Search

Electric vehicles (EVs) are being rapidly adopted due to their economic and societal benefits. Autonomous mobility-on-demand (AMoD) systems also embrace this trend. However, the long charging time and high recharging frequency of EVs pose challenges to efficiently managing EV AMoD systems. The complicated dynamic charging and mobility process of EV AMoD systems makes the demand and supply uncertainties significant when designing vehicle balancing algorithms. In this work, we design a data-driven distributionally robust optimization (DRO) approach to balance EVs for both the mobility service and the charging process. The optimization goal is to minimize the worst-case expected cost under both passenger mobility demand uncertainties and EV supply uncertainties. We then propose a novel distributional uncertainty sets construction algorithm that guarantees the produced parameters are contained in desired confidence regions with a given probability. To solve the proposed DRO AMoD EV balancing problem, we derive an equivalent computationally tractable convex optimization problem. Based on real-world EV data of a taxi system, we show that with our solution the average total balancing cost is reduced by 14.49%, and the average mobility fairness and charging fairness are improved by 15.78% and 34.51%, respectively, compared to solutions that do not consider uncertainties., 16 pages

Mirror descent (MD) is a powerful first-order optimization technique that subsumes several optimization algorithms including gradient descent (GD). In this work, we develop a semi-definite programming (SDP) framework to analyze the convergence rate of MD in centralized and distributed settings under both strongly convex and non-strongly convex assumptions. We view MD with a dynamical system lens and leverage quadratic constraints (QCs) to provide explicit convergence rates based on Lyapunov stability. For centralized MD under strongly convex assumption, we develop a SDP that certifies exponential convergence rates. We prove that the SDP always has a feasible solution that recovers the optimal GD rate as a special case. We complement our analysis by providing the $O(1/k)$ convergence rate for convex problems. Next, we analyze the convergence of distributed MD and characterize the rate using SDP. To the best of our knowledge, the numerical rate of distributed MD has not been previously reported in the literature. We further prove an $O(1/k)$ convergence rate for distributed MD in the convex setting. Our numerical experiments on strongly convex problems indicate that our framework certifies superior convergence rates compared to the existing rates for distributed GD.

We develop a probabilistic control algorithm, $\texttt{GTLProCo}$, for swarms of agents with heterogeneous dynamics and objectives, subject to high-level task specifications. The resulting algorithm not only achieves decentralized control of the swarm but also significantly improves scalability over state-of-the-art existing algorithms. Specifically, we study a setting in which the agents move along the nodes of a graph, and the high-level task specifications for the swarm are expressed in a recently-proposed language called graph temporal logic (GTL). By constraining the distribution of the swarm over the nodes of the graph, GTL can specify a wide range of properties, including safety, progress, and response. $\texttt{GTLProCo}$, agnostic to the number of agents comprising the swarm, controls the density distribution of the swarm in a decentralized and probabilistic manner. To this end, it synthesizes a time-varying Markov chain modeling the time evolution of the density distribution under the GTL constraints. We first identify a subset of GTL, namely reach-avoid specifications, for which we can reduce the synthesis of such a Markov chain to either linear or semi-definite programs. Then, in the general case, we formulate the synthesis of the Markov chain as a mixed-integer nonlinear program (MINLP). We exploit the structure of the problem to provide an efficient sequential mixed-integer linear programming scheme with trust regions to solve the MINLP. We empirically demonstrate that our sequential scheme is at least three orders of magnitude faster than off-the-shelf MINLP solvers and illustrate the effectiveness of $\texttt{GTLProCo}$ in several swarm scenarios., Comment: Initial submission to TAC

The problem of finding the unique low dimensional decomposition of a given matrix has been a fundamental and recurrent problem in many areas. In this paper, we study the problem of seeking a unique decomposition of a low rank matrix $Y\in \mathbb{R}^{p\times n}$ that admits a sparse representation. Specifically, we consider $Y = A X\in \mathbb{R}^{p\times n}$ where the matrix $A\in \mathbb{R}^{p\times r}$ has full column rank, with $r < \min\{n,p\}$, and the matrix $X\in \mathbb{R}^{r\times n}$ is element-wise sparse. We prove that this sparse decomposition of $Y$ can be uniquely identified, up to some intrinsic signed permutation. Our approach relies on solving a nonconvex optimization problem constrained over the unit sphere. Our geometric analysis for the nonconvex optimization landscape shows that any {\em strict} local solution is close to the ground truth solution, and can be recovered by a simple data-driven initialization followed with any second order descent algorithm. At last, we corroborate these theoretical results with numerical experiments., Accepted by 2021 Neurips, in IEEE Transactions on Information Theory, 2022

This paper studies the adaptive optimal stationary control of continuous-time linear stochastic systems with both additive and multiplicative noises, using reinforcement learning techniques. Based on policy iteration, a novel off-policy reinforcement learning algorithm, named optimistic least-squares-based policy iteration, is proposed which is able to find iteratively near-optimal policies of the adaptive optimal stationary control problem directly from input/state data without explicitly identifying any system matrices, starting from an initial admissible control policy. The solutions given by the proposed optimistic least-squares-based policy iteration are proved to converge to a small neighborhood of the optimal solution with probability one, under mild conditions. The application of the proposed algorithm to a triple inverted pendulum example validates its feasibility and effectiveness., Comment: 10 pages, 3 figures

Existing frameworks for transfer learning are incomplete from a systems theoretic perspective. They place emphasis on notions of domain and task, and neglect notions of structure and behavior. In doing so, they limit the extent to which formalism can be carried through into the elaboration of their frameworks. Herein, we use Mesarovician systems theory to define transfer learning as a relation on sets and subsequently characterize the general nature of transfer learning as a mathematical construct. We interpret existing frameworks in terms of ours and go beyond existing frameworks to define notions of transferability, transfer roughness, and transfer distance. Importantly, despite its formalism, our framework avoids the detailed mathematics of learning theory or machine learning solution methods without excluding their consideration. As such, we provide a formal, general systems framework for modeling transfer learning that offers a rigorous foundation for system design and analysis.

