propose simulation–optimization algorithms to achieve optimality guarantees with a reduced dependence on the dimension under moderate assumptions on the bias. Funding: H. Zhang and J. Lavaei were funded by grants from Air Force Office of Scientific Research (AFOSR), Army Research Office (ARO), Office of Naval Research (ONR), National Science Foundation (NSF) and C3.ai Digital Transformation Institute. Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2022.2295. [ABSTRACT FROM AUTHOR]

In this article, the problem of parameter estimation for a multiple‐input single‐output Hammerstein controlled autoregressive (MISO‐HCAR) model is solved. After establishing the identification model of MISO‐HCAR system, an improved adaptive moment estimation algorithm with decreasing weight (IADAM) is proposed. The improved algorithm transforms the nonlinear system identification problem into a parameter space optimization problem, according to the input and output data obtained from the system, and uses the parallel search ability of the IADAM algorithm to estimate all the parameters of the system simultaneously. Two numerical examples and the case study example of chemical continuously stirred tank reactor (CSTR) system show that the proposed IADAM algorithm with decreasing weight has better identification effect on the MISO‐HCAR model and CSTR system than the stochastic gradient descent (SGD) algorithm and the basic adaptive moment estimation (ADAM) algorithm, and the estimation accuracy and convergence speed are greatly improved. Thus, the IADAM can estimate the parameters of the MISO‐HCAR system and the CSTR system more effectively. [ABSTRACT FROM AUTHOR]

In an effort to overcome the problem that the traditional stochastic resonance system cannot adjust the structural parameters adaptively in bearing fault-signal detection, this article proposes an adaptive-parameter bearing fault-detection method. First of all, the four strategies of Sobol sequence initialization, exponential convergence factor, adaptive position update, and Cauchy–Gaussian hybrid variation are used to improve the basic grey wolf optimization algorithm, which effectively improves the optimization performance of the algorithm. Then, based on the multistable stochastic resonance model, the structure parameters of the multistable stochastic resonance are optimized through improving the grey wolf algorithm, so as to enhance the fault signal and realize the effective detection of the bearing fault signal. Finally, the proposed bearing fault-detection method is used to analyze and diagnose two open-source bearing data sets, and comparative experiments are conducted with the optimization results of other improved algorithms. Meanwhile, the method proposed in this paper is used to diagnose the fault of the bearing in the lifting device of a single-crystal furnace. The experimental results show that the fault frequency of the inner ring of the first bearing data set diagnosed using the proposed method was 158 Hz, and the fault frequency of the outer ring of the second bearing data set diagnosed using the proposed method was 162 Hz. The fault-diagnosis results of the two bearings were equal to the results derived from the theory. Compared with the optimization results of other improved algorithms, the proposed method has a faster convergence speed and a higher output signal-to-noise ratio. At the same time, the fault frequency of the bearing of the lifting device of the single-crystal furnace was effectively diagnosed as 35 Hz, and the bearing fault signal was effectively detected. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Guangdong University of Technology is the property of Journal of Guangdong University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A numerical technique was developed for solving nonlocal nonlinear stochastic delayed differential equations driven by fractional variable-order Brownian noise. Error analysis of the proposed technique was performed and discussed. The method was applied to the nonlocal stochastic fluctuations of the human body and the Nicholson's blowfly models, and its accuracy and computational time were assessed for different values of the nonlocal order parameters. A comparison with other techniques available in the literature revealed the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper describes one method for estimating the Hölder exponent based on the -complexity of continuous functions, a concept formulated lately. Computational experiments are carried out to estimate the Hölder exponent for smooth and fractal functions and study the trajectories of discrete deterministic and stochastic systems. The results of these experiments are presented and discussed. [ABSTRACT FROM AUTHOR]

This paper proposes a decentralised stochastic control framework for a class of large-scale and complex dynamic networks. The proposed framework describes a decentralised probabilistic control and message passing architecture of mutually interacting quasi-independent subsystems. Within this framework, the outputs of the subsystems are communicated back to topologically-connected neighbours through output probabilistic message passing. This communication approach constitutes the main contribution of the current paper and allow the achievement of the global system goal. The proposed framework reduces the amount of communication required given the low dimensionality of the output space compared to the state space. The updated knowledge through the output message passing is then applied to induce a fully probabilistic local control strategy affecting only the local subsystem. Finally, a numerical example is presented to illustrate the effectiveness and usefulness of our novel proposed framework. [ABSTRACT FROM AUTHOR]

