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Algebraic Conditions for Accessibility of Discrete-Time nonlinear control systems

IEEE TRANSACTIONS ON AUTOMATIC control 2025年第4期70卷 2334-2345页

作者： Bartosiewicz, Zbigniew Kaldmae, Arvo Kotta, Ulle Wyrwas, Malgorzata Bialystok Tech Univ Fac Comp Sci PL-15351 Bialystok Poland Tallinn Univ Technol Dept Software Sci EE-19086 Tallinn Estonia

In the article, accessibility of an analytic discrete-time control system given by a set of difference equations is studied. Ideals of germs of analytic functions and modules of germs of one-forms, associated with the considered system and invariant with respect to shift operators defined by the state equations, are used to present sufficient and necessary conditions for accessibility. The conditions are given both in terms of germs of analytic functions and germs of one-forms.

关键词： Vectors Orbits nonlinear control systems Space vehicles nonlinear systems Difference equations Upper bound Polynomials Manifolds Ink Accessibility algebraic methods nonlinear discrete-time systems

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control Synthesis for Discrete-Time nonlinear control systems Under State and Input Constraints

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IEEE TRANSACTIONS ON AUTOMATIC control 2024年第12期69卷 8418-8432页

作者： Wu, Jenq-Lang Natl Taiwan Ocean Univ Dept Elect Engn Keelung 202 Taiwan

In this article, the control synthesis of discrete-time nonlinear control systems with state and input constraints is considered. Functional inequalities are used to express these restrictions. Based on the barrier method, an online nonconvex optimization problem is solved to obtain a feasible control signal at each time step. The convergence of the solution algorithm is demonstrated. Results for a special case in which the constraints are in quadratic forms are presented. The necessary conditions for regional stabilization are derived. We also discuss the issue of modifying constraints when the original state constraints are infeasible. For validation and comparison, a numerical example is provided.

关键词： control systems nonlinear control systems Optimization Trajectory Convergence Safety Numerical stability Barrier method control Lyapunov function (CLF) discrete-time systems input constraint nonlinear control systems state constraint

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On feedback linearization of multi-input nonlinear control systems via time scaling and prolongation

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EUROPEAN JOURNAL OF control 2024年 77卷

作者： Fetisov, Dmitry A. Bauman Moscow State Tech Univ 2-ya Baumanskaya Ul 5-1 Moscow 105005 Russia

Currently, there are no necessary and sufficient conditions for linearizability of multi -input nonlinear control systems of general form in a class of transformations that include not only state and input changes, but also time scaling. In the present paper, we show that the problem of feedback linearizing a multi -input nonlinear control system via time scaling can be solved by constructing the Pfaffian system .7 naturally associated with the control system, followed by eliminating the time differential from .7. We prove that the Pfaffian system I obtained in this way is diffeomorphic to an extended Goursat normal form if and only if the control system is feedback linearizable via time scaling. We also prove that if a control system is not feedback linearizable via time scaling, but there exist coordinates in which the Pfaffian system I becomes an extended Goursat normal form, then the control system can be feedback linearized via time scaling and prolongation. We show that either a one -fold or a total prolongation may be required in this case. We give an example of a two -input control system that is not flat but is feedback linearizable via time scaling and a total prolongation.

关键词： nonlinear control systems Feedback linearization Time scaling Extended Goursat normal form

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Output tracking control design with anti-disturbance rejection for modified repetitive nonlinear control systems

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INTERNATIONAL JOURNAL OF systems SCIENCE 2023年第16期54卷 2999-3012页

作者： Priyanka, S. Sakthivel, R. Karimi, H. R. Saat, S. Bharathiar Univ Dept Appl Math Coimbatore India Sungkyunkwan Univ Dept Math Suwon South Korea Politecn Milan Dept Mech Engn Milan Italy Univ Tekn Malaysia Melaka Fac Elect & Comp Engn Ctr Telecommun Res & Innovat Malacca Malaysia Bharathiar Univ Dept Appl Math Coimbatore 641046 India Sungkyunkwan Univ Dept Math Suwon 440746 South Korea