Convergence (virtual) bidding is an important part of two-settlement electric power markets as it can effectively reduce discrepancies between the day-ahead and real-time markets. Consequently, there is extensive research into the bidding strategies of virtual participants aiming to obtain optimal bids to submit to the day-ahead market. In this paper, we introduce a price-based general stochastic optimization framework to obtain optimal convergence bid curves. Within this framework, we develop a computationally tractable linear programming-based optimization model, which produces bid prices and volumes simultaneously. We also show that different approximations and simplifications in the general model lead naturally to state-of-the-art convergence bidding approaches, such as self-scheduling and opportunistic approaches. Our general framework also provides a straightforward way to compare the performance of these models, which is demonstrated by numerical experiments on the California (CAISO) market.

One of the essential elements in implementing a closed-loop irrigation system is soil moisture estimation based on a limited number of available sensors. One associated problem is the determination of the optimal locations to install the sensors such that good soil moisture estimation can be obtained. In our previous work, the modal degree of observability was employed to address the problem of optimal sensor placement for soil moisture estimation of agro-hydrological systems. It was demonstrated that the optimally placed sensors can improve the soil moisture estimation performance. However, it is unclear whether the optimal sensor placement can significantly improve the soil moisture estimation performance in actual applications. In this work, we investigate the impact of sensor placement in soil moisture estimation for an actual agricultural field in Lethbridge, Alberta, Canada. In an experiment on the studied field, 42 soil moisture sensors were installed at different depths to collect the soil moisture measurements for one growing season. A three-dimensional agro-hydrological model with heterogeneous soil parameters of the studied field is developed. The modal degree of observability is applied to the three-dimensional system to determine the optimal sensor locations. The extended Kalman filter (EKF) is chosen as the data assimilation tool to estimate the soil moisture content of the studied field. Soil moisture estimation results for different scenarios are obtained and analyzed to investigate the effects of sensor placement on the performance of soil moisture estimation in the actual applications.

In this paper, we investigate the architecture of an optimal controller that maximizes the convergence speed of a consensus protocol with single-integrator dynamics. Under the assumption that communication delays increase with the number of hops from which information is allowed to reach each agent, we address the optimal control design under delayed feedback and show that the optimal controller features, in general, a sparsely connected architecture., 6 pages, 7 figures; published on IEEE Control Systems Letters

This paper presents a data-learned linear Koopman embedding of nonlinear networked dynamics and uses it to enable real-time model predictive emergency voltage control in a power network. The approach involves a novel data-driven ``basis-dictionary free" lifting of the system dynamics into a higher dimensional linear space over which an MPC (model predictive control) is exercised, making it both scalable and rapid for practical real-time implementation. A Koopman-inspired deep neural network (KDNN) encoder-decoder architecture for the linear embedding of the underlying dynamics under distributed controls is presented, in which the end-to-end components of the KDNN comprising of a triple of transforms is learned from the system trajectory data in one go: A Neural Network (NN)-based lifting to a higher dimension, a linear dynamics within that higher dimension, and an NN-based projection to the original space. This data-learned approach relieves the burden of the ad-hoc selection of the nonlinear basis functions (e.g., polynomial or radial) used in conventional approaches for lifting to higher dimensional linear space. We validate the efficacy and robustness of the approach via application to the standard IEEE 39-bus system.

Many robotic tasks, such as human-robot interactions or the handling of fragile objects, require tight control and limitation of appearing forces and moments alongside sensible motion control to achieve safe yet high-performance operation. We propose a learning-supported model predictive force and motion control scheme that provides stochastic safety guarantees while adapting to changing situations. Gaussian processes are used to learn the uncertain relations that map the robot's states to the forces and moments. The model predictive controller uses these Gaussian process models to achieve precise motion and force control under stochastic constraint satisfaction. As the uncertainty only occurs in the static model parts -- the output equations -- a computationally efficient stochastic MPC formulation is used. Analysis of recursive feasibility of the optimal control problem and convergence of the closed loop system for the static uncertainty case are given. Chance constraint formulation and back-offs are constructed based on the variance of the Gaussian process to guarantee safe operation. The approach is illustrated on a lightweight robot in simulations and experiments.

Robustness and stability of image-reconstruction algorithms have recently come under scrutiny. Their importance to medical imaging cannot be overstated. We review the known results for the topical variational regularization strategies ($\ell_2$ and $\ell_1$ regularization) and present novel stability results for $\ell_p$-regularized linear inverse problems for $p\in(1,\infty)$. Our results guarantee Lipschitz continuity for small $p$ and H\"{o}lder continuity for larger $p$. They generalize well to the $L_p(\Omega)$ function spaces., Comment: 11 pages, 6 figures, 1 appendix