This paper investigates the finite-time annular domain H 2 / H ∞ filtering for mean-field stochastic systems with external disturbance, Wiener and Poisson noises. Initially, the novel concept of finite-time annular domain (FTAD) H 2 / H ∞ filtering is introduced, which ensures the system's mean square finite-time annular domain boundedness (MSFTADB) and minimizes the H 2 and H ∞ filtering performance indices. Next, using the Itô-Levy formula and the reverse differential Gronwall inequality, a less conservative sufficient condition for the existence of finite-time annular domain H 2 / H ∞ filter is derived. Furthermore, a new algorithm is devised to establish the relationship between the ranges of adjustable parameters and the minimum value of H 2 performance index. Finally, a practical example is provided to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Compared to the conventional control algorithms that use mean and variance as indicators, predictive probability density function (PDF) control can effectively handle the output PDF control problem of non-Gaussian stochastic distribution systems. However, the existing predictive PDF control method does not consider the construction error between output PDF and weight, thus the control performance is still unsatisfactory. Therefore, this paper proposes a new Enhanced Predictive PDF control method (En-PDF) to improve the output PDF control performance of stochastic distribution systems. The proposed method mainly consists of two parts: the predictive PDF control part and the neural network compensation control part aiming to reduce the bias of output PDF. First, the Radical Basis Functions (RBFs) are used to approximate the PDF of the stochastic systems output, and then a prediction model representing the relationship between input and weight is established using the subspace identification algorithm to design the predictive PDF control for the stochastic systems. Next, the Kullback-Leibler (KL) divergence is used to measure the similarity between the output PDF and the set PDF, combined with the weight error and compensation to design a new performance index. Based on this, the parameters of the neural network are adjusted using the gradient descent algorithm to obtain the optimal compensation, and the stability and tracking performance of the proposed algorithm are analyzed using inductive reasoning method. Finally, the predictive PDF control input with the compensation work together on the controlled plant to achieve high-performance control of the output PDF of non-Gaussian stochastic distribution systems. Both simulation experiments and physical control experiments validate the effectiveness and superiority of the proposed method. • Enhanced Predictive PDF control (En-PDF) for stochastic distribution systems. • The En-PDF consists of the predictive PDF control part and the NN compensation part. • The NN compensator compensates the control input to enhance the control performance. • A novel performance index based on KL divergence for optimization of the compensation. • Both theoretical analysis and physical experiments validate the En-PDF method. [ABSTRACT FROM AUTHOR]

In this paper, we consider the parameter estimation problem for the multivariable system. A recursive least squares algorithm is studied by minimizing the accumulative prediction error. By employing the stochastic Lyapunov function and the martingale estimate methods, we provide the weakest possible data conditions for convergence analysis. The upper bound of accumulative regret is also provided. Various simulation examples are given, and the results demonstrate that the convergence rate of the algorithm depends on the parameter dimension and output dimension. [ABSTRACT FROM AUTHOR]

Recently, the study of fault diagnosis and prognosis of discrete-event systems (DESs) has received considerable attention. This article aims to investigate the decentralized fault prognosis of stochastic DESs (SDESs). The notion of $m$ -step stochastic-coprognosability, called $S_{m} $ -coprognosability, is formalized to capture the capability of stochastic systems to predict a fault at least $m$ steps in advance under the decentralized framework. The verifier is constructed from the stochastic decentralized system, in which $n$ local prognosers are deployed to send the local prognostic decisions to a coordinator for calculating the final prognostic decision. In particular, a necessary and sufficient condition of $S_{m}$ -coprognosability of stochastic systems is derived, and an algorithm for testing $S_{m} $ -coprognosability is given, which is polynomial to the number of states and events but exponential to the number of local sites. Furthermore, the maximum number of $m$ for making the given SDES to be $S_{m} $ -coprognosable is discussed. Note to Practitioners—This article extends the fault prognosis methods of SDESs from centralized framework to decentralized framework, such that for many technologically complex systems whose information collection is scattered in physically separated different sites, every local site makes decision based on information collected by own sensors, without communicating with other local sites, which is more appropriate than the centralized method. [ABSTRACT FROM AUTHOR]

