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Offline Robust Model Predictive Control Using linear matrix inequality-based Optimization

INTERNATIONAL JOURNAL OF CONTROL AUTOMATION AND SYSTEMS 2025年第2期23卷 655-663页

作者： Nam, Nguyen Ngoc Nguyen, Tam W. Han, Kyoungseok Kyungpook Natl Univ Sch Mech Engn Daegu 41566 South Korea Phenikaa Univ Fac Elect & Elect Engn Hanoi 12116 Vietnam Toyama Univ Dept Elect & Elect Engn Toyama 9308555 Japan Hanyang Univ Dept Automot Engn Seoul 04763 South Korea

This paper proposes a new approach to handle offline robust model predictive control (RMPC) using linear matrix inequality-based (LMI-based) optimization. To address system parameter uncertainties, we consider uncertain parameters within a polytope. A set of LMIs is then utilized to determine an optimal controller gain based on the polytope. The main contribution of this paper is establishing the upper bound of the cost function as a quadratic function of the state variable. It opens the opportunity to obtain the optimal controller gain in an offline environment, significantly reducing the computation burden. With this approach, robust stability of a closed-loop system can be achieved with a broad range of model uncertainties. Furthermore, the input and output constraints are enforced to ensure the system's operation in a specific range. To validate the efficacy of the proposed approach, our simulation results are provided and compared with the existing method.

关键词： linear matrix inequality model predictive control robust control

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linear matrix inequality approach for robust stability analysis for stochastic neural networks with time-varying delay

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Chinese Physics B 2011年第4期20卷 16-26页

作者： S.Lakshmanan P.Balasubramaniam Department of Mathematics Gandhigram Rural University

This paper studies the problem of linear matrix inequality （LMI） approach to robust stability analysis for stochastic neural networks with a time-varying delay. By developing a delay decomposition approach, the information of the delayed plant states can be taken into full consideration. Based on the new Lyapunov-Krasovskii functional, some inequality techniques and stochastic stability theory, new delay-dependent stability criteria are obtained in terms of LMIs. The proposed results prove the less conservatism, which are realized by choosing new Lyapunov matrices in the decomposed integral intervals. Finally, numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI method.

关键词： delay-dependent stability linear matrix inequality Lyapunov-Krasovskii functional stochastic neural networks

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linear matrix inequality approach for stability analysis of linear neutral systems in a critical case

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IET CONTROL THEORY AND APPLICATIONS 2010年第7期4卷 1290-1297页

作者： Quan, Q. Yang, D. Cai, K. -Y. Beijing Univ Aeronaut & Astronaut Natl Key Lab Sci & Technol Holist Control Dept Automat Control Beijing 100191 Peoples R China

This study mainly focuses on the stability of a class of linear neutral systems in a critical case, that is, the spectral radius of the principal neutral term (matrix H) is equal to 1. It is difficult to determine the stability of such systems by using existing methods. In this study, a sufficient stability criterion for the critical case is given in terms of the existence of solutions to a linear matrix inequality (LMI). Moreover, it is also shown that the proposed stability criterion conforms with a fact that the considered linear neutral systems are unstable when H has a Jordan block corresponding to the eigenvalue of modulus 1. An illustrative example is presented to determine the stability of a linear neutral system whose principal neutral term H has multiple eigenvalues of modulus 1 without Jordan chains. This is difficult in existing studies.

关键词： linear systems stability criterion linear neutral systems stability Stability in control theory principal neutral term Algebra delays stability analysis linear matrix inequality critical case Distributed parameter control systems linear matrix inequalities

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linear matrix inequality CONDITIONS AND DUALITY FOR A CLASS OF ROBUST MULTIOBJECTIVE CONVEX POLYNOMIAL PROGRAMS

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SIAM JOURNAL ON OPTIMIZATION 2018年第3期28卷 2466-2488页

作者： Thai Doan Chuong Saigon Univ Dept Math & Applicat Hochiminh City Vietnam

This paper is concerned with an uncertain multiobjective optimization problem, where the objective and constraint functions are sums-of-squares-convex (SOS-convex) polynomials, and the uncertainty sets are spectrahedra. Using a robust optimization approach, we first establish necessary and sufficient optimality conditions for weakly efficiencies of the corresponding robust multiobjective optimization problem. These optimality criteria are expressed in terms of sums-of-squares conditions and linear matrix inequalities, which provide a numerically checkable certificate of the solvability of the given optimality conditions. We then propose a dual multiobjective problem by means of sums-of-squares and linear matrix inequalities to the robust multiobjective SOS-convex polynomial optimization problem and examine weak, strong, and converse duality relations between them. In addition, we consider a semidefinite linear programming (SDP) weighted-sum relaxation problem for verifying weighted-sum efficient values of the primal problem.

