IA Scholar Query: Control Under Stochastic Multiplicative Uncertainties: Part I, Fundamental Conditions of Stabilizability.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgWed, 14 Sep 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Technical Report on Optimal Linear Multiple Estimation for Landmark-Based Planning via Control Synthesis
https://scholar.archive.org/work/dttsngcnlvhblbqlbgi4bgm2um
A common way to implement navigation in mobile robots is through the use of landmarks. In this case, the main goal of the controller is to make progress toward a goal location (stability), while avoiding the boundary of the environment (safety). In our previous work, we proposed a method to synthesize global controllers for environments with a polyhedral decomposition; our solution uses a Quadratically Constrained Quadratic Program with Chance Constraints to take into account the uncertainty in landmark measurements. Building upon this work, we introduce the concept of virtual landmarks, which are defined as linear combinations of actual landmark measurements that minimize the uncertainty in the resulting control actions. Interestingly, our results show that the first minimum-variance landmark is independent of the feedback control matrix, thus decoupling the design of the landmark from the one of the controller; attempting to derive additional, statistically independent landmarks, however, requires solving non-convex problems that involve also the controller. Numerical experiments demonstrate that, by minimizing the variance of the inputs, the resulting controller will be less conservative, and the robot is able to complete navigation tasks more effectively (faster and with less jitter in the trajectory).Chenfei Wang, Roberto Tronwork_dttsngcnlvhblbqlbgi4bgm2umWed, 14 Sep 2022 00:00:00 GMTStatistical Learning Theory for Control: A Finite Sample Perspective
https://scholar.archive.org/work/dsdurkmrznfirbumwmbohsoa74
This tutorial survey provides an overview of recent non-asymptotic advances in statistical learning theory as relevant to control and system identification. While there has been substantial progress across all areas of control, the theory is most well-developed when it comes to linear system identification and learning for the linear quadratic regulator, which are the focus of this manuscript. From a theoretical perspective, much of the labor underlying these advances has been in adapting tools from modern high-dimensional statistics and learning theory. While highly relevant to control theorists interested in integrating tools from machine learning, the foundational material has not always been easily accessible. To remedy this, we provide a self-contained presentation of the relevant material, outlining all the key ideas and the technical machinery that underpin recent results. We also present a number of open problems and future directions.Anastasios Tsiamis, Ingvar Ziemann, Nikolai Matni, George J. Pappaswork_dsdurkmrznfirbumwmbohsoa74Mon, 12 Sep 2022 00:00:00 GMTSafe End-to-end Learning-based Robot Autonomy via Integrated Perception, Planning, and Control
https://scholar.archive.org/work/czetxbsik5favafpkxjvfapvgy
Trustworthy robots must be able to complete tasks reliably while obeying safety constraints. While traditional methods for constrained motion planning and optimal control can achieve this if the environment is accurately modeled and the task is unambiguous, future robots will be deployed in unstructured settings with poorly-understood or inaccurate dynamics, observation models, and task specifications. Thus, to plan and perform control, robots will invariably need data to learn and refine their understanding of their environments and tasks. Though machine learning provides a means to obtain perception and dynamics models from data, blindly trusting these potentially-unreliable models when planning can cause unsafe and unpredictable behavior at runtime. To this end, this dissertation is motivated by the following questions: (1) To refine their understanding of the desired task, how can robots learn components of a constrained motion planner (e.g., constraints, task specifications) in a data-efficient manner? and (2) How can robots quantify and remain robust to the inevitable uncertainty and error in learned components within the broader perception-planning-control autonomy loop in order to provide system-level guarantees on safety and task completion at runtime? To address the first question, we propose methods that use successful human demonstrations to learn unknown constraints and task specifications. The crux of this problem relies on learning what not to do (i.e., behavior violating the unknown constraints or specifications) from only successful examples. We make the insight that the demonstrations' approximate optimality implicitly defines what the robot should not do, and that this information can be extracted by simulating lower-cost trajectories and by using the Karush-Kuhn-Tucker (KKT) optimality conditions. These strong optimality priors make our method highly data-efficient. We use these methods to learn a broad class of constraints, including nonconvex obstacle constraints, and linear temporal logic f [...]Glen Chou, University, Mywork_czetxbsik5favafpkxjvfapvgyTue, 06 Sep 2022 00:00:00 GMTRegret Analysis of Certainty Equivalence Policies in Continuous-Time Linear-Quadratic Systems
