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Functional interval estimation for continuous-time linear systems with time-invariant uncertainties

AUTOMATICA 2025年 172卷

作者： Ma, Youdao Wang, Zhenhua Meslem, Nacim Raissi, Tarek Harbin Inst Technol Dept Control Sci & Engn Harbin 150001 Peoples R China Univ Grenoble Alpes CNRS GIPSA Lab INP F-38000 Grenoble France Conservatoire Natl Arts & Metiers CNAM F-75141 Paris France

This paper investigates functional interval estimation for continuous-time linear systems subject to both time-varying and time-invariant uncertainties. Two novel methods are proposed based on peak-to-peak functional observer design and interval analysis. First, we present a splitting-based method that splits the estimation error dynamics into two subsystems to handle the time-invariant disturbances and provide accurate estimation results. Then, to further enhance the estimation accuracy, we present an augmentation-based method that considers the time invariance in both functional observer design and reliable interval estimation. The relationship between a state-of-art method and the proposed methods are analysed theoretically. Finally, simulation results are provided to demonstrate the performances of the proposed methods. (c) 2024 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

关键词： Functional interval estimation time invariance continuous-time linear systems Peak-to-peak performance index Interval analysis

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An Introduction to the Fractional continuous-time linear systems: The 21^st Century systems

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IEEE CIRCUITS AND systems MAGAZINE 2008年第3期8卷 19-26页

作者： Ortigueira, Manuel Duarte Univ Nova Lisboa Fac Ciencias & Tecnol P-1200 Lisbon Portugal

A brief introduction to the fractional continuous-time linear systems is presented. It will be done without needing a deep study of the fractional derivatives. We will show that the computation of the impulse and step responses is very similar to the classic. The main difference lies in the substitution of the exponential by the Mittag-Leffler function. We will present also the main formulae defining the fractional derivatives.

关键词： calculus continuous time systems linear systems step response transient response Mittag-Leffler function continuous-time linear systems fractional calculus impulse response TRANSIENT RESPONSE Step response continuous time systems IMPULSE RESPONSE Fractional calculus linear system

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Model-free distributed optimal control for continuous-time linear systems

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IET CONTROL THEORY AND APPLICATIONS 2022年第16期16卷 1685-1695页

作者： Feng, Xinjun Zhao, Zhiyun East China Univ Sci & Technol Dept Automat Shanghai Peoples R China

This paper studies the distributed optimal consensus problem for a group of continuous-time linear systems in the scenario that the dynamics of linear systems are completely unknown. Both an optimal state feedback control law and an optimal output feedback control law are constructed by solving the Algebraic Riccati Equation (ARE) that contains no global information, which guarantees the consensus of linear systems and the global optimality. Adaptive Dynamic Programming (ADP) method is presented to solve the ARE, thus the control algorithms are not relying on the dynamics of linear systems any more. Finally, numerical simulation results are presented to demonstrate the efficiency of proposed approach.

关键词： model-free distributed optimal control Riccati equations ARE linear systems optimal state feedback control law ADP method adaptive dynamic programming method dynamic programming global optimality continuous time systems algebraic Riccati equation optimal output feedback control law state feedback optimal control distributed optimal consensus problem continuous-time linear systems

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H-INFINITY GUARANTEED COST CONTROL FOR UNCERTAIN continuous-time linear-systems

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systems & CONTROL LETTERS 1993年第6期20卷 413-418页

作者： PERES, PLD GEROMEL, JC SOUZA, SR UNICAMP FAC ELECT ENGNLAC-DTBR-13081 CAMPINASSPBRAZIL

This paper deals with the H(infinity) guaranteed cost control problem for continuous-time uncertain systems. It consists of the determination of a stabilizing state feedback gain which imposes on all possible closed-loop models an H(infinity)-norm upper bound gamma > 0. Assuming that the uncertain domain is convex-bounded and the uncertain system is quadratic-stabilizable with gamma disturbance attenuation, it is shown how to determine, by means of a convex programming problem, the global minimum of gamma. As a particular and important case, for precisely known linear systems, the last problem reduces to the classical H(infinity) optimal control problem. The results follow from the definition of a special parameter space on which the above-mentioned problems are convex.

