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Sylvester's Matrix Equation in the Problem of the Direct Synthesis of Stabilizing Feedback of a linear discrete-time Stationary system Based on the Data on Its States

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JOURNAL OF COMPUTER AND systemS SCIENCES INTERNATIONAL 2024年第6期63卷 896-903页

作者： Perepelkin, E. A. St Petersburg State Univ Russia Aerosp Instrumenta St Petersburg 190000 Russia

This paper presents a solution of the problem of designing a stabilizing state feedback for a linear multivariable discrete-time stationary system based on the data of the system's behavior. It is assumed that the system's matrices are unknown. An algorithm for directly designing a feedback matrix based on the Sylvester matrix equation without solving the identification problem is considered. The conditions for the existence of a solution of the design problem are obtained. A numerical example is considered.

关键词： linear discrete-time system stabilizing state feedback data-driven design matrix Sylvester equation

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Robust Model Predictive Control for linear discrete-time system With Saturated Inputs and Randomly Occurring Uncertainties

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ASIAN JOURNAL OF CONTROL 2018年第1期20卷 425-436页

作者： Wang, Jianhua Song, Yan Zhang, Sunjie Liu, Shuai Dobaie, Abdullah M. Univ Shanghai Sci & Technol Key Lab Modern Opt Syst Dept Control Sci & Engn Shanghai 200093 Peoples R China Univ Shanghai Sci & Technol Business Sch Shanghai 200093 Peoples R China King Abdulaziz Univ Dept Elect & Comp Engn Fac Engn Jeddah 21589 Saudi Arabia

This paper investigates the robust model predictive control (RMPC) problem for a class of linear discrete-time systems subject to saturated inputs and randomly occurring uncertainties (ROUs). Due to limited bandwidth of the network channels, the networked transmission would inevitably lead to incomplete measurements and subsequently unavoidable network-induced phenomenon that include saturated inputs as a special case. The saturated inputs are assumed to be sector-bounded in the underlying system. In addition, the ROUs are taken into account to reflect the difficulties in precise system modelling, where the norm-bounded uncertainties are governed by certain uncorrelated Bernoulli-distributed white noise sequences with known conditional probabilities. Based on the invariant set theory, a sufficient condition is derived to guarantee the robust stability in the mean-square sense of the closed-loop system. By employing the convex optimization technique, the controller gain is obtained by solving an optimization problem with some inequality constraints. Finally, a simulation example is employed to demonstrate the effectiveness of the proposed RMPC scheme.

关键词： linear discrete-time system saturated inputs randomly occurring uncertainties robust model predictive control

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Data-based controllability analysis for generalised linear discrete-time system

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INTERNATIONAL JOURNAL OF systemS SCIENCE 2017年第10期48卷 2104-2110页

作者： Wang, Fengjun Zhang, Qingling Liu, Wanquan Northeastern Univ Inst Syst Sci Shenyang Peoples R China Northeastern Univ State Key Lab Synthet Automat Proc Ind Shenyang Peoples R China Curtin Univ Dept Comp Perth WA Australia

In this paper, we aim to propose a data-based method to testify whether the system is a normal linear system or a generalised linear system and then analyse its controllability via the measured state data and the control input satisfying certain condition. For this purpose, we first describe a linear discrete-time system in a general form and derive a necessary and sufficient condition for the equivalent condition of complete controllability with a normal linear discrete time system. Second, we check whether the system is normal or singular, and then construct the controllability matrices only based on the input and measured state data. Third, the controllability of the corresponding system is investigated thoroughly based on available data without identifying system parameters. Finally, a numerical example and a stock price example are used to show the effectiveness and feasibility of the proposed data-based method.