https://scholar.archive.org/work/kl7z6hxqqvca3cfnzthr5duf3a
This work theoretically studies a ubiquitous reinforcement learning policy for controlling the canonical model of continuous-time stochastic linear-quadratic systems. We show that randomized certainty equivalent policy addresses the exploration-exploitation dilemma in linear control systems that evolve according to unknown stochastic differential equations and their operating cost is quadratic. More precisely, we establish square-root of time regret bounds, indicating that randomized certainty equivalent policy learns optimal control actions fast from a single state trajectory. Further, linear scaling of the regret with the number of parameters is shown. The presented analysis introduces novel and useful technical approaches, and sheds light on fundamental challenges of continuous-time reinforcement learning.Mohamad Kazem Shirani Faradonbehwork_kl7z6hxqqvca3cfnzthr5duf3aMon, 22 Aug 2022 00:00:00 GMTSparse Structure Design for Stochastic Linear Systems via a Linear Matrix Inequality Approach
https://scholar.archive.org/work/oxgp45cujfckbht72rgdu66apu
In this paper, we propose a sparsity-promoting feedback control design for stochastic linear systems with multiplicative noise. The objective is to identify a sparse control architecture that optimizes the closed-loop performance while stabilizing the system in the mean-square sense. The proposed approach approximates the nonconvex combinatorial optimization problem by minimizing various matrix norms subject to the Linear Matrix Inequality (LMI) stability condition. We present two design problems to reduce the number of actuators via the static state-feedback and a low-dimensional output. A regularized linear quadratic regulator with multiplicative noise (LQRm) optimal control problem and its convex relaxation are presented to demonstrate the tradeoff between the suboptimal closed-loop performance and the sparsity degree of control structure. Case studies on power grids for wide-area frequency control show that the proposed sparsity-promoting control can considerably reduce the number of actuators without significant loss in system performance. The sparse control architecture is robust to substantial system-level disturbances while achieving mean-square stability.Yi Guo and Ognjen Stanojev and Gabriela Hug and Tyler Summerswork_oxgp45cujfckbht72rgdu66apuFri, 19 Aug 2022 00:00:00 GMTContinuation with Non-invasive Control Schemes: Revealing Unstable States in a Pedestrian Evacuation Scenario
https://scholar.archive.org/work/f4egktsqvrexldpx7qnqjvpjrq
This paper presents a framework to perform bifurcation analysis in laboratory experiments or simulations. We employ control-based continuation to study the dynamics of a macroscopic variable of a microscopically defined model, exploring the potential viability of the underlying feedback control techniques in an experiment. In contrast to previous experimental studies that used iterative root-finding methods on the feedback control targets, we propose a feedback control law that is inherently non-invasive. That is, the control discovers the location of equilibria and stabilizes them simultaneously. We call the proposed control zero-in-equilibrium feedback control and we prove that it is able to stabilize branches of equilibria, except at singularities of codimension n+1, where n is the number of state space dimensions the feedback can depend on. We apply the method to a simulated evacuation scenario were pedestrians have to reach an exit after maneuvering left or right around an obstacle. The scenario shows a hysteresis phenomenon with bistability and tipping between two possible steady pedestrian flows in microscopic simulations. We demonstrate for the evacuation scenario that the proposed control law is able to uniformly discover and stabilize steady flows along the entire branch, including points where other non-invasive approaches to feedback control become singular.Ilias Panagiotopoulos, Jens Starke, Jan Sieber, Wolfram Justwork_f4egktsqvrexldpx7qnqjvpjrqMon, 01 Aug 2022 00:00:00 GMTThompson Sampling Efficiently Learns to Control Diffusion Processes