关键词： multiobjective optimization duality robust optimization SOS-convex polynomial linear matrix inequality

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linear matrix inequality-based novel stability criteria of the primal-dual algorithm with heterogeneous communication delays

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IET CONTROL THEORY AND APPLICATIONS 2010年第3期4卷 461-471页

作者： Guo, S. Dang, C. Liao, X. Liu, D. Chongqing Univ Coll Comp Sci State Key Lab Power Transmiss Equipment & Syst Se Chongqing 400044 Peoples R China City Univ Hong Kong Dept Mfg Engn & Engn Management Hong Kong Hong Kong Peoples R China Chongqing Univ Coll Bioengn Chongqing 400044 Peoples R China

A fundamental and required property of congestion control algorithms in computer networks is stability. In this study, a class of appropriate Lyapunov functionals is proposed to investigate asymptotic stability in the second-order congestion control systems with heterogeneous communication delays. Novel linear matrix inequality-based delay-dependent stability criteria are given by exploiting free weighting matrices, which can overcome conservativeness of most methods involving a fixed model transformation. Simulation results show that the stability criteria proposed in this study are less conservative in the sense that larger range of control gains and communication delays can be accommodated.

关键词： primal-dual algorithm stability criteria Telecommunication applications heterogeneous communication delays Lyapunov functionals computer networks communication delays Algebra Lyapunov methods congestion control algorithms linear matrix inequality delay-dependent stability criteria linear matrix inequalities asymptotic stability telecommunication congestion control

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linear matrix inequality-based repetitive controller design for linear systems with time-varying input delay

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IET CONTROL THEORY AND APPLICATIONS 2010年第6期4卷 1071-1078页

作者： Chen, W. Chang, S. Zhang, W. Shanghai Jiao Tong Univ Dept Automat Shanghai 200240 Peoples R China Beijing Univ Aeronaut & Astronaut Dept Human Machine & Environm Engn Beijing 100083 Peoples R China

This style deals with the problem of delay-dependent stability criterion and repetitive controller design for linear systems with time-varying input delay. First, based on the existing literature, a rate-dependent state feedback controller is designed so that the closed-loop system is stabilised and the effect of disturbances is reduced to an ideal level. Second, by combining the state vectors of the stabilised system and repetitive controller, a delay-dependent stability criterion is derived in the form of linear matrix inequality (LMI) for the augmented system. Third, by reformulating the LMIs given in the stability criterion, the design problem of the repetitive controller is transformed to an optimisation problem subject to LMI constraints. Two simulation examples are provided to illustrate the validity of the proposed method.

关键词： Optimisation techniques optimisation problem time-varying systems repetitive controller design Time-varying control systems Stability in control theory control system synthesis linear matrix inequality Control system analysis and synthesis methods state feedback closed loop systems time-varying input delay linear systems stability criteria Algebra delays delay-dependent stability criterion linear matrix inequalities closed-loop system state feedback controller optimisation Distributed parameter control systems

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linear matrix inequality-based robust model predictive control for time-delayed systems

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IET CONTROL THEORY AND APPLICATIONS 2012年第1期6卷 37-50页

作者： Capron, B. D. O. Uchiyama, M. T. Odloak, D. Univ Sao Paulo Dept Chem Engn BR-05508900 Sao Paulo Brazil

This work addresses the solution to the problem of robust model predictive control (MPC) of systems with model uncertainty. The case of zone control of multi-variable stable systems with multiple time delays is considered. The usual approach of dealing with this kind of problem is through the inclusion of non-linear cost constraint in the control problem. The control action is then obtained at each sampling time as the solution to a non-linear programming (NLP) problem that for high-order systems can be computationally expensive. Here, the robust MPC problem is formulated as a linear matrix inequality problem that can be solved in real time with a fraction of the computer effort. The proposed approach is compared with the conventional robust MPC and tested through the simulation of a reactor system of the process industry.