This paper intends to analyse the disturbance rejection and output tracking control for a class of nonlinear control systems with disturbances. In this connection, we present a method that combines a proportional-integral observer and nonlinear-equivalent-input-disturbance estimator for superior disturbance rejection performance. Specifically, the nonlinear-equivalent-input-disturbance estimator comprises of equivalent-input-disturbance estimator and nonlinear feedback term, which is employed to estimate and reject the disturbances from the nonlinear system. Notably, the proportional-integral loop in the proportional-integral observer reduces the estimation inaccuracy of the nonlinear-equivalent-input-disturbance. Then the estimated disturbance is intertwined into the repetitive control input to compensate it efficiently. In order to obtain the required results, the proposed control system is converted into a two-dimensional modified repetitive control system to describe the learning and control actions. In particular, the proposed controller enables to adjust the gains directly to improve the learning and control performance and as a result, the tracking accuracy increases. Using a general Lyapunov-Krasovskii functional, singular value decomposition technique and linear matrix inequalities approach, a design algorithm for establishing proportional-integral observer and feedback gains is developed for the system under consideration. Finally, simulation results are given to illustrate the developed method's validity and superiority.

关键词： nonlinear control systems modified repetitive tracking control disturbance rejection proportional-integral observer

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Design of Event-Triggered State-Constrained Stabilizing controllers for nonlinear control systems

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IEEE ACCESS 2022年 10卷 3659-3667页

作者： Jhang, Jia-Yao Wu, Jenq-Lang Yung, Chee-Fai Natl Taiwan Ocean Univ Dept Elect Engn Keelung 202301 Taiwan

This paper addresses the event-triggered stabilization problem for nonlinear control-affine systems under state constraints. First, a strong control Lyapunov barrier function (CLBF) method is applied for constructing continuous state-constrained stabilizing controllers. Additionally, sufficient conditions for the existence of strong CLBFs are derived. With the obtained state-constrained feedback laws, a new event-triggered policy is proposed for reducing the number of communication events without the input-to-state stability (ISS) assumption. It is proved that the Zeno behavior is excluded under this event-triggered policy, that is, the inter-execution times are lower bounded away from zero. Finally, two examples are included to illustrate the theoretical results.

关键词： nonlinear control systems control systems State feedback Safety nonlinear systems Lyapunov methods Output feedback control Lyapunov functions control Lyapunov barrier functions event-triggered state constraint state feedback nonlinear systems

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Implementation of the algorithm for constructing homogeneous approximations of nonlinear control systems

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MATHEMATICS OF control SIGNALS AND systems 2022年第4期34卷 883-907页

作者： Sklyar, Grigory Barkhayev, Pavel Ignatovich, Svetlana Rusakov, Viktor West Pomeranian Univ Technol Szczecin Fac Comp Sci & Informat Technol Zolnierska 49 PL-71210 Szczecin Poland Univ Szczecin Inst Math Wielkopolska 15 PL-70451 Szczecin Poland Norwegian Univ Sci & Technol Dept Math Sci Hogskoleringen 1 N-7491 Trondheim Norway Ukrainian Acad Sci B Verkin Inst Low Temp Phys & Engn Nauki Ave 47 UA-61103 Kharkiv Ukraine Kharkov Natl Univ Dept Appl Math Svobody Sq 4 UA-61022 Kharkiv Ukraine

We present a "calculator" for constructing a homogeneous approximation of nonlinear control systems, which is based on the algebraic approach developed by the authors in their previous papers. This approach mainly uses linear algebraic and combinatorial tools, so, it is perfectly adapted to computer realization. We describe the algorithm and discuss its capabilities and limitations. We present its implementation as a web application and show by example how this app works.

关键词： nonlinear control systems Homogeneous approximation nonlinear power moments Free algebra Algorithm for constructing an approximating system

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Performance-Oriented Fault Detection for nonlinear control systems via Data-Driven T-S Fuzzy Modeling Technique

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IEEE TRANSACTIONS ON FUZZY systems 2022年第1期30卷 133-146页

作者： Liu, Ruijie Yang, Ying Li, Linlin Han, Huayun Peking Univ Coll Engn Dept Mech & Engn Sci State Key Lab Turbulence & Complex Syst Beijing 100871 Peoples R China Univ Sci & Technol Beijing Sch Automat & Elect Engn Minist Educ Key Lab Knowledge Automat Ind Proc Beijing 100083 Peoples R China Beijing Univ Technol Fac Informat Technol Engn Res Ctr Digital Community Minist Educ Beijing 100124 Peoples R China

This article studies the performance-oriented fault detection (FD) for nonlinear control systems in the data-driven framework. Unlike the traditional residual- or test statistic-based FD methods, the proposed approach focuses on evaluating the system performance changes/degradations caused by the faults. Specifically, the regulation performance described by an infinite-time cost function is first introduced as a control performance index of the feedback system. Using only the process input and output (I/O) data, a Takagi-Sugeno fuzzy dynamic model is constructed with the aid of subspace identification method. Then, the internal system state variables are expressed in terms of the I/O data and a fuzzy cost function is proposed to approximate the performance index. On this basis, the temporal difference error induced by the Bellman equation is adopted as the process evaluation indicator, whose threshold is determined through the randomized algorithm. To demonstrate the effectiveness of the proposed FD approach, case studies are performed in the end on a ship propulsion system and a three-tank system.