https://scholar.archive.org/work/jlnbux3auzekzeloqcw5xf2wki
Diffusion processes that evolve according to linear stochastic differential equations are an important family of continuous-time dynamic decision-making models. Optimal policies are well-studied for them, under full certainty about the drift matrices. However, little is known about data-driven control of diffusion processes with uncertain drift matrices as conventional discrete-time analysis techniques are not applicable. In addition, while the task can be viewed as a reinforcement learning problem involving exploration and exploitation trade-off, ensuring system stability is a fundamental component of designing optimal policies. We establish that the popular Thompson sampling algorithm learns optimal actions fast, incurring only a square-root of time regret, and also stabilizes the system in a short time period. To the best of our knowledge, this is the first such result for Thompson sampling in a diffusion process control problem. We validate our theoretical results through empirical simulations with real parameter matrices from two settings of airplane and blood glucose control. Moreover, we observe that Thompson sampling significantly improves (worst-case) regret, compared to the state-of-the-art algorithms, suggesting Thompson sampling explores in a more guarded fashion. Our theoretical analysis involves characterization of a certain optimality manifold that ties the local geometry of the drift parameters to the optimal control of the diffusion process. We expect this technique to be of broader interest.Mohamad Kazem Shirani Faradonbeh, Mohamad Sadegh Shirani Faradonbeh, Mohsen Bayatiwork_jlnbux3auzekzeloqcw5xf2wkiMon, 20 Jun 2022 00:00:00 GMTAmbiguity Tube MPC
https://scholar.archive.org/work/jeb7nezg3fhvnm76vze7euynmm
This paper is about a class of distributionally robust model predictive controllers (MPC) for nonlinear stochastic processes that evaluate risk and control performance measures by propagating ambiguity sets in the space of state probability measures. A framework for formulating such ambiguity tube MPC controllers is presented, which is based on modern measure-theoretic methods from the field of optimal transport theory. Moreover, a supermartingale based analysis technique is proposed, leading to stochastic stability results for a large class of distributionally robust controllers for linear and nonlinear systems. In this context, we also discuss how to construct terminal cost functions for stochastic and distributionally robust MPC that ensure closed-loop stability and asymptotic convergence to robust invariant sets. The corresponding theoretical developments are illustrated by tutorial-style examples and a numerical case study.Fan Wu, Mario E. Villanueva, Boris Houskawork_jeb7nezg3fhvnm76vze7euynmmSat, 18 Jun 2022 00:00:00 GMTLogarithmic regret for episodic continuous-time linear-quadratic reinforcement learning over a finite-time horizon
https://scholar.archive.org/work/7f5thfl4grhr7atq2e3g4wkbqi
We study finite-time horizon continuous-time linear-quadratic reinforcement learning problems in an episodic setting, where both the state and control coefficients are unknown to the controller. We first propose a least-squares algorithm based on continuous-time observations and controls, and establish a logarithmic regret bound of order O((ln M)(lnln M)), with M being the number of learning episodes. The analysis consists of two parts: perturbation analysis, which exploits the regularity and robustness of the associated Riccati differential equation; and parameter estimation error, which relies on sub-exponential properties of continuous-time least-squares estimators. We further propose a practically implementable least-squares algorithm based on discrete-time observations and piecewise constant controls, which achieves similar logarithmic regret with an additional term depending explicitly on the time stepsizes used in the algorithm.Matteo Basei, Xin Guo, Anran Hu, Yufei Zhangwork_7f5thfl4grhr7atq2e3g4wkbqiFri, 17 Jun 2022 00:00:00 GMTZero-Error Feedback Capacity for Bounded Stabilization and Finite-State Additive Noise Channels
https://scholar.archive.org/work/xki7l4tsjjb6hir3y5nyvcvcua
This article studies the zero-error feedback capacity of causal discrete channels with memory. First, by extending the classical zero-error feedback capacity concept, a new notion of uniform zero-error feedback capacity C_0f for such channels is introduced. Using this notion a tight condition for bounded stabilization of unstable noisy linear systems via causal channels is obtained, assuming no channel state information at either end of the channel.Amir Saberi, Farhad Farokhi, Girish Nairwork_xki7l4tsjjb6hir3y5nyvcvcuaWed, 01 Jun 2022 00:00:00 GMTStability Analysis and Stabilization of Continuous-Time Linear Systems with Distributed Delays