关键词： UNCERTAIN systems GUARANTEED COST CONTROL H-INFINITY OPTIMAL CONTROL continuous-time linear systems CONVEX PROGRAMMING

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H2 GUARANTEED COST CONTROL FOR UNCERTAIN continuous-time linear-systems

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systems & CONTROL LETTERS 1992年第1期19卷 23-27页

作者： GEROMEL, JC PERES, PLD SOUZA, SR UNIV CAMPINAS FAC ELECT ENGNLAC DTBR-13081 CAMPINASSPBRAZIL

This paper proposes a solution to the H-2 guaranteed cost control problem for uncertain, continuous-time linear systems. It consists of the determination of a constant state feedback stabilizing matrix gain and a H-2-norm upper bound, valid for all feasible models. The uncertainties are only assumed to be convex-bounded, a concept which generalizes the important case of interval matrices uncertainties. The results follow from a new parameterization of all stabilizing gains over a convex set. As an additional property, the above mentioned H-2-norm upper bound reduces to the minimum H-2 cost in case of precisely known linear systems.

关键词： UNCERTAIN systems QUADRATIC STABILIZABILITY H2 OPTIMAL CONTROL continuous-time linear systems CONVEX PROGRAMMING

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Necessary and sufficient condition for robust stability and stabilizability of continuous-time linear systems with Markovian jumps

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1998年第2期99卷 359-379页

作者： Costa, OLV Boukas, EK Univ Sao Paulo Sao Paulo Brazil Ecole Polytech Dept Mech Engn Montreal PQ H3C 3A7 Canada Gerad Montreal PQ Canada

In this paper, we investigate the quadratic stability and quadratic stabilizability of the class of continuous-time linear systems with Markovian jumps and norm-bound uncertainties in the parameters. Under some appropriate assumptions, a necessary and sufficient condition is established for mean-square quadratic stability and mean-square quadratic stabilizability of this class of systems. The quadratic guaranteed cost control problem is also addressed via a LMI optimization problem.

关键词： continuous-time linear systems parameter uncertainties Riccati equation linear systems with Markovian jumps

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Mean square stabilizability of continuous-time linear systems with partial information on the Markovian jumping parameters

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STOCHASTIC ANALYSIS AND APPLICATIONS 2004年第1期22卷 99-111页

作者： Fragoso, MD Costa, OLV CNPq LNCC Natl Lab Sci Comp BR-25651075 Rio De Janeiro Brazil Univ Sao Paulo Escola Politecn Dept Engn Eletron BR-05508 Sao Paulo SP Brazil

We provide necessary and sufficient conditions for mean square (MS) stabilizability of continuous-time linear systems with Markovian jumps in the parameters (LSMJP) subject to partial information on this jump variable. We assume that the Markovian jump parameter is not exactly known, but instead an estimate of it is available to the controller. Under some additional assumptions, a Solution via LMI (linear matrix inequality) is also provided. The results apply, in a unified basis, to the homogeneous case and two scenarios regarding additive disturbances: the one in which the system is driven by a Wiener process. and the one characterized by functions in L-2"'(R+), which is the usual scenario for the H-infinity approach. It is also shown that MS stabilizability is equivalent to L-2"-stabilizability whenever the disturbances are in L-2"'(R+).

关键词： mean square stabilizability jump parameter continuous-time linear systems partial information

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Functional Interval Estimation for continuous-time linear systems 22

Functional Interval Estimation for Continuous-Time Linear Sy...