Information compression is essential to reduce communication cost in distributed optimization over peer-to-peer networks. This paper proposes a communication-efficient linearly convergent distributed (COLD) algorithm to solve strongly convex optimization problems. By compressing innovation vectors, which are the differences between decision vectors and their estimates, COLD is able to achieve linear convergence for a class of $\delta$-contracted compressors. We explicitly quantify how the compression affects the convergence rate and show that COLD matches the same rate of its uncompressed version. To accommodate a wider class of compressors that includes the binary quantizer, we further design a novel dynamical scaling mechanism and obtain the linearly convergent Dyna-COLD. Importantly, our results strictly improve existing results for the quantized consensus problem. Numerical experiments demonstrate the advantages of both algorithms under different compressors., Comment: 14 pages

We study an optimal targeting problem for super-modular games with binary actions and finitely many players. The considered problem consists in the selection of a subset of players of minimum size such that, when the actions of these players are forced to a controlled value while the others are left to repeatedly play a best response action, the system will converge to the greatest Nash equilibrium of the game. Our main contributions consist in showing that the problem is NP-complete and in proposing an efficient iterative algorithm with provable convergence properties for its solution. We discuss in detail the special case of network coordination games and its relation with the notion of cohesiveness. Finally, we show with simulations the strength of our approach with respect to naive heuristics based on classical network centrality measures.

This paper considers a distributed reinforcement learning problem for decentralized linear quadratic control with partial state observations and local costs. We propose a Zero-Order Distributed Policy Optimization algorithm (ZODPO) that learns linear local controllers in a distributed fashion, leveraging the ideas of policy gradient, zero-order optimization and consensus algorithms. In ZODPO, each agent estimates the global cost by consensus, and then conducts local policy gradient in parallel based on zero-order gradient estimation. ZODPO only requires limited communication and storage even in large-scale systems. Further, we investigate the nonasymptotic performance of ZODPO and show that the sample complexity to approach a stationary point is polynomial with the error tolerance's inverse and the problem dimensions, demonstrating the scalability of ZODPO. We also show that the controllers generated throughout ZODPO are stabilizing controllers with high probability. Lastly, we numerically test ZODPO on multi-zone HVAC systems.

Robust model predictive control (MPC) is a well-known control technique for model-based control with constraints and uncertainties. In classic robust tube-based MPC approaches, an open-loop control sequence is computed via periodically solving an online nominal MPC problem, which requires prior model information and frequent access to onboard computational resources. In this paper, we propose an efficient robust MPC solution based on receding horizon reinforcement learning, called r-LPC, for unknown nonlinear systems with state constraints and disturbances. The proposed r-LPC utilizes a Koopman operator-based prediction model obtained off-line from pre-collected input-output datasets. Unlike classic tube-based MPC, in each prediction time interval of r-LPC, we use an actor-critic structure to learn a near-optimal feedback control policy rather than a control sequence. The resulting closed-loop control policy can be learned off-line and deployed online or learned online in an asynchronous way. In the latter case, online learning can be activated whenever necessary; for instance, the safety constraint is violated with the deployed policy. The closed-loop recursive feasibility, robustness, and asymptotic stability are proven under function approximation errors of the actor-critic networks. Simulation and experimental results on two nonlinear systems with unknown dynamics and disturbances have demonstrated that our approach has better or comparable performance when compared with tube-based MPC and LQR, and outperforms a recently developed actor-critic learning approach.

This paper considers controlling automated vehicles (AVs) to form a platoon with human-driven vehicles (HVs) under consideration of unknown HV model parameters and propulsion time constants. The proposed design is a data-driven dual-loop control strategy for the ego AVs, where the inner loop controller ensures platoon stability and the outer loop controller keeps a safe inter-vehicular spacing under control input limits. The inner loop controller is a constant-gain state feedback controller solved from a semidefinite program (SDP) using the online collected data of platooning errors. The outer loop is a model predictive control (MPC) that embeds a data-driven internal model to predict the future platooning error evolution. The proposed design is evaluated on a mixed platoon with a representative aggressive reference velocity profile, the SFTP-US06 Drive Cycle. The results confirm efficacy of the design and its advantages over the existing single loop data-driven MPC in terms of platoon stability and computational cost., 10 pages, 6 figures. This paper has been accepted by IET Intelligent Transport Systems

The recently introduced DeepONet operator-learning framework for PDE control is extended from the results for basic hyperbolic and parabolic PDEs to an advanced hyperbolic class that involves delays on both the state and the system output or input. The PDE backstepping design produces gain functions that are outputs of a nonlinear operator, mapping functions on a spatial domain into functions on a spatial domain, and where this gain-generating operator's inputs are the PDE's coefficients. The operator is approximated with a DeepONet neural network to a degree of accuracy that is provably arbitrarily tight. Once we produce this approximation-theoretic result in infinite dimension, with it we establish stability in closed loop under feedback that employs approximate gains. In addition to supplying such results under full-state feedback, we also develop DeepONet-approximated observers and output-feedback laws and prove their own stabilizing properties under neural operator approximations. With numerical simulations we illustrate the theoretical results and quantify the numerical effort savings, which are of two orders of magnitude, thanks to replacing the numerical PDE solving with the DeepONet.

Trajectory optimization under uncertainty underpins a wide range of applications in robotics. However, existing methods are limited in terms of reasoning about sources of epistemic and aleatoric uncertainty, space and time correlations, nonlinear dynamics, and non-convex constraints. In this work, we first introduce a continuous-time planning formulation with an average-value-at-risk constraint over the entire planning horizon. Then, we propose a sample-based approximation that unlocks an efficient, general-purpose, and time-consistent algorithm for risk-averse trajectory optimization. We prove that the method is asymptotically optimal and derive finite-sample error bounds. Simulations demonstrate the high speed and reliability of the approach on problems with stochasticity in nonlinear dynamics, obstacle fields, interactions, and terrain parameters.

