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arXiv 2025年

作者： Stamouli, Charis Tsiamis, Anastasios Morari, Manfred Pappas, George J. University of Pennsylvania United States ETH Zürich Switzerland

Layered control architectures have been a standard paradigm for efficiently managing complex constrained systems. A typical architecture consists of: i) a higher layer, where a low-frequency planner controls a simple model of the system, and ii) a lower layer, where a high-frequency tracking controller guides a detailed model of the system toward the output of the higher-layer model. A fundamental problem in this layered architecture is the design of planners and tracking controllers that guarantee both higher- and lower-layer system constraints are satisfied. Toward addressing this problem, we introduce a principled approach for layered multirate control of linear systems subject to output and input constraints. Inspired by discrete-time simulation functions, we propose a streamlined control design that guarantees the lower-layer system tracks the output of the higher-layer system with computable precision. Using this design, we derive conditions and present a method for propagating the constraints of the lower-layer system to the higher-layer system. The propagated constraints are integrated into the design of an arbitrary planner that can handle higher-layer system constraints. Our framework ensures that the output constraints of the lower-layer system are satisfied at all high-level time steps, while respecting its input constraints at all low-level time steps. We apply our approach in a scenario of motion planning, highlighting its critical role in ensuring collision avoidance. Copyright © 2025, The Authors. All rights reserved.

关键词： linear control systems

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linear-quadratic control of Volterra integral systems and extensions

arXiv

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arXiv 2021年

作者： Belbas, S.A. Schmidt, W.H. Mathematics Department University of Alabama TuscaloosaAL35487-0350 United States Institut für Mathematik und Informatik Universität Greifswald Germany

We study linear-quadratic optimal control problems for Voterra systems, and Volterra optimal control problems that are linear-quadratic in the control but generally nonlinear in the state. In the case of linear-quadratic Volterra control, we obtain sharp necessary and sufficient conditions for optimality. For problems that are linear-quadratic in the control only, we obtain a novel form of necessary conditions in the form of double Volterra equations, for which we use the appellation "Riccati-Volterra equations";we prove the solvability of such equations, which are the Volterra integral counterpart of the so-called "state-dependent Riccati equations".MSC Codes 45D05, 49K21, 49N10 © 2021, CC BY-NC-ND.

关键词： linear control systems

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Non-fragile H∞ control for LPV-based CACC systems subject to denial-of-service attacks

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IET control THEORY AND APPLICATIONS 2021年第9期15卷 1246-1256页

作者： Huang, Cong Karimi, Hamid Reza Donghua Univ Sch Informat Sci & Technol Shanghai Peoples R China Minist Educ Engn Res Ctr Digitalized Text & Fash Technol Shanghai Peoples R China Politecn Milan Dept Mech Engn Via La Masa 1 I-20156 Milan Italy Nantong Univ Sch Transportat & Civil Engn Nantong Peoples R China

This paper is concerned with a non-fragile H infinity state feedback control issue for linear parameter-varying collaborative adaptive cruise control systems subject to denial-of-service attacks. The dynamics of the collaborative adaptive cruise control system is described by a linear model where the deviation of the position and the velocity are selected as the state variables. The attack model is utilized, thereby better reflecting the randomly occurring phenomenon of the denial-of-service attacks based on a sequence of binary random variables. The main objective of this note is to develop a non-fragile state feedback control scheme such that, for denial-of-service attacks and possible parameter variations in controller gains, the exponential mean-square stability and the predefined performance index for the system states are guaranteed simultaneously. By using the matrix analysis techniques and Lyapunov stability theory, sufficient conditions for the desired controller are established and solved based on the solutions to the linear matrix inequality conditions. Finally, a three-car model is provided to check the feasibility of the designed control scheme.

关键词： Velocity, acceleration and rotation control Interpolation and function approximation (numerical analysis) Algebra Other topics in statistics linear control systems control system analysis and synthesis methods Stability in control theory Optimal control Self-adjusting control systems Nonlinear control systems

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Transfer property and separate principle of finite time observers in linear control systems

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Journal of Chemical and Pharmaceutical Research 2014年第7期6卷 700-707页

作者： Shu-Fan, Wang Yong, Wen Changchun Institute of Technology China

A parametric design problem of the finite time observers for the linear time-invariant systems and some important properties of finite time observers are investigated in this paper. Based on the parametric solutions for a class of Sylvester matrix equations, the parametric expressions of all the gain matrices for the finite time observers are proposed. Based on the above design results of finite time observers, the corresponding transfer property and separate principle for the finite time observers are proved, respectively. Finally, a numerical example shows the effectiveness of the proposed design method, the transfer property and the separate principle of the parametric finite time observers in the linear time-invariant systems. © 2014, Journal of Chemical and Pharmaceutical Research. All rights reserved.