关键词： Data-based method linear discrete-time system generalised system unknown parameters controllability analysis

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STOCHASTIC OPTIMAL DESIGN FOR UNKNOWN linear discrete-time system ZERO-SUM GAMES IN INPUT-OUTPUT FORM UNDER COMMUNICATION CONSTRAINTS

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ASIAN JOURNAL OF CONTROL 2014年第5期16卷 1263-1276页

作者： Xu, Hao Jagannathan, S. Lewis, F. L. Missouri Univ Sci & Technol Dept Elect & Comp Engn Rolla MO 65401 USA Univ Texas Arlington Dept Elect Engn Arlington TX 76118 USA

In this paper, stochastic optimal strategy for unknown linear discrete-time system quadratic zero-sum games in input-output form with communication imperfections such as network-induced delays and packet losses, otherwise referred to as networked control system (NCS) zero-sum games, relating to the H optimal control problem is solved in a forward-in-time manner. First, the linear discrete-time zero sum state space representation is transformed into a linear NCS in the state space form after incorporating random delays and packet losses and then into the input-output form. Subsequently, the stochastic optimal approach, referred to as adaptive dynamic programming (ADP), is introduced which estimates the cost or value function to solve the infinite horizon optimal regulation of unknown linear NCS quadratic zero-sum games in the presence of communication imperfections. The optimal control and worst case disturbance inputs are derived based on the estimated value function in the absence of state measurements. An update law for tuning the unknown parameters of the value function estimator is derived and Lyapunov theory is used to show that all signals are asymptotically stable (AS) and that the estimated control and disturbance signals converge to optimal control and worst case disturbances, respectively. Simulation results are included to verify the theoretical claims.

关键词： linear discrete-time system networked control system adaptive estimation optimal adaptive strategy zero-sum games

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On the External Estimation of Reachable and Null-Controllable Limit Sets for linear discrete-time systems with a Summary Constraint on the Scalar Control

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AUTOMATION AND REMOTE CONTROL 2024年第4期85卷 321-340页

作者： Ibragimov, D. N. Natl Res Univ Moscow Aviat Inst Moscow Russia

The problem of constructing reachable and null-controllable sets for stationary linear discrete-time systems with a summary constraint on the scalar control is considered. For the case of quadratic constraints and a diagonalizable matrix of the system, these sets are built explicitly in the form of ellipsoids. In the general case, the limit reachable and null-controllable sets are represented as fixed points of a contraction mapping in the metric space of compact sets. On the basis of the method of simple iteration, a convergent procedure for constructing their external estimates with an indication of the a priori approximation error is proposed. Examples are given.

关键词： linear discrete-time system controllable limit set reachable limit set Hausdorff distance contraction mapping principle

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On the stability of delayed linear discrete-time systems with periodic coefficients

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JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS 2022年第11-12期28卷 1449-1457页

作者： Sadkane, Miloud Univ Brest Lab Math Bretagne Atlantique CNRS UMR 6205 6 Av Le Gorgeu F-29238 Brest 3 France

Stability estimates are obtained for delayed linear periodic discrete-time systems. Bounds on the decay of the solution are derived via a suitable Lyapunov-Krasovskii-type functional and the solvability of some period... 详细信息

关键词： linear discrete-time system periodic delay system periodic discrete-time Lyapunov equation decay rate

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Parity Space Vector Machine Approach to Robust Fault Detection for linear discrete-time systems

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IEEE TRANSACTIONS ON systemS MAN CYBERNETICS-systemS 2021年第7期51卷 4251-4261页

作者： Zhong, Maiying Xue, Ting Song, Yang Ding, Steven X. Ding, Eve L. Shandong Univ Sci & Technol Coll Elect Engn & Automat Qingdao 266590 Peoples R China Univ Duisburg Essen Inst Automat Control & Complex Syst D-47057 Duisburg Germany Beihang Univ Sch Instrumentat Sci & Optoelect Engn Beijing 100191 Peoples R China Univ Appl Sci Gelsenkirchen Dept Elect Engn & Appl Nat Sci D-45877 Gelsenkirchen Germany

