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Computation of stable convex combinations of a set of matrices through LMIs with application in H∞ control of switched linear systems 通过 LMI 计算一组矩阵的稳定凸组合，并将其应用于开关线性系统的 H∞ 控制
IF 2.6 3区 计算机科学
Systems & Control Letters Pub Date : 2024-05-27 DOI: 10.1016/j.sysconle.2024.105833
Andressa M. Souza, Ricardo C.L.F. Oliveira, Pedro L.D. Peres
{"title":"Computation of stable convex combinations of a set of matrices through LMIs with application in H∞ control of switched linear systems","authors":"Andressa M. Souza,&nbsp;Ricardo C.L.F. Oliveira,&nbsp;Pedro L.D. Peres","doi":"10.1016/j.sysconle.2024.105833","DOIUrl":"https://doi.org/10.1016/j.sysconle.2024.105833","url":null,"abstract":"<div><p>This paper proposes an LMI-based algorithm to compute a stable (Hurwitz) convex combination of a set of (unstable) matrices as primary contribution. Using stability analysis conditions based on Finsler’s lemma and a simplicial partitioning of the unit simplex, a semidecidable procedure is provided. As immediate application, the problem of <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> state- and output-feedback control of continuous-time switched linear systems is addressed. Exploring the connection between stable convex combination and the Lyapunov–Metzler inequalities, the synthesis conditions are also formulated in terms of an LMI-based algorithm, which presents advantages when compared with the existing techniques for switching control. The technical novelty in this context is a new linearization strategy to deal with the product between matrix and scalar variables. Numerical experiments illustrate the quality of the achievements.</p></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141164330","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Control-theoretic methods for solving linear algebraic equations: A continuous-time perspective 解决线性代数方程的控制论方法：连续时间视角
IF 2.6 3区 计算机科学
Systems & Control Letters Pub Date : 2024-05-25 DOI: 10.1016/j.sysconle.2024.105822
Yuxin Wu, Deyuan Meng
{"title":"Control-theoretic methods for solving linear algebraic equations: A continuous-time perspective","authors":"Yuxin Wu,&nbsp;Deyuan Meng","doi":"10.1016/j.sysconle.2024.105822","DOIUrl":"https://doi.org/10.1016/j.sysconle.2024.105822","url":null,"abstract":"<div><p>In the applications of control theory, how to improve the solution methods of mathematical problems with some control methods is an attractive problem. This paper aims at exploiting a class of continuous-time solvers for linear algebraic equations (LAEs) via the incorporation of the idea of “control design”. The equivalence is established between the solving problem of LAEs and two basic control problems of continuous-time systems, namely, the output tracking problem and the state observation problem, in a unified manner. Then, the equivalence between the properties of LAEs and the controllability and observability properties of continuous-time systems are disclosed from the perspective of the output tracking and the state observation, respectively. Moreover, a continuous-time solver is developed based on the feedback control design such that all (least squares) solutions to any (un)solvable LAE can be determined by the selection of different initial conditions. Particularly, the design conditions to derive the best approximate solutions to LAEs are presented for the continuous-time solver.</p></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2024-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141097599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Statistical linearization for robust motion planning 稳健运动规划的统计线性化
IF 2.6 3区 计算机科学
Systems & Control Letters Pub Date : 2024-05-22 DOI: 10.1016/j.sysconle.2024.105825
Clara Leparoux , Riccardo Bonalli , Bruno Hérissé , Frédéric Jean
{"title":"Statistical linearization for robust motion planning","authors":"Clara Leparoux ,&nbsp;Riccardo Bonalli ,&nbsp;Bruno Hérissé ,&nbsp;Frédéric Jean","doi":"10.1016/j.sysconle.2024.105825","DOIUrl":"https://doi.org/10.1016/j.sysconle.2024.105825","url":null,"abstract":"<div><p>The goal of robust motion planning consists of designing open-loop controls which optimally steer a system to a specific target region while mitigating uncertainties and disturbances which affect the dynamics. Recently, stochastic optimal control has enabled particularly accurate formulations of the problem. Nevertheless, despite interesting progresses, these problem formulations still require expensive numerical computations. In this paper, we start bridging this gap by leveraging statistical linearization. Specifically, through statistical linearization we reformulate the robust motion planning problem as a simpler deterministic optimal control problem subject to additional constraints. We rigorously justify our method by providing estimates of the approximation error, as well as some controllability results for the new constrained deterministic formulation. Finally, we apply our method to the powered descent of a space vehicle, showcasing the consistency and efficiency of our approach through numerical experiments.</p></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141078626","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Two-stage stochastic optimal control problem under G-expectation G 期望下的两阶段随机优化控制问题