In our work, we build upon the established connection between Residual Neural Networks (ResNets) and continuous-time control systems known as NeurODEs. By construction, NeurODEs have been limited to constant-width layers, making them unsuitable for modeling deep learning architectures with width-varying layers. In this paper, we propose a continuous-time Autoencoder, which we call AutoencODE, and we extend to this case the mean-field control framework already developed for usual NeurODEs. In this setting, we tackle the case of low Tikhonov regularization, resulting in potentially non-convex cost landscapes. While the global results obtained for high Tikhonov regularization may not hold globally, we show that many of them can be recovered in regions where the loss function is locally convex. Inspired by our theoretical findings, we develop a training method tailored to this specific type of Autoencoders with residual connections, and we validate our approach through numerical experiments conducted on various examples., 34 pages, 11 figures

Breaking safety constraints in control systems can lead to potential risks, resulting in unexpected costs or catastrophic damage. Nevertheless, uncertainty is ubiquitous, even among similar tasks. In this paper, we develop a novel adaptive safe control framework that integrates meta learning, Bayesian models, and control barrier function (CBF) method. Specifically, with the help of CBF method, we learn the inherent and external uncertainties by a unified adaptive Bayesian linear regression (ABLR) model, which consists of a forward neural network (NN) and a Bayesian output layer. Meta learning techniques are leveraged to pre-train the NN weights and priors of the ABLR model using data collected from historical similar tasks. For a new control task, we refine the meta-learned models using a few samples, and introduce pessimistic confidence bounds into CBF constraints to ensure safe control. Moreover, we provide theoretical criteria to guarantee probabilistic safety during the control processes. To validate our approach, we conduct comparative experiments in various obstacle avoidance scenarios. The results demonstrate that our algorithm significantly improves the Bayesian model-based CBF method, and is capable for efficient safe exploration even with multiple uncertain constraints.

Given a compact subset of a Banach space, the Chebyshev center problem consists of finding a minimal circumscribing ball containing the set. In this article we establish a numerically tractable algorithm for solving the Chebyshev center problem in the context of optimal learning from a finite set of data points. For a hypothesis space realized as a compact but not necessarily convex subset of a finite-dimensional subspace of some underlying Banach space, this algorithm computes the Chebyshev radius and the Chebyshev center of the hypothesis space, thereby solving the problem of optimal recovery of functions from data. The algorithm itself is based on, and significantly extends, recent results for near-optimal solutions of convex semi-infinite problems by means of targeted sampling, and it is of independent interest. Several examples of numerical computations of Chebyshev centers are included in order to illustrate the effectiveness of the algorithm., 22 pages, 16 figures

We focus on the problem of uncertainty informed allocation of medical resources (vaccines) to heterogeneous populations for managing epidemic spread. We tackle two related questions: (1) For a compartmental ordinary differential equation (ODE) model of epidemic spread, how can we estimate and integrate parameter uncertainty into resource allocation decisions? (2) How can we computationally handle both nonlinear ODE constraints and parameter uncertainties for a generic stochastic optimization problem for resource allocation? To the best of our knowledge current literature does not fully resolve these questions. Here, we develop a data-driven approach to represent parameter uncertainty accurately and tractably in a novel stochastic optimization problem formulation. We first generate a tractable scenario set by estimating the distribution on ODE model parameters using Bayesian inference with Gaussian processes. Next, we develop a parallelized solution algorithm that accounts for scenario-dependent nonlinear ODE constraints. Our scenario-set generation procedure and solution approach are flexible in that they can handle any compartmental epidemiological ODE model. Our computational experiments on two different non-linear ODE models (SEIR and SEPIHR) indicate that accounting for uncertainty in key epidemiological parameters can improve the efficacy of time-critical allocation decisions by 4-8%. This improvement can be attributed to data-driven and optimal (strategic) nature of vaccine allocations, especially in the early stages of the epidemic when the allocation strategy can crucially impact the long-term trajectory of the disease.

Demand flexibility plays a vital role in maintaining grid balance, reducing peak demand, and saving customers' energy bills. Given their highly shiftable load and significant contribution to a building's energy consumption, Heating, Ventilation, and Air Conditioning (HVAC) systems can provide valuable demand flexibility to the power systems by adjusting their energy consumption in response to electricity price and power system needs. To exploit this flexibility in both operation time and power, it is imperative to accurately model and aggregate the load flexibility of a large population of HVAC systems as well as designing effective control algorithms. In this paper, we tackle the curse of dimensionality issue in modeling and control by utilizing the concept of laxity to quantify the emergency level of each HVAC operation request. We further propose a two-level approach to address energy optimization for a large population of HVAC systems. The lower level involves an aggregator to aggregate HVAC load laxity information and use least-laxity-first (LLF) rule to allocate real-time power for individual HVAC systems based on the controller's total power. Due to the complex and uncertain nature of HVAC systems, we leverage a reinforcement learning (RL)-based controller to schedule the total power based on the aggregated laxity information and electricity price. We evaluate the temperature control and energy cost saving performance of a large-scale group of HVAC systems in both single-zone and multi-zone scenarios, under varying climate and electricity market conditions. The experiment results indicate that proposed approach outperforms the centralized methods in the majority of test scenarios, and performs comparably to model-based method in some scenarios., In Submission