This paper investigated the fault detection problem in finite-frequency domain for nonlinear networked systems under stochastic cyber-attacks. To save limited network resource, this paper introduced a novel dynamic event-triggered scheme. Firstly, under the consideration of fault sensitivity and disturbance robustness, the paper converted the addressed fault detection problem into an auxiliary H-/Ｈ∞ filtering problem by augmenting the states of the original system and the fault detection filter. Taking sector bounded nonlinearity and stochastic cyber-attacks into consideration, the design of Hperformance index included the frequency characteristics of fault signals. Combined with finite-frequency input characteristics, the paper proposed the joint design algorithm for fault detection filter and dynamic event-triggered scheme under the finite-frequency fault input. Finally, a simulation example of stirred tank reactor system verified the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Copyright of Control Theory & Applications / Kongzhi Lilun Yu Yinyong is the property of Editorial Department of Control Theory & Applications and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A Hammerstein system comprises a nonlinear static subsystem and a linear dynamic subsystem. Herein, semirecursive nonparametric estimators are proposed for the nonlinear static subsystem, and its asymptotic unbiasedness and consistency properties are demonstrated. The estimators are competitive in terms of computational cost and data storage capacity. The performance of the proposed algorithms was examined through both Monte Carlo simulation and application to empirical data. [ABSTRACT FROM AUTHOR]

The author proposes a decomposition algorithm for predicting the trajectories of nonlinear stochastic systems whose dynamics contain subprocesses significantly different in speed. The algorithm is focused on reducing the time to obtain predictive results for substantially nonlinear objects and systems, when calculations based on their complete mathematical models are associated with a large amount of computation and the complexity of temporary adjustment of parameters. [ABSTRACT FROM AUTHOR]

Aiming at the problem of permanent loss of system observations during the fault prediction of stochastic discrete-event systems ( SDESs), resulting in inaccurate predictions, this paper proposed an algorithm for verification of fault prediction under permanent loss of observations. Firstly, it formalized the notion of U-predictability of SDESs under permanent loss of observations. Secondly, it constructed a U-predictor from the given system using stochastic predictors to perform fault prediction of SDESs. Based on the U-predictor, it proposed a necessary and sufficient condition and an algorithm for verifying U-predictability of SDESs, and the introduction of a pairwise approach significantly improved the complexity of the verification algorithm. Simulation results show that the verification algorithm made the fault prediction of the system accurate under permanent loss of observations. Finally, an example illustrates the application of fault prediction verification algorithm under permanent loss of observations. Compared with the existing similar algorithm, the verification algorithm has a wider range of applications and the verification results are more accurate. [ABSTRACT FROM AUTHOR]

Stochastic inventory systems with lead times are often challenging to optimize, including single-sourcing lost-sales and dual-sourcing systems. Recent numerical results suggest that capped policies demonstrate superior performance over existing heuristics. However, the superior performance lacks a theoretical foundation. In "1.79-Approximation Algorithms for Continuous Review Single-Sourcing Lost-Sales and Dual-Sourcing Inventory Models," the author provides a theoretical foundation for this phenomenon in two classical inventory models. First, in a continuous review lost-sales model with lead times and Poisson demand, he proves that a capped base-stock policy has a worst-case performance guarantee of 1.79 by conducting an asymptotic analysis under a large penalty cost and lead time. Second, in a more complex continuous review dual-sourcing model with general lead times and Poisson demand, he proves that a similar capped dual-index policy has a worst-case performance guarantee of 1.79 under large lead time and ordering cost differences. The results provide a deeper understanding of the superior numerical performance of capped policies and present a new approach to proving worst-case performance guarantees of simple policies in hard inventory problems. Stochastic inventory systems with lead times are often challenging to optimize, including single-sourcing lost-sales and dual-sourcing inventory systems. Recent numerical results suggest that capped policies demonstrate superior performance over existing heuristics. However, the superior performance lacks a theoretical foundation, and why such policies generally perform so well remains a major open question. In this paper, we provide a theoretical foundation for this phenomenon in two classical inventory models with lead times. First, in a continuous-review lost-sales inventory model with lead times and Poisson demand, we prove that a so-called capped base-stock policy has a worst-case performance guarantee of 1.79 by conducting an asymptotic analysis under a large penalty cost and lead time. Second, we extend the analysis to a more complex continuous-review dual-sourcing inventory model with general lead times and Poisson demand and also prove that a so-called capped dual-index policy has a worst-case performance guarantee of 1.79 under large lead time and ordering cost differences. Our results provide a deeper understanding of the superior numerical performance of capped policies and present a new approach to proving worst-case performance guarantees of simple policies in hard inventory problems. [ABSTRACT FROM AUTHOR]