https://scholar.archive.org/work/bqgkmchlgfbaxnzhj6bp7zkymy
This book is an extension of my Ph.D. thesis which is devoted to the methods for the stability (dissipativity) analysis and stabilization of linear systems with non-trivial distributed delays based on the application of the Liapunov- Krasovskiĭ functional (LKF) approach.Qian Fengwork_bqgkmchlgfbaxnzhj6bp7zkymyMon, 30 May 2022 00:00:00 GMTLinear quantum systems: a tutorial
https://scholar.archive.org/work/ivpi74qr2baj3ozt23y2t4zcyy
The purpose of this tutorial is to give a brief introduction to linear quantum control systems. The mathematical model of linear quantum control systems is presented first, then some fundamental control-theoretic notions such as stability, controllability and observability are given, which are closely related to several important concepts in quantum information science such as decoherence-free subsystems, quantum non-demolition variables, and back-action evasion measurements. After that, quantum Gaussian states are introduced, in particular, an information-theoretic uncertainty relation is presented which often gives a better bound for mixed Gaussian states than the well-known Heisenberg uncertainty relation. The quantum Kalman filter is presented for quantum linear systems, which is the quantum analogy of the Kalman filter for classical (namely, non-quantum-mechanical) linear systems. The quantum Kalman canonical decomposition for quantum linear systems is recorded, and its application is illustrated by means of a recent experiment. As single- and multi-photon states are useful resources in quantum information technology, the response of quantum linear systems to these types of input is presented. Finally, coherent feedback control of quantum linear systems is briefly introduced, and a recent experiment is used to demonstrate the effectiveness of quantum linear systems and networks theory.dback control of quantum linear systems is briefly introduced, and a recent experiment is used to demonstrate the effectiveness of quantum linear systems and networks theory.Guofeng Zhang, Zhiyuan Dongwork_ivpi74qr2baj3ozt23y2t4zcyyWed, 25 May 2022 00:00:00 GMTPrivacy-Preserving Data-Enabled Predictive Leading Cruise Control in Mixed Traffic
https://scholar.archive.org/work/hhe6fahodnegjaobnqlm57ejvm
Data-driven predictive control of connected and automated vehicles (CAVs) has received increasing attention as it can achieve safe and optimal control without relying on explicit dynamical models. However, employing the data-driven strategy involves the collection and sharing of privacy-sensitive vehicle information, which is vulnerable to privacy leakage and might further lead to malicious activities. In this paper, we develop a privacy-preserving data-enabled predictive control scheme for CAVs in a mixed traffic environment, where human-driven vehicles and CAVs coexist. We tackle external eavesdropper and honest-but-curious central unit eavesdropper who wiretap the communication channel of the mixed traffic system and intend to infer the CAVs' state and input information. An affine masking-based privacy protection method is designed to conceal the true state and input signals, and an extended form of the data-enabled predictive leading cruise control under different matrix structures is derived to achieve privacy-preserving optimal control for CAVs. The proposed scheme can protect the privacy of CAVs against the attackers without affecting control performance or incurring heavy computations. Numerical simulations demonstrate the efficacy of the developed approach.Kaixiang Zhang, Kaian Chen, Zhaojian Li, Jun Chen, Yang Zhengwork_hhe6fahodnegjaobnqlm57ejvmSun, 22 May 2022 00:00:00 GMTSVR-based Observer Design for Unknown Linear Systems: Complexity and Performance
https://scholar.archive.org/work/xlxjfq762vafzexhwplonrftjq
In this paper we consider estimating the system parameters and designing stable observer for unknown noisy linear time-invariant (LTI) systems. We propose a Support Vector Regression (SVR) based estimator to provide adjustable asymmetric error interval for estimations. This estimator is capable to trade-off bias-variance of the estimation error by tuning parameter γ > 0 in the loss function. This method enjoys the same sample complexity of 𝒪(1/√(N)) as the Ordinary Least Square (OLS) based methods but achieves a 𝒪(1/(γ+1)) smaller variance. Then, a stable observer gain design procedure based on the estimations is proposed. The observation performance bound based on the estimations is evaluated by the mean square observation error, which is shown to be adjustable by