In this paper, we consider the network slicing (NS) problem which attempts to map multiple customized virtual network requests to a common shared network infrastructure and allocate network resources to meet diverse service requirements. We propose an efficient decomposition algorithm for solving this NP-hard problem. The proposed algorithm decomposes the large-scale hard NS problem into two relatively easy function placement (FP) and traffic routing (TR) subproblems and iteratively solves them enabling information feedback between each other, which makes it particularly suitable to solve large-scale problems. Specifically, the FP subproblem is to place service functions into cloud nodes in the network, and solving it can return a function placement strategy based on which the TR subproblem is defined; and the TR subproblem is to find paths connecting two nodes hosting two adjacent functions in the network, and solving it can either verify that the solution of the FP subproblem is an optimal solution of the original problem, or return a valid inequality to the FP subproblem that cuts off the current infeasible solution. The proposed algorithm is guaranteed to find the global solution of the NS problem. We demonstrate the effectiveness and efficiency of the proposed algorithm via numerical experiments., 5 pages, 4 figures, accepted for publication in IEEE SPAWC 2023

In this paper, we present a toolbox for interval analysis in numpy, with an application to formal verification of neural network controlled systems. Using the notion of natural inclusion functions, we systematically construct interval bounds for a general class of mappings. The toolbox offers efficient computation of natural inclusion functions using compiled C code, as well as a familiar interface in numpy with its canonical features, such as n-dimensional arrays, matrix/vector operations, and vectorization. We then use this toolbox in formal verification of dynamical systems with neural network controllers, through the composition of their inclusion functions.

In the classical communication setting multiple senders having access to the same source of information and transmitting it over channel(s) to a receiver in general leads to a decrease in estimation error at the receiver as compared with the single sender case. However, if the objectives of the information providers are different from that of the estimator, this might result in interesting strategic interactions and outcomes. In this work, we consider a hierarchical signaling game between multiple senders (information designers) and a single receiver (decision maker) each having their own, possibly misaligned, objectives. The senders lead the game by committing to individual information disclosure policies simultaneously, within the framework of a non-cooperative Nash game among themselves. This is followed by the receiver's action decision. With Gaussian information structure and quadratic objectives (which depend on underlying state and receiver's action) for all the players, we show that in general the equilibrium is not unique. We hence identify a set of equilibria and further show that linear noiseless policies can achieve a minimal element of this set. Additionally, we show that competition among the senders is beneficial to the receiver, as compared with cooperation among the senders. Further, we extend our analysis to a dynamic signaling game of finite horizon with Markovian information evolution. We show that linear memoryless policies can achieve equilibrium in this dynamic game. We also consider an extension to a game with multiple receivers having coupled objectives. We provide algorithms to compute the equilibrium strategies in all these cases. Finally, via extensive simulations, we analyze the effects of multiple senders in varying degrees of alignment among their objectives., This work has been submitted for possible journal publication

Moving horizon estimation (MHE) is a widely studied state estimation approach in several practical applications. In the MHE problem, the state estimates are obtained via the solution of an approximated nonlinear optimization problem. However, this optimization step is known to be computationally complex. Given this limitation, this paper investigates the idea of iteratively preconditioned gradient-descent (IPG) to solve MHE problem with the aim of an improved performance than the existing solution techniques. To our knowledge, the preconditioning technique is used for the first time in this paper to reduce the computational cost and accelerate the crucial optimization step for MHE. The convergence guarantee of the proposed iterative approach for a class of MHE problems is presented. Additionally, sufficient conditions for the MHE problem to be convex are also derived. Finally, the proposed method is implemented on a unicycle localization example. The simulation results demonstrate that the proposed approach can achieve better accuracy with reduced computational costs.

This study presents a constructive methodology for designing accelerated convex optimisation algorithms in continuous-time domain. The two key enablers are the classical concept of passivity in control theory and the time-dependent change of variables that maps the output of the internal dynamic system to the optimisation variables. The Lyapunov function associated with the optimisation dynamics is obtained as a natural consequence of specifying the internal dynamics that drives the state evolution as a passive linear time-invariant system. The passivity-based methodology provides a general framework that has the flexibility to generate convex optimisation algorithms with the guarantee of different convergence rate bounds on the objective function value. The same principle applies to the design of online parameter update algorithms for adaptive control by re-defining the output of internal dynamics to allow for the feedback interconnection with tracking error dynamics., 10 pages, 1 figure

Based on the variational framework of the image denoising problem, we introduce a novel image denoising regularizer that combines anisotropic total variation model (ATV) and structure tensor total variation model (STV) in this paper. The model can effectively capture the first-order information of the image and maintain local features during the denoising process by applying the matrix weighting operator proposed in the ATV model to the patch-based Jacobian matrix in the STV model. Denoising experiments on grayscale and RGB color images demonstrate that the suggested model can produce better restoration quality in comparison to other well-known methods based on total-variation-based models and the STV model.

This paper considers a single-trajectory system identification problem for linear systems under general nonlinear and/or time-varying policies with i.i.d. random excitation noises. The problem is motivated by safe learning-based control for constrained linear systems, where the safe policies during the learning process are usually nonlinear and time-varying for satisfying the state and input constraints. In this paper, we provide a non-asymptotic error bound for least square estimation when the data trajectory is generated by any nonlinear and/or time-varying policies as long as the generated state and action trajectories are bounded. This significantly generalizes the existing non-asymptotic guarantees for linear system identification, which usually consider i.i.d. random inputs or linear policies. Interestingly, our error bound is consistent with that for linear policies with respect to the dependence on the trajectory length, system dimensions, and excitation levels. Lastly, we demonstrate the applications of our results by safe learning with robust model predictive control and provide numerical analysis.