关键词： nonlinear control systems Feedback control nonlinear systems Fault detection Cost function Performance analysis Data models nonlinear control systems performance-oriented fault detection (FD) randomized algorithm (RA) subspace identification method (SIM) Takagi-Sugeno (T-S) fuzzy dynamic modeling

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Invariant sets for a class of nonlinear control systems tractable by symbolic computation 22

Invariant sets for a class of nonlinear control systems trac...

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

作者： Harms, Melanie Schilli, Christian Zerz, Eva Rhein Westfal TH Aachen Lehrstuhl Algebra & Zahlentheorie Aachen Germany

ISBN: (纸本)9781713872344

A set S is said to be controlled invariant with respect to a control system if a state feedback law exists such that the closed loop system has S as an invariant set. In the present paper we generalise results on input-affine polynomial control systems and algebraic varieties (i.e. sets described by the zeros of polynomial equations) considered in Zerz and Walcher (2012) to an extended class of vector fields. More precisely, we consider vector fields of the form f = F-o h, where F is a polynomial vector and h is a continuously differentiable function with certain (algebraic) properties, as well as sets V-h as the preimages of varieties under h. We will see that for example polynomial expressions in sine and cosine satisfy the mentioned properties. The main advantage of the considered function class is that it is accessible to symbolic computation. We give computational methods (based on the theory of Grobner bases) to decide the controlled invariance of Vh.

关键词： nonlinear control systems Polynomial methods Structural properties Invariance State feedback Algebraic systems theory Symbolic computation

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Design of nonlinear predictive generalized minimum variance control for performance monitoring of nonlinear control systems

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JOURNAL OF PROCESS control 2021年 106卷 54-71页

作者： Sheikhi, Mohammad Amin Khaki-Sedigh, Ali Nikoofard, Amirhossein KN Toosi Univ Technol Fac Elect Engn Ind Control Ctr Excellence Adv Proc Automat & Control APAC Res Grp Tehran Iran

In this paper, a nonlinear predictive generalized minimum variance (NPGMV) controller is proposed and explicitly formulated for a class of nonlinear systems modeled by autoregressive second-order Volterra series, applying the polynomial approach. Hence, a new benchmark controller for performance assessment is introduced to improve the achievable control performance. Furthermore, to have an efficient control assessment, a data-driven algorithm based on the NPGMV control is presented that uses only the closed-loop operating data. In the design procedure, a multi-step cost function is defined to incorporate predictive action. Exploiting the predictive control concept enables the control scheme to handle constrained problems. Also, the proposed control algorithm utilizes an inherent integrating effect, which is essential for practical purposes. Volterra series are employed for modeling and identification of the nonlinear processes, using conventional least-squares methods. To show the effectiveness of the proposed methodology, simulation results and comparison studies are provided on a cascade Wiener model and a continuous stirred tank reactor (CSTR) chemical pilot plant. Finally, an experimental study on a pressure pilot plant is used to demonstrate the applicability of the proposed control scheme. The simulation and experimental results indicate satisfactory performance of the proposed controller. (C) 2021 Elsevier Ltd. All rights reserved.

关键词： Minimum variance control Predictive control control performance assessment nonlinear control systems Volterra model

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Robustness under control sampling of reachability in fixed time for nonlinear control systems

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MATHEMATICS OF control SIGNALS AND systems 2021年第3期33卷 515-551页

作者： Bourdin, Loic Trelat, Emmanuel Univ Limoges XLIM Res Inst F-87000 Limoges France Sorbonne Univ Lab Jacques Louis Lions F-75005 Paris France

Under a regularity assumption we prove that reachability in fixed time for nonlinear control systems is robust under control sampling.

关键词： nonlinear control systems Reachability Sampled-data controls Piecewise constant controls Regular controls

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