In this paper, a novel robust fault detection (FD) approach called parity space vector machine (PSVM) is proposed for linear discrete-time systems. Aiming to achieve a tradeoff between false alarm rate (FAR) and FD rate (FDR) simultaneously, we focus our study on an integrated design of parity space-based FD in the context of residual generation and residual evaluation. Without a prior knowledge of the distribution of the unknown inputs, we propose to construct a PSVM model and formulate the underlying FD problem as a distribution-free Bayes optimal classifier, where the FAR and FDR indicate the worst-case classification accuracies of future residuals for the fault free case and faulty case. Then a bank of parity space vectors and corresponding thresholds can be designed integratedly by applying the techniques of the minimum error minimax probability machine and, at the same time, an optimal tradeoff between FAR and FDR is achieved. Finally, the effectiveness of the proposed approach is demonstrated on a longitudinal control system of unmanned aerial vehicle and further comparison with a traditional parity space-based FD is also addressed.

关键词： Integrated design Covariance matrices Support vector machines Fault detection discrete-time systems Aerospace electronics Probability distribution False alarm rate (FAR) fault detection rate (FDR) linear discrete-time system parity space vector machine (PSVM) robust fault detection

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Robust Stability Conditions for a Family of linear discrete-time systems Subjected to Uncertainties

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AUTOMATION AND REMOTE CONTROL 2021年第8期82卷 1456-1462页

作者： Khlebnikov, M., V Kvinto, Ya, I Russian Acad Sci Trapeznikov Inst Control Sci Moscow 117997 Russia

Robust stability conditions are established for a family of linear discrete-time systems subjected to uncertainties. The traditional approach, which involves the construction of a common quadratic Lyapunov function for the entire family of systems with uncertainty, often leads to the problem of conservatism. In this connection, constructing parametric quadratic Lyapunov functions seems promising. The main tools of the proposed approach are the apparatus of linear matrix inequalities and a modification, presented here, of the well-known Petersen's lemma. A simple approach to finding the robust quadratic stability radius of the family in question is proposed in the paper as well. The corresponding optimization problems have the form of semidefinite programming and one-dimensional minimization, which can be easily solved numerically. The efficiency of our approach is demonstrated via a numerical example. The results obtained can be generalized to design problems for linear discrete-time systems subjected to uncertainties, to other robust statements, and to the case of exogenous disturbances.

关键词： linear discrete-time system parametric Lyapunov function structured matrix uncertainty robustness linear matrix inequality

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Suppressing Exogenous Disturbances in a discrete-time Control system As an Optimization Problem

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AUTOMATION AND REMOTE CONTROL 2023年第10期84卷 1088-1097页

作者： Khlebnikov, M. V. Russian Acad Sci Trapeznikov Inst Control Sci Moscow Russia

This paper proposes a novel approach to suppressing bounded exogenous disturbances in a linear discrete-time control system by a static state- or output-feedback control law. The approach is based on reducing the original problem to a nonconvex matrix optimization problem with the gain matrix as one variable. The latter problem is solved by the gradient method;its convergence is theoretically justified for several important special cases. An example is provided to demonstrate the effectiveness of the iterative procedure proposed.

关键词： linear discrete-time system exogenous disturbances output feedback state feedback optimization gradient method Newton's method convergence

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Optimal Control of linear time-Invariant discrete-time systems without Prior Parametric Identification

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AUTOMATION AND REMOTE CONTROL 2022年第2期83卷 165-179页

作者： Dmitruk, N. M. Manzhulina, E. A. Belarusian State Univ Minsk 220030 BELARUS

We consider the problem of optimal control of a linear time-invariant discrete-time system by inaccurate measurements of its output signals subject to guaranteed satisfaction of geometric constraints on the output signals. We study the case in which a minimal realization of the system in the state space is known and the case where the parametric model of the system is not known. A novel method is proposed for solving the problem in the case of an unknown model. The method is based on a single observed trajectory of the input and output signals of the system and allows omitting the stage of parametric identification of the system.

关键词： optimal control linear discrete-time system inaccurate measurement unknown model data-driven control

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