Learning to control unknown nonlinear dynamical systems is a fundamental problem in reinforcement learning and control theory. A commonly applied approach is to first explore the environment (exploration), learn an accurate model of it (system identification), and then compute an optimal controller with the minimum cost on this estimated system (policy optimization). While existing work has shown that it is possible to learn a uniformly good model of the system~\citep{mania2020active}, in practice, if we aim to learn a good controller with a low cost on the actual system, certain system parameters may be significantly more critical than others, and we therefore ought to focus our exploration on learning such parameters. In this work, we consider the setting of nonlinear dynamical systems and seek to formally quantify, in such settings, (a) which parameters are most relevant to learning a good controller, and (b) how we can best explore so as to minimize uncertainty in such parameters. Inspired by recent work in linear systems~\citep{wagenmaker2021task}, we show that minimizing the controller loss in nonlinear systems translates to estimating the system parameters in a particular, task-dependent metric. Motivated by this, we develop an algorithm able to efficiently explore the system to reduce uncertainty in this metric, and prove a lower bound showing that our approach learns a controller at a near-instance-optimal rate. Our algorithm relies on a general reduction from policy optimization to optimal experiment design in arbitrary systems, and may be of independent interest. We conclude with experiments demonstrating the effectiveness of our method in realistic nonlinear robotic systems.

We model a system of n asymmetric firms selling a homogeneous good in a common market through a pay-as-bid auction. Every producer chooses as its strategy a supply function returning the quantity S(p) that it is willing to sell at a minimum unit price p. The market clears at the price at which the aggregate demand intersects the total supply and firms are paid the bid prices. We study a game theoretic model of competition among such firms and focus on its equilibria (Supply function equilibrium). The game we consider is a generalization of both models where firms can either set a fixed quantity (Cournot model) or set a fixed price (Bertrand model). Our main result is to prove existence and provide a characterization of (pure strategy) Nash equilibria in the space of K-Lipschitz supply functions., 6 pages, 5 figures, to appear Proc. of the 22nd International Federation of Automatic Control World Congress (IFAC 2023)

Trajectory optimization of a robot manipulator consists of both optimization of the robot movement as well as optimization of the robot end-effector path. This paper aims to find optimum movement parameters including movement type, speed, and acceleration to minimize robot energy. Trajectory optimization by minimizing the energy would increase the longevity of robotic manipulators. We utilized the particle swarm optimization method to find the movement parameters leading to minimum energy consumption. The effectiveness of the proposed method is demonstrated on different trajectories. Experimental results show that 49% efficiency was obtained using a UR5 robotic arm.

Sparse signal recovery is one of the most fundamental problems in various applications, including medical imaging and remote sensing. Many greedy algorithms based on the family of hard thresholding operators have been developed to solve the sparse signal recovery problem. More recently, Natural Thresholding (NT) has been proposed with improved computational efficiency. This paper proposes and discusses convergence guarantees for stochastic natural thresholding algorithms by extending the NT from the deterministic version with linear measurements to the stochastic version with a general objective function. We also conduct various numerical experiments on linear and nonlinear measurements to demonstrate the performance of StoNT.

The increasing installation rate of wind power poses great challenges to the global power system. In order to ensure the reliable operation of the power system, it is necessary to accurately forecast the wind speed and power of the wind turbines. At present, deep learning is progressively applied to the wind speed prediction. Nevertheless, the recent deep learning methods still reflect the embarrassment for practical applications due to model interpretability and hardware limitation. To this end, a novel deep knowledge-based learning method is proposed in this paper. The proposed method hybridizes pre-training method and auto-encoder structure to improve data representation and modeling of the deep knowledge-based learning framework. In order to form knowledge and corresponding absorbers, the original data is preprocessed by an optimization model based on correlation to construct multi-layer networks (knowledge) which are absorbed by sequence to sequence (Seq2Seq) models. Specifically, new cognition and memory units (CMU) are designed to reinforce traditional deep learning framework. Finally, the effectiveness of the proposed method is verified by three wind prediction cases from a wind farm in Liaoning, China. Experimental results show that the proposed method increases the stability and training efficiency compared to the traditional LSTM method and LSTM/GRU-based Seq2Seq method for applications of wind speed forecasting.

Security-constrained unit commitment (SCUC) is a computationally complex process utilized in power system day-ahead scheduling and market clearing. SCUC is run daily and requires state-of-the-art algorithms to speed up the process. The constraints and data associated with SCUC are both geographically and temporally correlated to ensure the reliability of the solution, which further increases the complexity. In this paper, an advanced machine learning (ML) model is used to study the patterns in power system historical data, which inherently considers both spatial and temporal (ST) correlations in constraints. The ST-correlated ML model is trained to understand spatial correlation by considering graph neural networks (GNN) whereas temporal sequences are studied using long short-term memory (LSTM) networks. The proposed approach is validated on several test systems namely, IEEE 24-Bus system, IEEE-73 Bus system, IEEE 118-Bus system, and synthetic South-Carolina (SC) 500-Bus system. Moreover, B-{\theta} and power transfer distribution factor (PTDF) based SCUC formulations were considered in this research. Simulation results demonstrate that the ST approach can effectively predict generator commitment schedule and classify critical and non-critical lines in the system which are utilized for model reduction of SCUC to obtain computational enhancement without loss in solution quality, Comment: 8 Figures, 5 Tables, 1 Algorithm