Copyright of Control Theory & Applications / Kongzhi Lilun Yu Yinyong is the property of Editorial Department of Control Theory & Applications and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

As transport is a vital component in the modern tourism industry, determining reliable-performance tourism transport networks is critical for tour operators and travel agencies. The performance of a tourism transport network in this study is investigated by evaluating system reliability, which is the probability of successfully transporting requested passengers between multiple origins and multiple destinations within a time constraint when tardiness may occur. A stochastic multiple-origin-destination tourism transport network with tardiness (SMTNT) is formulated for system reliability evaluation. Identify all minimal travel paths (MTP) and corresponding maximum tardiness vectors that successfully connect each origin–destination pair under a time constraint. System reliability is derived from all flow vectors enabling delivery via MTPs a requested number of passengers at different tardiness levels. The proposed algorithm is successful in handling a combination of time constraints in the case of tardiness with multiple origin–destination pairs. Furthermore, it helps travel agencies obtain an insight into the performance of their SMTNT. An example describing the working of the proposed algorithm with an analysis of system reliability is provided. The results of the study can be used for improving the algorithm in the future. [ABSTRACT FROM AUTHOR]

We study the problem of optimizing a dynamic stochastic state-linear and control-nonlinear system operating on an infinite time horizon with respect to a quadratic cost functional. Several algorithms for the successive improvement of a given time-varying program control are proposed. They can be used, in particular, for designing high-performance dynamic incomplete-feedback controllers in deterministic linear time-invariant systems. A number of rigorous statements regarding the original optimization problem are stated and proved to justify the improvement algorithms. [ABSTRACT FROM AUTHOR]

This paper considers the problem of the ground target positioning and tracking algorithm for multi UAVs formation cooperative detection, and a real time and fast algorithm is proposed based on UAV airborne electro optical sensors. One state estimation problem for nonlinear stochastic system is studied by means of the unscented Kalman filter algorithm from target tracking process. To extend the single target tracking to multiple target tracking, one improved unscented Kalman filter algorithm is advised based on iterative multiple models. Furthermore, to relax the strict condition on white noise in Kalman filtering, the target tracking or state estimation is reduced to derive the inner and outer ellipsoidal approximations for the state in case of unknown but bounded noise. Finally, one simulation example confirms our theoretical results. [ABSTRACT FROM AUTHOR]

The adaptive neural network asymptotic tracking control issue of nonstrict feedback stochastic nonlinear systems is studied in our article by adopting backstepping algorithm. Compared with the existing research, the hypothesis about unknown virtual control coefficients (UVCC) is overcome in the control design. By using the bound estimation scheme and some smooth functions, associating with approximation-based neural network, the asymptotic tracking controller is recursively constructed. With the aid of Lyapunov function and beneficial inequalities, the asymptotic convergence character and stability with stochastic disturbance and unknown UVCC can be ensured. Finally, the theoretical finding is verified via a simulation example. [ABSTRACT FROM AUTHOR]

Solving the optimal mean-field control problem usually requires complete system information. In this paper, a Q-learning algorithm is discussed to solve the optimal control problem of the unknown mean-field discrete-time stochastic system. First, through the corresponding transformation, we turn the stochastic mean-field control problem into a deterministic problem. Second, the H matrix is obtained through Q-function, and the control strategy relies only on the H matrix. Therefore, solving H matrix is equivalent to solving the mean-field optimal control. The proposed Q-learning method iteratively solves H matrix and gain matrix according to input system state information, without the need for system parameter knowledge. Next, it is proved that the control matrix sequence obtained by Q-learning converge to the optimal control, which shows theoretical feasibility of the Q-learning. Finally, two simulation cases verify the effectiveness of Q-learning algorithm. [ABSTRACT FROM AUTHOR]