关键词： linear control systems

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Guaranteed cost stabilization control of discrete-time switched systems

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IET control THEORY AND APPLICATIONS 2021年第3期15卷 404-415页

作者： Du, Shengli Zhao, Xudong Qiao, Junfei Zong, Guangdeng Beijing Univ Technol Coll Automat Fac Informat Technol Beijing 100124 Peoples R China Dalian Univ Technol Sch Control Sci & Engn Dalian Peoples R China Qufu Normal Univ Sch Engn Rizhao Peoples R China

This paper is concerned with the guaranteed cost control problem of a class of linear discrete-time switched systems with parametric uncertainties. Both state-based and dynamic output-based robust stabilization problems are investigated by using mode-dependent dwell time technique. Different from the existing results, here, the designed controllers are both mode-dependent and quasi-time-dependent, which are less conservative. On the basis of the designed quasi-time-dependent Lyapunov functions, robust stabilization criteria are presented for the system under consideration. The solvable conditions are formulated as linear matrix inequalities, which are thus easy to be solved. Some comparative simulations are given to show the effectiveness of the proposed method.

关键词： Algebra linear control systems control system analysis and synthesis methods Stability in control theory Discrete control systems Time-varying control systems Nonlinear control systems

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Finite-time dissipative control for time-delay Markov jump systems with conic-type non-linearities under guaranteed cost controller and quantiser

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IET control THEORY AND APPLICATIONS 2021年第4期15卷 489-498页

作者： Zhang, Xiang Yin, Yanyan Wang, Hai He, Shuping Anhui Univ Sch Elect Engn & Automat Key Lab Intelligent Comp & Signal Proc Minist Educ Hefei Peoples R China Curtin Univ Sch Elect Engn Comp & Math Sci Perth WA Australia Murdoch Univ Discipline Engn & Energy Murdoch WA Australia

For a class of conic-type non-linear time-delay Markov jump systems, the asynchronous dissipative output feedback controller based on the guaranteed cost control and quantiser is designed in this study. In real applications, the system and the controller modes are always non-synchronous, so we introduce the hidden Markov model to solve this problem. Furthermore, we define three novel auxiliary variables and use quantisers to accomplish the output feedback controller design. Then, the finite-time boundedness and strict dissipativity of the closed-loop systems are guaranteed by sufficient conditions, and the controller also meets the guaranteed cost-control performance. By solving a set of linear matrix inequalities, we get the controller gains, the guaranteed cost control performance index J*, and the dissipative performance index alpha. Finally, the correctness and feasibility of this designed approach are demonstrated by a given example.

关键词： Algebra Markov processes linear control systems control system analysis and synthesis methods Stability in control theory Optimal control Discrete control systems Nonlinear control systems

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Quantised control of delayed Markovian jump systems with partly known transition probabilities

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IET control THEORY AND APPLICATIONS 2021年第3期15卷 372-389页

作者： Yang, Ning Chen, Dongyan Hu, Jun Harbin Univ Sci & Technol Dept Math Harbin 150080 Peoples R China Univ South Wales Sch Engn Pontypridd M Glam Wales

This paper is devoted to solve the quantised control problem of the continuous-time uncertain Markovian jump systems with mixed time delays and partly known transition probabilities. For the Markov chain, the transition rates are assumed to be partly known. The involved mixed time delays comprise both time-varying delays and distributed delays. The logarithmic quantiser is introduced in the design of the state feedback controller and the uncertainty is entered into the quantization error matrix represented by an interval matrix. Based on the generalised Ito's formula, the free-connection weighting matrix method and the stochastic analysis theory, several novel sufficient conditions are derived to guarantee that the trivial solution of the closed-loop system is robustly exponentially stable in the mean square. Then, the concrete expression form of the desired controller gain is obtained via the solutions to a set of linear matrix inequalities. In addition, the corresponding stability criteria are given for three special situations of Markovian jump systems. Finally, a numerical example and a practical example (the wheeled mobile manipulator) are provided to show the feasibility and availability of the proposed theoretical results.