tuning the parameter γ, thus achieving higher scalability than the OLS methods. The advantages of the estimation error bias-variance trade-off for observer design are also demonstrated through matrix spectrum and observation performance optimality analysis. Extensive simulation validations are conducted to verify the computed estimation error and performance optimality with different γ and noise settings. The variances of the estimation error and the fluctuations in performance are smaller with a properly-designed parameter γ compared with the OLS methods.Xuda Ding, Han Wang, Jianping He, Cailian Chen, Xinping Guanwork_xlxjfq762vafzexhwplonrftjqSat, 14 May 2022 00:00:00 GMTRobust Online Control with Model Misspecification
https://scholar.archive.org/work/row2qoeq55g7beu36a6627tzne
We study online control of an unknown nonlinear dynamical system that is approximated by a time-invariant linear system with model misspecification. Our study focuses on robustness, a measure of how much deviation from the assumed linear approximation can be tolerated by a controller while maintaining finite ℓ_2-gain. A basic methodology to analyze robustness is via the small gain theorem. However, as an implication of recent lower bounds on adaptive control, this method can only yield robustness that is exponentially small in the dimension of the system and its parametric uncertainty. The work of Cusumano and Poolla shows that much better robustness can be obtained, but the control algorithm is inefficient, taking exponential time in the worst case. In this paper we investigate whether there exists an efficient algorithm with provable robustness beyond the small gain theorem. We demonstrate that for a fully actuated system, this is indeed attainable. We give an efficient controller that can tolerate robustness that is polynomial in the dimension and independent of the parametric uncertainty; furthermore, the controller obtains an ℓ_2-gain whose dimension dependence is near optimal.Xinyi Chen, Udaya Ghai, Elad Hazan, Alexandre Megretskiwork_row2qoeq55g7beu36a6627tzneTue, 05 Apr 2022 00:00:00 GMTDeeP-LCC: Data-EnablEd Predictive Leading Cruise Control in Mixed Traffic Flow
https://scholar.archive.org/work/b5ktkvuhmzhrdjdaab5j4575fy
For the control of connected and autonomous vehicles (CAVs), most existing methods focus on model-based strategies. They require explicit knowledge of car-following dynamics of human-driven vehicles that are non-trivial to identify accurately. In this paper, instead of relying on a parametric car-following model, we introduce a data-driven non-parametric strategy, called DeeP-LCC (Data-EnablEd Predictive Leading Cruise Control), to achieve safe and optimal control of CAVs in mixed traffic. We first utilize Willems' fundamental lemma to obtain a data-centric representation of mixed traffic behavior. This is justified by rigorous analysis on controllability and observability properties of mixed traffic. We then employ a receding horizon strategy to solve a finite-horizon optimal control problem at each time step, in which input/output constraints are incorporated for collision-free guarantees. Numerical experiments validate the performance of DeeP-LCC compared to a standard predictive controller that requires an accurate model. Extensive nonlinear traffic simulations further confirm its great potential on improving traffic efficiency, driving safety, and fuel economy.Jiawei Wang, Yang Zheng, Keqiang Li, Qing Xuwork_b5ktkvuhmzhrdjdaab5j4575fySun, 20 Mar 2022 00:00:00 GMTUniformly Bounded State Estimation over Multiple Access Channels
https://scholar.archive.org/work/2npwt4l34ncfxcba7vdjk4k4im
This paper addresses the problem of distributed state estimation via multiple access channels (MACs). We consider a scenario where two encoders are simultaneously communicating their measurements through a noisy channel. Firstly, the zero-error capacity region of the general M-input, single-output MAC is characterized using tools from nonstochastic information theory. Next, we show that a tight condition to be able to achieve uniformly bounded state estimation errors can be given in terms of the channel zero-error capacity region. This criterion relates the channel properties to the plant dynamics. These results pave the way towards understanding information flows in networked control systems with multiple transmitters.Ghassen Zafzouf, Girish N. Nair, Farhad Farokhiwork_2npwt4l34ncfxcba7vdjk4k4imFri, 11 Mar 2022 00:00:00 GMTAutomated Verification and Synthesis of Stochastic Hybrid Systems: A Survey
https://scholar.archive.org/work/lt6cxflpb5cbdhc3v6foxgpniq