Gossip protocols are popular methods for average consensus problems in distributed computing. We prove new convergence guarantees for a variety of such protocols, including path, clique, and synchronous pairwise gossip. These arise by exploiting the connection between these protocols and the block randomized Kaczmarz method for solving linear systems. Moreover, we extend existing convergence results for block randomized Kaczmarz to allow for a more general choice of blocks, rank-deficient systems, and provide a tighter convergence rate guarantee. We furthermore apply this analysis to inconsistent consensus models and obtain similar guarantees. An extensive empirical analysis of these methods is provided for a variety of synthetic networks., 21 pages, 19 figures

The dictionary learning problem can be viewed as a data-driven process to learn a suitable transformation so that data is sparsely represented directly from example data. In this paper, we examine the problem of learning a dictionary that is invariant under a pre-specified group of transformations. Natural settings include Cryo-EM, multi-object tracking, synchronization, pose estimation, etc. We specifically study this problem under the lens of mathematical representation theory. Leveraging the power of non-abelian Fourier analysis for functions over compact groups, we prescribe an algorithmic recipe for learning dictionaries that obey such invariances. We relate the dictionary learning problem in the physical domain, which is naturally modelled as being infinite dimensional, with the associated computational problem, which is necessarily finite dimensional. We establish that the dictionary learning problem can be effectively understood as an optimization instance over certain matrix orbitopes having a particular block-diagonal structure governed by the irreducible representations of the group of symmetries. This perspective enables us to introduce a band-limiting procedure which obtains dimensionality reduction in applications. We provide guarantees for our computational ansatz to provide a desirable dictionary learning outcome. We apply our paradigm to investigate the dictionary learning problem for the groups SO(2) and SO(3). While the SO(2) orbitope admits an exact spectrahedral description, substantially less is understood about the SO(3) orbitope. We describe a tractable spectrahedral outer approximation of the SO(3) orbitope, and contribute an alternating minimization paradigm to perform optimization in this setting. We provide numerical experiments to highlight the efficacy of our approach in learning SO(3) invariant dictionaries, both on synthetic and on real world data., 30 pages, 2 figures

Hit rate is a key performance metric in predicting process product quality in integrated industrial processes. It represents the percentage of products accepted by downstream processes within a controlled range of quality. However, optimizing hit rate is a non-convex and challenging problem. To address this issue, we propose a data-driven quasi-convex approach that combines factorial hidden Markov models, multitask elastic net, and quasi-convex optimization. Our approach converts the original non-convex problem into a set of convex feasible problems, achieving an optimal hit rate. We verify the convex optimization property and quasi-convex frontier through Monte Carlo simulations and real-world experiments in steel production. Results demonstrate that our approach outperforms classical models, improving hit rates by at least 41.11% and 31.01% on two real datasets. Furthermore, the quasi-convex frontier provides a reference explanation and visualization for the deterioration of solutions obtained by conventional models.

Virtual power plants and load aggregation are becoming increasingly common. There, one regulates the aggregate power output of an ensemble of distributed energy resources (DERs). Marecek et al. [Automatica, Volume 147, January 2023, 110743, arXiv:2110.03001] recently suggested that long-term averages of prices or incentives offered should exist and be independent of the initial states of the operators of the DER, the aggregator, and the power grid. This can be seen as predictability, which underlies fairness. Unfortunately, the existence of such averages cannot be guaranteed with many traditional regulators, including the proportional-integral (PI) regulator with or without deadband. Here, we consider the effects of losses in the alternating current model and the deadband in the controller. This yields a non-linear dynamical system (due to the non-linear losses) exhibiting discontinuities (due to the deadband). We show that Filippov invariant measures enable reasoning about predictability and fairness while considering non-linearity of the alternating-current model and deadband., arXiv admin note: substantial text overlap with arXiv:2110.03001

Generalized from the concept of consensus, this paper considers a group of edge agreements, i.e. constraints defined for neighboring agents, in which each pair of neighboring agents is required to satisfy one edge agreement constraint. Edge agreements are defined locally to allow more flexibility than a global consensus. This work formulates a multi-agent optimization problem under edge agreements and proposes a continuous-time distributed augmented Lagrangian algorithm. Both analytical proof and numerical examples are provided to validate the effectiveness of the proposed distributed algorithm.

The outer Lowner-John method is widely used in sensor fusion applications to find the smallest ellipsoid that can approximate the intersection of a set of ellipsoids, described by positive definite covariance matrices modeling the quality of each sensor. We propose a distributed algorithm to solve this problem when these matrices are defined over the network's nodes. This is of particular significance as it is the first decentralized algorithm capable of computing the covariance intersection ellipsoid by combining information from the entire network using only local interactions. The solution is based on a reformulation of the centralized problem, leading to a local protocol based on exact dynamic consensus tools. After reaching consensus, the protocol converges to an outer Lowner-John ellipsoid in finite time, and to the global optimum asymptotically. Formal convergence analysis and numerical experiments are provided to validate the proposal's advantages., This is the accepted version of the manuscript: "Distributed outer approximation of the intersection of ellipsoids," Rodrigo Aldana-Lopez, Eduardo Sebastian, Rosario Aragues, Eduardo Montijano and Carlos Sagues, in IEEE Control Systems Letters, 2023, DOI: 10.1109/LCSYS.2023.3280259

Meta-Reinforcement Learning (MRL) is a promising framework for training agents that can quickly adapt to new environments and tasks. In this work, we study the MRL problem under the policy gradient formulation, where we propose a novel algorithm that uses Moreau envelope surrogate regularizers to jointly learn a meta-policy that is adjustable to the environment of each individual task. Our algorithm, called Moreau Envelope Meta-Reinforcement Learning (MEMRL), learns a meta-policy that can adapt to a distribution of tasks by efficiently updating the policy parameters using a combination of gradient-based optimization and Moreau Envelope regularization. Moreau Envelopes provide a smooth approximation of the policy optimization problem, which enables us to apply standard optimization techniques and converge to an appropriate stationary point. We provide a detailed analysis of the MEMRL algorithm, where we show a sublinear convergence rate to a first-order stationary point for non-convex policy gradient optimization. We finally show the effectiveness of MEMRL on a multi-task 2D-navigation problem.