IF 2.6 3区 计算机科学
Systems & Control Letters Pub Date : 2024-05-18 DOI: 10.1016/j.sysconle.2024.105824
Zhuangzhuang Xing
{"title":"Two-stage stochastic optimal control problem under G-expectation","authors":"Zhuangzhuang Xing","doi":"10.1016/j.sysconle.2024.105824","DOIUrl":"https://doi.org/10.1016/j.sysconle.2024.105824","url":null,"abstract":"<div><p>This paper is dedicated to a kind of stochastic two-stage optimal control problem (TSOC) under <span><math><mi>G</mi></math></span>-expectation. The system’s state switches at a given time point and the cost function involves stages on two time horizons in order to achieve two-stage management. A motivation of Problem TSOC is presented. A novel sufficient optimality condition (SOCD) is given via a sequence of adjoint processes coupled by jump boundary conditions under a maximal reference probability, which is more concise and applicable compared to previous results. Analytical results in two-stage linear-quadratic (TSLQ) case are presented, where a feedback optimal control (OC) is designed and a maximal reference probability is determined. Moreover, some interesting impacts of probability uncertainty and additional cost term to Problem TSLQ are analyzed, which are meaningful to practical risk management. Numerical simulations are presented to illustrate our theoretical results.</p></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2024-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141067800","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Energy-shaping and entropy-assignment boundary control of the heat equation 热方程的能量塑造和熵分配边界控制
IF 2.6 3区 计算机科学
Systems & Control Letters Pub Date : 2024-05-17 DOI: 10.1016/j.sysconle.2024.105821
Luis A. Mora , Yann Le Gorrec , Hector Ramirez
{"title":"Energy-shaping and entropy-assignment boundary control of the heat equation","authors":"Luis A. Mora ,&nbsp;Yann Le Gorrec ,&nbsp;Hector Ramirez","doi":"10.1016/j.sysconle.2024.105821","DOIUrl":"https://doi.org/10.1016/j.sysconle.2024.105821","url":null,"abstract":"<div><p>This paper shows a finite-dimensional controller design for the boundary control of the heat equation on a 1D spatial domain. The controller exponentially stabilizes the plant at the desired equilibrium profile. The controller is defined using irreversible port-Hamiltonian systems formulation, and it is motivated by passivity-based control techniques developed for port-Hamiltonian systems defined on 1D spatial domains. The boundary controller is designed to have an exponentially stabilizing energy-shaping and entropy-assignment effect. It works with an actuation at one boundary and a reflective boundary condition at the other. The controller can handle situations where measurements are available at only one or both boundaries. The paper characterizes the existence of structural invariant functions to shape the closed-loop energy and assign the required closed-loop entropy. The design approach is illustrated through numerical simulations.</p></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141067799","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bias-policy iteration based optimal control for unknown continuous-time linear periodic systems 基于偏置策略迭代的未知连续时间线性周期系统优化控制
IF 2.6 3区 计算机科学
Systems & Control Letters Pub Date : 2024-05-11 DOI: 10.1016/j.sysconle.2024.105819
Xiang Li, Huaiyuan Jiang, Bin Zhou
{"title":"Bias-policy iteration based optimal control for unknown continuous-time linear periodic systems","authors":"Xiang Li,&nbsp;Huaiyuan Jiang,&nbsp;Bin Zhou","doi":"10.1016/j.sysconle.2024.105819","DOIUrl":"https://doi.org/10.1016/j.sysconle.2024.105819","url":null,"abstract":"<div><p>In this paper, the optimal control problem for unknown continuous-time linear periodic (CTLP) systems is investigated. A model-based bias-policy iteration algorithm for CTLP systems with its convergence proof is established firstly. Based on that, the data-driven implementation is proposed to approximate the optimal controller without the knowledge of system dynamics. Compared with the existing methods, the advantages of the proposed method are that, the initial stabilizing controller requirement is relaxed, and the approximate optimal controller can be obtained without solving nonlinear differential equations. The numerical simulation verifies the effectiveness of the proposed method.</p></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140914060","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Discretization of prescribed-time observers in the presence of noises and perturbations 存在噪音和扰动时规定时间观测器的离散化
IF 2.6 3区 计算机科学
Systems & Control Letters Pub Date : 2024-05-07 DOI: 10.1016/j.sysconle.2024.105820
Denis Efimov , Yury Orlov