This paper is devoted to the practical tracking control and disturbance rejection for a class of discrete-time stochastic linear systems (DTSLSs). Firstly, a criterion on practical stability in probability (PS-P) of discrete-time stochastic systems is given. Secondly, based on internal model principle (IMP) and pole assignment algorithm, a dynamic controller is designed such that practical tracking in mean square (PTMS) sense and disturbance rejection are realised, while maintaining the PS-P of DTSLSs. In the end, the feasibility of the proposed method is verified by the application to the mass-spring-damper system, and the efficiency is illustrated by the simulation results. [ABSTRACT FROM AUTHOR]

This article studies the problem of adaptive fuzzy fixed-time decentralized control for nonlinear interconnected systems with stochastic disturbances and unknown nonlinearities. In control design, fuzzy logic systems are utilized to identify the unknown nonlinear functions. Combining stochastic fixed-time Lyapunov stability theory with adaptive backstepping control technique, a fuzzy adaptive fixed-time decentralized control design algorithm is developed by adopting smooth projection operator. It is proved that all the state variables of the closed-loop system are globally fixed-time stable in probability. Finally, both numerical and practical examples are provided to elucidate the feasibility of the proposed control algorithm. [ABSTRACT FROM AUTHOR]

We propose a novel belief space planning technique for continuous dynamics by viewing the belief system as a hybrid dynamical system with time-driven switching. Our approach is based on the perturbation theory of differential equations and extends sequential action control to stochastic dynamics. The resulting algorithm, which we name SACBP, does not require discretization of spaces or time and synthesizes control signals in near real-time. SACBP is an anytime algorithm that can handle general parametric Bayesian filters under certain assumptions. We demonstrate the effectiveness of our approach in an active sensing scenario and a model-based Bayesian reinforcement learning problem. In these challenging problems, we show that the algorithm significantly outperforms other existing solution techniques including approximate dynamic programming and local trajectory optimization. [ABSTRACT FROM AUTHOR]

Summary: An adaptive finite‐time decentralized control algorithm for a class of large‐scale stochastic nonlinear systems is presented. The fuzzy logic system is used to estimate uncertain nonlinearities. One advantage of the developed scheme is that each subsystem only needs to update one adaptive parameter, which alleviates the burden of online estimation. The dynamic surface control method is employed to reduce the "complexity explosion" caused by the repetitive derivation of the intermediate variable function in the backstepping control scheme. A new decentralized controller is designed so that all signals of the controlled system are bounded and the tracking error converges to a small residual set around the origin within a finite time. The simulation results of a numerical example illustrate the effectiveness of the method. [ABSTRACT FROM AUTHOR]

Copyright of Automatisierungstechnik is the property of De Gruyter and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper we study the numerical approximation of the stochastic Cahn–Hilliard–Navier–Stokes system on a bounded polygonal domain of |$\mathbb{R}^{d}$|⁠ , |$d=2,3$|⁠. We propose and analyze an algorithm based on the finite element method and a semiimplicit Euler scheme in time for a fully discretization. We prove that the proposed numerical scheme satisfies the discrete mass conservative law, has finite energies and constructs a weak martingale solution of the stochastic Cahn–Hilliard–Navier–Stokes system when the discretization step (both in time and in space) tends to zero. [ABSTRACT FROM AUTHOR]

We explore reinforcement learning methods for finding the optimal policy in the linear quadratic regulator (LQR) problem. In particular we consider the convergence of policy gradient methods in the setting of known and unknown parameters. We are able to produce a global linear convergence guarantee for this approach in the setting of finite time horizon and stochastic state dynamics under weak assumptions. The convergence of a projected policy gradient method is also established in order to handle problems with constraints. We illustrate the performance of the algorithm with two examples. The first example is the optimal liquidation of a holding in an asset. We show results for the case where we assume a model for the underlying dynamics and where we apply the method to the data directly. The empirical evidence suggests that the policy gradient method can learn the global optimal solution for a larger class of stochastic systems containing the LQR framework, and that it is more robust with respect to model misspecification when compared to a model-based approach. The second example is an LQR system in a higher dimensional setting with synthetic data. [ABSTRACT FROM AUTHOR]