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22nd World Congress of the International Federation of Automatic Control (IFAC)

作者： Ma, Youdao Wang, Zhenhua Meslem, Nacim Raissi, Tarek Luo, Hao Harbin Inst Technol Sch Astronaut Harbin 150001 Peoples R China Univ Grenoble Alpes CNRS GIPSA lab F-38000 Grenoble France Conservatoire Natl Arts & Metiers CNAM F-75141 Paris France

ISBN: (纸本)9781713872344

This paper presents a functional interval estimation method for continuous-time systems subject to disturbances and noise. First, a robust functional observer is synthesised to attenuate the effects of uncertainties. Then, based on interval analysis, an interval-based method is proposed to achieve tight functional interval estimation. The proposed method can provide accurate functional interval estimation results for continuous-time systems without using the stringent cooperativity condition and the traditionally required condition on the time derivative of the measurement noise. Simulation results are given to illustrate the effectiveness and superiority of the proposed method. Copyright (c) 2023 The Authors. This is an open access article under the CC BY-NC- ND license (https://***/licenses/by-nc-nd/4.0/)

关键词： Functional interval estimation continuous-time linear systems robust functional observer interval analysis

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Robust Static Output Feedback Stabilization of continuous-time linear systems via Enhanced LMI Conditions 21st

Robust Static Output Feedback Stabilization of Continuous-Ti...

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21st IFAC World Congress on Automatic Control - Meeting Societal Challenges

作者： Gritli, Hassene Zemouche, Ali Belghith, Safya Laleg-Kirati, Taous-Meriem Univ Carthage Higher Inst Informat & Commun Technol 1164 Borj Cedria Tunis Tunisia Univ Lorraine CRAN CNRS UMR 7039 F-4400 Cosnes Et Romain France Univ Tunis El Manar Lab Robot Informat & Complex Syst RISC Lab LR16ES Natl Engn Sch Tunis BP 37 Tunis 1002 Tunisia King Abdullah Univ Sci & Technol KAUST Math & Computat Sci & Engn Div Thuwal Saudi Arabia

This paper addresses the problem of Static Output Feedback (SOF) stabilization for continuous-time linear systems subject to norm-bounded parameter uncertainties. Usually this issue leads to the feasibility of a Bilinear Matrix Inequality (BMI), which is difficult to linearize to get non conservative linear matrix inequality (LMI) conditions. In this paper, by means of some technical lemmas, we transform the BMI into a new LMI with a line search over two scalar variables. The obtained LMI conditions are less conservative than those existing in the literature. Numerical evaluations are presented to show the superiority of the proposed method. Copyright (C) 2020 The Authors.

关键词： continuous-time linear systems Robust control Parametric uncertainty Static output feedback linear matrix inequality (LMI)

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Reliable Unknown Input Observer for continuous-time linear systems 11th

Reliable Unknown Input Observer for Continuous-Time Linear S...

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11th International-Federation-of-Automatic-Control (IFAC) Symposium on Fault Detection, Supervision and Safety for Technical Processes (SAFEPROCESS)

作者： Meslem, Nacim Hably, Ahmad Raissi, Tarek Wang, Zhenhua Univ Grenoble Alpes GIPSA Lab Grenoble INP CNRS F-38000 Grenoble France Conservatoire Natl Arts & Metiers 292 Rue St Martin F-75141 Paris France Harbin Inst Technol Dept Control Sci & Engn Harbin 150001 Peoples R China

This work proposes a set-valued extension of the classical unknown input observers for linear continuous-time systems without using set-by-step set-membership computations or imposing the positivity property of the dynamics of the estimation error. In fact, based on an explicit set-integration method of the estimation error, the framing and convergence properties of the proposed set-valued unknown input observer are demonstrated. Moreover, thanks to the proposed design approach, robust threshold on the residual can be established a priori. Simulation results are reported to highlight the effectiveness of the proposed state estimator in the presence of unknown inputs. Copyright (C) 2022 The Authors.

关键词： State estimation continuous-time linear systems unknown input observer interval observer set-membership estimation reachability analysis

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