{"title":"Discretization of prescribed-time observers in the presence of noises and perturbations","authors":"Denis Efimov ,&nbsp;Yury Orlov","doi":"10.1016/j.sysconle.2024.105820","DOIUrl":"https://doi.org/10.1016/j.sysconle.2024.105820","url":null,"abstract":"<div><p>An implicit Euler discretization scheme of the prescribed-time converging observer from Holloway and Krstic, (2019) is proposed, which preserves all main properties of the continuous-time counterpart, and it is investigated how to apply recursively this discretization on any interval of time. In addition, it is demonstrated that the estimation error is robustly stable with respect to the measurement noise with a linear gain (the property that does not hold in the continuous-time setting). The efficiency of the suggested discrete-time observer is illustrated through numeric experiments.</p></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140880365","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Optimal control problem with state constraints via penalty functions 通过惩罚函数实现状态约束的最优控制问题
IF 2.6 3区 计算机科学
Systems & Control Letters Pub Date : 2024-05-03 DOI: 10.1016/j.sysconle.2024.105816
M.d.R. de Pinho , M. Margarida A. Ferreira , Georgi Smirnov
{"title":"Optimal control problem with state constraints via penalty functions","authors":"M.d.R. de Pinho ,&nbsp;M. Margarida A. Ferreira ,&nbsp;Georgi Smirnov","doi":"10.1016/j.sysconle.2024.105816","DOIUrl":"https://doi.org/10.1016/j.sysconle.2024.105816","url":null,"abstract":"<div><p>In this paper, we derive necessary conditions of optimality for problems with state constraints using the method of penalty functions similar to the one we previously used to solve optimization problems for control sweeping processes (see, e.g., de Pinho et al., 2022). Our aim is to provide a proof of the Maximum Principle that can be easily followed by those with basic knowledge of classical optimal control and elementary functional analysis. We intentionally consider a smooth case and the simplest boundary conditions; we consider global minimum and assume that the set of trajectories of the control system is compact.</p></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140822359","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Small-disturbance input-to-state stability of perturbed gradient flows: Applications to LQR problem 扰动梯度流的小扰动输入到状态稳定性：LQR 问题的应用
IF 2.6 3区 计算机科学
Systems & Control Letters Pub Date : 2024-04-30 DOI: 10.1016/j.sysconle.2024.105804
Leilei Cui , Zhong-Ping Jiang , Eduardo D. Sontag
{"title":"Small-disturbance input-to-state stability of perturbed gradient flows: Applications to LQR problem","authors":"Leilei Cui ,&nbsp;Zhong-Ping Jiang ,&nbsp;Eduardo D. Sontag","doi":"10.1016/j.sysconle.2024.105804","DOIUrl":"https://doi.org/10.1016/j.sysconle.2024.105804","url":null,"abstract":"<div><p>This paper studies the effect of perturbations on the gradient flow of a general nonlinear programming problem, where the perturbation may arise from inaccurate gradient estimation in the setting of data-driven optimization. Under suitable conditions on the objective function, the perturbed gradient flow is shown to be small-disturbance input-to-state stable (ISS), which implies that, in the presence of a small-enough perturbation, the trajectories of the perturbed gradient flow must eventually enter a small neighborhood of the optimum. This work was motivated by the question of robustness of direct methods for the linear quadratic regulator problem, and specifically the analysis of the effect of perturbations caused by gradient estimation or round-off errors in policy optimization. We show small-disturbance ISS for three of the most common optimization algorithms: standard gradient flow, natural gradient flow, and Newton gradient flow.</p></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140816460","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Optimal stopping of conditional McKean–Vlasov jump diffusions 条件麦金-弗拉索夫跃迁扩散的最优停止
IF 2.6 3区 计算机科学
Systems & Control Letters Pub Date : 2024-04-30 DOI: 10.1016/j.sysconle.2024.105815
Nacira Agram , Bernt Øksendal
{"title":"Optimal stopping of conditional McKean–Vlasov jump diffusions","authors":"Nacira Agram ,&nbsp;Bernt Øksendal","doi":"10.1016/j.sysconle.2024.105815","DOIUrl":"https://doi.org/10.1016/j.sysconle.2024.105815","url":null,"abstract":"<div><p>The purpose of this paper is to study the optimal stopping problem of conditional McKean–Vlasov (mean-field) stochastic differential equations with jumps (conditional McKean–Vlasov jump diffusions, for short). We obtain sufficient variational inequalities for a function to be the value function of such a problem and for a stopping time to be optimal.</p><p>The key is that we combine the conditional McKean–Vlasov equation with the associated stochastic Fokker–Planck partial integro-differential equation for the conditional law of the state. This leads to a Markovian system which can be handled by using a version of a Dynkin formula.</p><p>Our verification result is illustrated by finding the optimal time to sell in a market with common noise and jumps.</p></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167691124001038/pdfft?md5=cb45a953274a8c87726064870e12fe80&pid=1-s2.0-S0167691124001038-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140816462","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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