Edge networks call for communication efficient (low overhead) and robust distributed optimization (DO) algorithms. These are, in fact, desirable qualities for DO frameworks, such as federated edge learning techniques, in the presence of data and system heterogeneity, and in scenarios where internode communication is the main bottleneck. Although computationally demanding, Newton-type (NT) methods have been recently advocated as enablers of robust convergence rates in challenging DO problems where edge devices have sufficient computational power. Along these lines, in this work we propose Q-SHED, an original NT algorithm for DO featuring a novel bit-allocation scheme based on incremental Hessian eigenvectors quantization. The proposed technique is integrated with the recent SHED algorithm, from which it inherits appealing features like the small number of required Hessian computations, while being bandwidth-versatile at a bit-resolution level. Our empirical evaluation against competing approaches shows that Q-SHED can reduce by up to 60% the number of communication rounds required for convergence.

Optimization problems over dynamic networks have been extensively studied and widely used in the past decades to formulate numerous real-world problems. However, (1) traditional optimization-based approaches do not scale to large networks, and (2) the design of good heuristics or approximation algorithms often requires significant manual trial-and-error. In this work, we argue that data-driven strategies can automate this process and learn efficient algorithms without compromising optimality. To do so, we present network control problems through the lens of reinforcement learning and propose a graph network-based framework to handle a broad class of problems. Instead of naively computing actions over high-dimensional graph elements, e.g., edges, we propose a bi-level formulation where we (1) specify a desired next state via RL, and (2) solve a convex program to best achieve it, leading to drastically improved scalability and performance. We further highlight a collection of desirable features to system designers, investigate design decisions, and present experiments on real-world control problems showing the utility, scalability, and flexibility of our framework., 9 pages, 4 figures

Although Connected Vehicles (CVs) have demonstrated tremendous potential to enhance traffic operations, they can impose privacy risks on individual travelers, e.g., leaking sensitive information about their frequently visited places, routing behavior, etc. Despite the large body of literature that devises various algorithms to exploit CV information, research on privacy-preserving traffic control is still in its infancy. In this paper, we aim to fill this research gap and propose a privacy-preserving adaptive traffic signal control method using CV data. Specifically, we leverage secure Multi-Party Computation and differential privacy to devise a privacy-preserving CV data aggregation mechanism, which can calculate key traffic quantities without any CVs having to reveal their private data. We further develop a linear optimization model for adaptive signal control based on the traffic variables obtained via the data aggregation mechanism. The proposed linear programming problem is further extended to a stochastic programming problem to explicitly handle the noises added by the differentially private mechanism. Evaluation results show that the linear optimization model preserves privacy with a marginal impact on control performance, and the stochastic programming model can significantly reduce residual queues compared to the linear programming model, with almost no increase in vehicle delay. Overall, our methods demonstrate the feasibility of incorporating privacy-preserving mechanisms in CV-based traffic modeling and control, which guarantees both utility and privacy.

Convex optimization methods have been extensively used in the fields of communications and signal processing. However, the theory of quaternion optimization is currently not as fully developed and systematic as that of complex and real optimization. To this end, we establish an essential theory of convex quaternion optimization for signal processing based on the generalized Hamilton-real (GHR) calculus. This is achieved in a way which conforms with traditional complex and real optimization theory. For rigorous, We present five discriminant theorems for convex quaternion functions, and four discriminant criteria for strongly convex quaternion functions. Furthermore, we provide a fundamental theorem for the optimality of convex quaternion optimization problems, and demonstrate its utility through three applications in quaternion signal processing. These results provide a solid theoretical foundation for convex quaternion optimization and open avenues for further developments in signal processing applications.

Dynamic traffic assignment and vehicle route guidance have been important problems in ITS for some time. This paper proposes a new model for VRGS, which takes into consideration of the information propagation, user selection and information reaction. Parameter p is then defined as the updating weight for computing cost of traffic based on a distributive learning scheme. p is calculated through a function which denotes information propagation over time and space and the function needs further optimization. Comparison to static traffic assignment, DTA and feasible strategies are given, and future work is also stated., 12 pages

Safety has been a critical issue for the deployment of learning-based approaches in real-world applications. To address this issue, control barrier function (CBF) and its variants have attracted extensive attention for safety-critical control. However, due to the myopic one-step nature of CBF and the lack of principled methods to design the class-$\mathcal{K}$ functions, there are still fundamental limitations of current CBFs: optimality, stability, and feasibility. In this paper, we proposed a novel and unified approach to address these limitations with Adaptive Multi-step Control Barrier Function (AM-CBF), where we parameterize the class-$\mathcal{K}$ function by a neural network and train it together with the reinforcement learning policy. Moreover, to mitigate the myopic nature, we propose a novel \textit{multi-step training and single-step execution} paradigm to make CBF farsighted while the execution remains solving a single-step convex quadratic program. Our method is evaluated on the first and second-order systems in various scenarios, where our approach outperforms the conventional CBF both qualitatively and quantitatively.