Stochastic hybrid systems have received significant attentions as a relevant modelling framework describing many systems, from engineering to the life sciences: they enable the study of numerous applications, including transportation networks, biological systems and chemical reaction networks, smart energy and power grids, and beyond. Automated verification and policy synthesis for stochastic hybrid systems can be inherently challenging: this is due to the heterogeneity of their dynamics (presence of continuous and discrete components), the presence of uncertainty, and in some applications the large dimension of state and input sets. Over the past few years, a few hundred articles have investigated these models, and developed diverse and powerful approaches to mitigate difficulties encountered in the analysis and synthesis of such complex stochastic systems. In this survey, we overview the most recent results in the literature and discuss different approaches, including (in)finite abstractions, verification and synthesis for temporal logic specifications, stochastic similarity relations, (control) barrier certificates, compositional techniques, and a selection of results on continuous-time stochastic systems; we finally survey recently developed software tools that implement the discussed approaches. Throughout the manuscript we discuss a few open topics to be considered as potential future research directions: we hope that this survey will guide younger researchers through a comprehensive understanding of the various challenges, tools, and solutions in this enticing and rich scientific area.Abolfazl Lavaei, Sadegh Soudjani, Alessandro Abate, Majid Zamaniwork_lt6cxflpb5cbdhc3v6foxgpniqThu, 10 Mar 2022 00:00:00 GMTApproximate Midpoint Policy Iteration for Linear Quadratic Control
https://scholar.archive.org/work/vyqmoa5ernbobi63ndm544onh4
We present a midpoint policy iteration algorithm to solve linear quadratic optimal control problems in both model-based and model-free settings. The algorithm is a variation of Newton's method, and we show that in the model-based setting it achieves cubic convergence, which is superior to standard policy iteration and policy gradient algorithms that achieve quadratic and linear convergence, respectively. We also demonstrate that the algorithm can be approximately implemented without knowledge of the dynamics model by using least-squares estimates of the state-action value function from trajectory data, from which policy improvements can be obtained. With sufficient trajectory data, the policy iterates converge cubically to approximately optimal policies, and this occurs with the same available sample budget as the approximate standard policy iteration. Numerical experiments demonstrate effectiveness of the proposed algorithms.Benjamin Gravell, Iman Shames, Tyler Summerswork_vyqmoa5ernbobi63ndm544onh4Tue, 15 Feb 2022 00:00:00 GMTTurnpike in optimal control of PDEs, ResNets, and beyond
https://scholar.archive.org/work/qkyfqupdifgyldxidnndjspifu
The turnpike property in contemporary macroeconomics asserts that if an economic planner seeks to move an economy from one level of capital to another, then the most efficient path, as long as the planner has enough time, is to rapidly move stock to a level close to the optimal stationary or constant path, then allow for capital to develop along that path until the desired term is nearly reached, at which point the stock ought to be moved to the final target. Motivated in part by its nature as a resource allocation strategy, over the past decade, the turnpike property has also been shown to hold for several classes of partial differential equations arising in mechanics. When formalized mathematically, the turnpike theory corroborates the insights from economics: for an optimal control problem set in a finite-time horizon, optimal controls and corresponding states, are close (often exponentially), during most of the time, except near the initial and final time, to the optimal control and corresponding state for the associated stationary optimal control problem. In particular, the former are mostly constant over time. This fact provides a rigorous meaning to the asymptotic simplification that some optimal control problems appear to enjoy over long time intervals, allowing the consideration of the corresponding stationary problem for computing and applications. We review a slice of the theory developed over the past decade –the controllability of the underlying system is an important ingredient, and can even be used to devise simple turnpike-like strategies which are nearly optimal–, and present several novel applications, including, among many others, the characterization of Hamilton-Jacobi-Bellman asymptotics, and stability estimates in deep learning via residual neural networks.Borjan Geshkovski, Enrique Zuazuawork_qkyfqupdifgyldxidnndjspifuTue, 08 Feb 2022 00:00:00 GMT