This paper presents a solution to the filtering problem for a class of stochastic discrete-time nonlinear polynomial systems with switching in the state equation over linear observations and its application to a mechatronic system. The switching in the state equation is performed between two different nonlinear functions according to a sequence of independent Bernoulli random variables that take the quantities of zero and one. The mean-square filtering solution is obtained for a general nonlinear discrete-time polynomial system and a finite-dimensional system of filtering equations is then obtained for a second degree polynomial system as a particular case. The mean-square estimates of polynomial state terms are expressed as functions of the estimate and covariance matrix. Finally, some numerical simulations are carried out to reconstruct the variable states given a vector output measurement for a linear system, a second degree polynomial system, and an induction motor model to show effectiveness of the proposed algorithm. The proposed method is compared with an extended Kalman filter-based algorithm for discrete-time switched nonlinear systems. [ABSTRACT FROM AUTHOR]

We consider a polling system with adaptive dynamic polling order for modeling a broadband wireless network with a centralized control mechanism. A new algorithm has been developed for calculating the steady-state probability distribution of the number of packets in subscriber stations. The algorithm makes it possible to calculate the average waiting time and other network performance characteristics. We investigate a queuing system with several queues in which the server serves queues in a dynamic polling order. This order of queuing involves skipping queues that had been empty in the previous polling cycle. The queues that have been skipped in the current cycle can be polled by the server only in the next cycle. The specified queue servicing algorithm allows one to reduce the queue polling time and thus increase the system performance. A comparative numerical analysis of various options for constructing and evaluating the performance characteristics of broadband wireless IEEE 802.11 networks with a centralized control mechanism is presented. Numerical studies have been carried out using a software package for evaluating stochastic polling systems. [ABSTRACT FROM AUTHOR]

An improved algorithm is proposed to manage with the huge computation burden of the quaternion particle filter in aircraft attitude estimation. Based on the particle filtering frame, the new filter provides robust performance for nonlinear and non-Gaussian stochastic systems. And the posterior distribution of the new estimator is approximated as a new quaternion distribution to realize parallel computation. In addition, similar to the extended Kalman filter, this new method implements time update by replacing particles update with linear transformation to reduce computational complexity. Numerical simulations are carried out to compare the new algorithm to the extended Kalman filter and to quaternion particle filter in simulation results. The simulation results indicate that this estimation technique has faster convergence rate than the extended Kalman filter and takes less computation times than quaternion particle filter under the same accuracy as quaternion particle filter. [ABSTRACT FROM AUTHOR]

We propose a novel belief space planning technique for continuous dynamics by viewing the belief system as a hybrid dynamical system with time-driven switching. Our approach is based on the perturbation theory of differential equations and extends sequential action control to stochastic dynamics. The resulting algorithm, which we name SACBP, does not require discretization of spaces or time and synthesizes control signals in near real-time. SACBP is an anytime algorithm that can handle general parametric Bayesian filters under certain assumptions. We demonstrate the effectiveness of our approach in an active sensing scenario and a model-based Bayesian reinforcement learning problem. In these challenging problems, we show that the algorithm significantly outperforms other existing solution techniques including approximate dynamic programming and local trajectory optimization. [ABSTRACT FROM AUTHOR]

This paper proposes an innovative identification approach of nonlinear stochastic systems using Hammerstein–Wiener (HW) model with output-error autoregressive (OEA) noise. Two fuzzy systems are suggested for the identification of the input and output nonlinear blocks of a proposed model from given input-output data measurements. In this work, the need for the commonly used assumptions including well-known structure of input and/or output nonlinearities and/or reversible nonlinear output is eliminated by replacing the intermediate variables and noise with their estimates. Four parametric estimation algorithms to identify the proposed fuzzy-type stochastic output-error autoregressive HW (FSOEAHW) model are derived based on backpropagation algorithm and multi-innovation and data filtering identification techniques. The proposed algorithms are improved backpropagation gradient (IBPG) algorithm, multi-innovation IBPG (MIIBPG) algorithm, a data filtering IBPG (FIBPG) algorithm, and a multi-innovation-based FIBPG (MIFIBPG) algorithm. The convergence of the parameter estimation algorithms is studied. The effectiveness of the proposed algorithms is shown by a given simulation example. [ABSTRACT FROM AUTHOR]