关键词： Algebra Markov processes Other topics in statistics linear control systems control system analysis and synthesis methods Stability in control theory Discrete control systems Time-varying control systems Distributed parameter control systems

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Finite-Horizon controllability and Reachability for Deterministic and Stochastic linear control systems with Convex Constraints

Finite-Horizon Controllability and Reachability for Determin...

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American control Conference

作者： Daniel Dueri Behcet Acikmese Morgan Baldwin Richard S. Erwin Department of Aerospace Engineering and Engineering Mechanics University of Texas Austin TX 78712-1221 USA Air Force Research Laboratory Kirtland Air Force Base Albuquerque NM 87117 USA

ISBN: (纸本)9781479932757

This paper presents a method for rapidly generating controllability and reachability sets for constrained finite horizon linear Time Varying (LTV) control systems by using convex optimization techniques. Set generation is accomplished by first solving a Semi-Definite Programming (SDP) problem and then solving a series of Second Order Cone Programming (SOCP) problems. Recent advances in convex optimization solvers have made it possible to find the solutions to these problems very quickly. From a geometric stand-point, we first find the largest volume symmetric simplex that fits within the constrained control problem, then grow new simplices out of the faces of the original simplex. This process is repeated until the growing polytope converges to the constraint boundaries of the actual set. Additionally, a method for incorporating stochastic constraints and uncertainties into the deterministic framework is developed by posing the stochastic constraints as chance-constrained constraints. Finally, the controllability set for a two-vehicle Low Earth Orbit (LEO) rendezvous problem with stochastic uncertainties is generated using the new algorithm.

关键词： Accessibility controllability deterministic control systems Stochastic linear control systems Constraint random uncertainty Simplex

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Distributed static output feedback control for interconnected systems in finite-frequency domain

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IET control THEORY AND APPLICATIONS 2021年第8期15卷 1068-1081页

作者： Chen, Xuefeng Xu, Huiling Wang, Hui Nanjing Univ Sci & Technol Sch Sci Nanjing 210094 Jiangsu Peoples R China

This paper aims at designing a distributed static output feedback (DSOF) controller for the interconnected system in finite-frequency domain. Motivated by the fact that the signal transmitting process is usually affected by surrounding environments, the interconnection communication between subsystems are assumed to be non-ideal. By introducing some dilated multipliers into the extended condition that guarantees the well-posedness, stability and finite-frequency H infinity performance of non-ideally interconnected systems, a new equivalent condition is derived, which is more effective for parameterizing the DSOF controller. A two-stage approach is then developed for constructing a DSOF controller: design an initial distributed full information (DFI) controller first and then derive a desired DSOF from the DFI controller. Moreover, two iterative linear matrix inequality based algorithms are proposed to improve the solvability of the DFI controller and DSOF controller design problems. Finally, an example is given to show the effectiveness of the proposed two-stage DSOF controller design method.

关键词： Interpolation and function approximation (numerical analysis) Algebra linear control systems control system analysis and synthesis methods Stability in control theory Multivariable control systems

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Predefined formation-containment control of high-order multi-agent systems under communication delays and switching topologies

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IET control THEORY AND APPLICATIONS 2021年第12期15卷 1661-1672页

作者： Zhou, Shiyu Dong, Xiwang Hua, Yongzhao Yu, Jianglong Ren, Zhang Beihang Univ Sch Automat Sci & Elect Engn 37Xueyuan Rd Beijing 100191 Peoples R China Chongqing Univ Key Lab Dependable Serv Comp Cyber Phys Soc Chongqing Peoples R China Beihang Univ Inst Artificial Intelligence Beijing Peoples R China

This paper concerns the problem of formation-containment control for general-linear multi-agent systems (MASs) with both communication delays and switching interaction topologies. On the one hand, the leaders can communicate with each other to form the desired formation and on the other, the followers need to enter the convex envelope spanned by the multiple leaders. Firstly, by using the neighbouring relative information, formation-containment protocols are designed for each leader and follower, where an edge-based state observer is incorporated into the formation-containment controller to evaluate the whole leaders' state. Secondly, according to the linear matrix inequality technology, an algorithm is given to determine the unknown feedback matrixes in the protocol. Then, based on Lyapunov theory, the formation-containment error is proved to be convergent and formation feasibility conditions are also presented for the MASs to achieve formation-containment. Finally, a simulation on several MASs is provided to demonstrate the theoretical results.

关键词： Algebra Combinatorial mathematics linear control systems control system analysis and synthesis methods Stability in control theory Multivariable control systems Time-varying control systems

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