关键词： time-delayed systems zone control Optimisation techniques Multivariable control systems robust model predictive control predictive control multivariable control systems high-order systems Stability in control theory linear matrix inequality robust MPC problem nonlinear cost constraint NLP problem robust control delays multivariable stable system nonlinear programming problem uncertain systems model uncertainty linear matrix inequalities Optimal control nonlinear programming multiple time delays Distributed parameter control systems

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linear matrix inequality versus Root-locus approach for damping inter-area oscillations in power systems

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2001年第6期23卷 481-489页

作者： Pal, BC Coonick, AH Cory, BJ Indian Inst Technol Dept Elect & Elect Engn Kanpur 208016 Uttar Pradesh India

This paper describes the merits of robust damping controllers designed using a linear matrix inequality (LMI) approach as compared to conventional Root-locus technique. The design in both methods aims at improving the damping of inter-area modes employing two small superconducting magnetic energy storage (SMES) devices. The LMI based control ensures adequate damping for widely varying system operating conditions and is compared with that obtained by the root-locus technique. It is shown that the LMI based approach has advantages over root-locus based control for the same control effort. (C) 2001 Elsevier Science Ltd. All rights reserved.

关键词： linear matrix inequality inter-area oscillation power system damping controller

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linear matrix inequality characterisation for H_∞ and H₂ guaranteed cost gain-scheduling quadratic stabilisation of linear time-varying polytopic systems

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IET CONTROL THEORY AND APPLICATIONS 2007年第6期1卷 1726-1735页

作者： Montagner, V. F. Oliveira, R. C. L. F. Peres, P. L. D. Bliman, P. -A. Univ Fed Santa Maria Elect & Control Res Grp BR-97105900 Santa Maria RS Brazil Univ Estadual Campinas Sch Elect & Comp Engn BR-13083970 Campinas SP Brazil Inst Natl Rech Informat & Automat F-78153 Le Chesnay France

Necessary and sufficient linear matrix inequality (LMI) conditions are provided to compute parameter-dependent state feedback control gains that ensure closed-loop quadratic stability for linear systems affected by arbitrarily fast time-varying parameters inside a polytope. The proposed conditions, based on an extension of Polya's theorem and on the systematic construction of homogeneous polynomial solutions for parameter-dependent LMIs, are written as a sequence of progressively less and less conservative LMI conditions. Necessity is attained as the level of relaxation increases, providing a parameter-dependent state feedback gain that quadratically stabilises the system whenever such a gain exists. Moreover, parameter-dependent gains of arbitrary degree assuring quadratic stability with H-infinity and H-2 guaranteed costs are also provided. The convergence to the minimum values of the attainable H-infinity and H-2 guaranteed costs under closed-loop quadratic stability occurs as the degree of the polynomially parameter-dependent gain increases. Numerical results illustrate the efficiency of the proposed conditions.

关键词： closed-loop quadratic stability linear systems stability linear matrix inequalities H linear time-varying polytopic system control time-varying systems parameter-dependent state feedback control closed loop systems linear matrix inequality state feedback cost gain-scheduling quadratic stabilisation

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linear matrix inequality-based observer design methods for a class of nonlinear systems with delayed output measurements

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART I-JOURNAL OF SYSTEMS AND CONTROL ENGINEERING 2023年第3期237卷 433-446页

作者： Nechaf, Hassiba Zemouche, Ali Mostefai, Mohammed Laleg-Kirati, Taous-Meriem Djeghali, Nadya Bedouhene, Fazia UMMTO Fac Elect & Comp Engn L2CSP Tizi Algeria Univ Lorraine CRAN CNRS UMR 7039 Cosnes Et Romain France Ferhat Abbes Set Univ 1 Elect Engn Dept Setif Algeria King Abdullah Univ Sci & Technol Elect Engn Dept Thuwal Saudi Arabia UMMTO Lab Math Pures & Appl LMPA Tizi Algeria Univ Lorraine CRAN CNRS UMR 7039 186 Rue Lorraine F-54400 Cosnes Et Romain France

This article deals with observer design for a class of nonlinear systems subject to delayed output measurements. Using an observer structure borrowed from Targui et al., we propose novel linear matrix inequality conditions ensuring the asymptotic convergence of the estimation error towards zero. We demonstrate analytically that the established linear matrix inequalities are less conservative than that of Targui et al., from a feasibility viewpoint, in the sense that they tolerate larger values of the upper bounds of the delay while guaranteeing the asymptotic convergence of the observer. Such linear matrix inequality conditions are obtained due to the use of a specific Lyapunov-Krasovskii functional, the Young inequality in a judicious way and a reformulation of the Lipschitz condition in a convenient way. We provide two illustrative examples to support the efficiency and superiority of the proposed linear matrix inequality-based techniques.

关键词： Lipschitz nonlinear systems delay systems Lyapunov-Krasovskii functional linear matrix inequality

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