Large deviations for additive path functionals of stochastic processes have attracted significant research interest, in particular in the context of stochastic particle systems and statistical physics. Efficient numerical 'cloning' algorithms have been developed to estimate the scaled cumulant generating function, based on importance sampling via cloning of rare event trajectories. So far, attempts to study the convergence properties of these algorithms in continuous time have led to only partial results for particular cases. Adapting previous results from the literature of particle filters and sequential Monte Carlo methods, we establish a first comprehensive and fully rigorous approach to bound systematic and random errors of cloning algorithms in continuous time. To this end we develop a method to compare different algorithms for particular classes of observables, based on the martingale characterization of stochastic processes. Our results apply to a large class of jump processes on compact state space, and do not involve any time discretization in contrast to previous approaches. This provides a robust and rigorous framework that can also be used to evaluate and improve the efficiency of algorithms. [ABSTRACT FROM AUTHOR]

Aiming at the problem of large error and long time of early warning response in the traditional system, this paper designs a hazard identification early warning system based on random forest algorithm in underground coal mine. By random classification decision forest created dangerous content in different areas of the downhole information input into the decision tree as a test sample, according to the result of the output of the leaf node determine the risk level of decision trees, and USES the high precision of decision forest classification ability the threat level assessment test sample, radically reducing hazards identification error. Then, based on the evaluation results, combined with the threshold value of warning criteria to identify the gas exceeding limit area, and determine the fire source warning level, so as to realize the hazard source identification and warning. The simulation results show that the average hazard location identification error of the system is only 4.1%, and the warning response time can be controlled within 9 s. [ABSTRACT FROM AUTHOR]

In this paper, a new path integration algorithm is proposed for the non-autonomous vibro-impact system. It can be used to obtain the stochastic response of the system at the impact instant. The innovation of this algorithm is that the fixed excitation phase at the impact instant is introduced. The fixed excitation phase and the impact surface are combined as the special impact surface, and the algorithm sets up the different evolution methods of the probability density function and the impact completion condition. It can directly capture the stochastic response of the system at the impact instant without any non-smooth approximations. The non-smooth characteristics of the impact can be well preserved. This new path integration algorithm has good applicability. It has no limitation on the restitution coefficient. The design idea of this algorithm may provide a framework for the non-smooth system subject to the periodic excitation. In the end, a linear vibro-impact system and a nonlinear vibro-impact system excited by the external periodic force are used as examples to show how our method could be implemented. The stochastic P-bifurcation phenomena induced by parameters also are considered. The Monte Carlo simulations verify the effectiveness and accuracy of the proposed path integration algorithm. [ABSTRACT FROM AUTHOR]

We consider a class of hyperbolic systems of linear inhomogeneous partial differential equations with one spatial variable. As a rule, in the case of systems of partial differential equations, when solving particular problems, additional conditions are immediately used to ensure the uniqueness of the solution. However, this greatly complicates the construction of a solution in the case of additional conditions of nonstandard form. For a similar situation in the case of ordinary differential equations, one tries to find a general solution, for which one can then try to use the given additional conditions. However, for systems of partial differential equations, this approach is difficult, since, as a rule, in this case it is not possible to construct the general solution. For the class of systems of linear inhomogeneous partial differential equations considered in the present paper, it was possible to find an algorithm for constructing a general solution. A distinctive feature of the considered systems of equations is the multiplicity of the corresponding characteristics. As an application of the proposed algorithm, a general solution of the Kolmogorov system of equations for the probabilities of the states of a process is obtained, which describes the behavior of a popular model of a stochastic system of the type -out-of- with a general distribution of the repair time for failing components. The indicated system of Kolmogorov equations is a system of partial differential equations of the mentioned class. Therefore, it is possible to construct a general solution for this system. [ABSTRACT FROM AUTHOR]

This article investigates the problem of finite-time fuzzy adaptive event-triggered control design for stochastic nonlinear nonstrict feedback systems with unmodeled dynamics. The fuzzy logic systems are adopted to identify the unknown nonlinearities and a state observer is designed to estimate the unmeasured states. Using backstepping recursive design and combining it with a varying threshold event-triggered condition, a novel event-triggered-based fuzzy adaptive finite-time control algorithm is developed, where the dynamical signal function is employed to deal with the unmodeled dynamics. A power form of the errors is used to ensure a continuous stabilizer. The semi-global finite-time stability in probability of the closed-loop system is proved based on an It $\hat{\text{o}}$ differential equation and finite-time stability theory. Simulations are provided to verify the effectiveness of the developed control algorithm. [ABSTRACT FROM AUTHOR]