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Infinite-dimensional sliding mode observer analysis for a disturbed linear reaction-convection-diffusion model

systems & CONTROL LETTERS 2023年第1期179卷

作者： Mohet, Judicael Hastir, Anthony Dimassi, Habib Winkin, Joseph J. Vande Wouwer, Alain Univ Namur Dept Math Rue Bruxelles 61 B-5000 Namur Belgium naXys Rue Bruxelles 61 B-5000 Namur Belgium Univ Sousse High Inst Appl Sci & technol Sousse Cite Taffala Ibn Khaldoun Sousse 4003 Tunisia Univ Mons Syst Estimat Control & Optimizat SECO B-7000 Mons Belgium

Significant improvements and a thorough complementary analysis are proposed for an infinitedimensional sliding mode state observer for a linear reaction-convection-diffusion system subject to bounded disturbances, that was analyzed in Dimassi et al. (2018). Compared to the previous article, the observer model features a simplified discontinuous input applied on the error dynamics such that the on-line computation of the state time derivative at the boundary is no longer needed. An abstract representation of the state observer is given, and a particular attention is paid to its well-posedness on a Sobolev space despite the discontinuity. The exponential stability of the error dynamics is established by considering one boundary measurement and a continuous approximation of the discontinuous input. The results are illustrated by means of numerical simulations. (c) 2023 Elsevier B.V. All rights reserved.

关键词： distributed parameter systems State observer Strongly continuous semigroup Sliding mode Sobolev space

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Predictor methods for finite-dimensional observer-based control of stochastic PDEs

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systems & CONTROL LETTERS 2023年 181卷

作者： Wang, Pengfei Fridman, Emilia Tel Aviv Univ Sch Elect Engn IL-6997801 Tel Aviv Israel

We study output-feedback control of 1D stochastic semilinear heat equations with nonlinear multiplicative noise and uncertain time-varying input/output delays or sawtooth delays (that correspond to network-based control), where the nonlinearities satisfy globally Lipschitz condition. We assume that the input delay has a large constant known part r. We consider Neumann actuation with non-local measurement. To compensate r, we consider a chain of M sub-predictors (conventional sub-predictors as in the deterministic case) and a novel chain of M+1 sub-predictors, respectively, both in the form of ODEs that correspond to the delay fraction r/M. For both cases, we construct Lyapunov functionals that depend on the deterministic and stochastic parts of the finite-dimensional part of the closed-loop systems, and employ the corresponding Ito's formulas for stochastic ODEs and PDEs, respectively. We provide the mean-square L2 exponential stability analysis of the full-order closed-loop system, leading to LMIs that are feasible for any r provided M and the observer dimension are large enough, and Lipschitz constants, as well as the upper bounds of unknown delays, are small enough. For the novel sub-predictors, we add an additional sub-predictor to the chain that leads to the closed-loop system with the stochastic infinite-dimensional tail and the stochastic finite-dimensional part where the delay fraction r/M and the stochastic term appear in separate equations, which essentially simplifies stochastic Lyapunov functional structure and the resulting LMIs. We also consider a classical observer-based predictor for linear heat equations with nonlinear multiplicative noise and show that the corresponding LMI stability conditions are feasible for any r provided the observer dimension is large enough, and the upper bounds of unknown delays and noise intensity are small enough. A numerical example demonstrates that for comparatively large M and upper bound of noise intensity, the intro

关键词： distributed parameter systems Stochastic systems Time-delay systems Predictor-based control

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Leader-Follower Synchronization and ISS Analysis for a Network of Boundary-Controlled Wave PDEs

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IEEE CONTROL systems LETTERS 2021年第2期5卷 683-688页

作者： Aguilar, Luis Orlov, Yury Pisano, Alessandro Inst Politecn Nacl Ctr Invest & Desarrollo Tecnol Digital Tijuana 22435 Mexico CICESE Res Ctr Elect & Telecommun Dept Ensenada 22860 Baja California Mexico Univ Cagliari Dept Elect & Elect Engn I-09123 Cagliari Italy

A network of agents, modeled by a class of wave PDEs, is under investigation. One agent in the network plays the role of a leader, and all the remaining "follower" agents are required to asymptotically track the state of the leader. Only boundary sensing of the agent's state is assumed, and each agent is controlled through the boundary by Neumann-type actuation. A linear interaction protocol is proposed and analyzed by means of a Lyapunov-based approach. A simple set of tuning rules, guaranteeing the exponential achievement of synchronization, is obtained. In addition, an exponential ISS relation, characterizing the effects on the tracking accuracy of boundary and in-domain disturbances, is derived for the closed loop system.

关键词： distributed control distributed parameter systems uncertain systems multi-agent systems

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Control of age-structured population dynamics with intraspecific competition in context of bioreactors?

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AUTOMATICA 2023年第1期152卷

作者： Kurth, Anna -Carina Sawodny, Oliver Univ Stuttgart Inst Syst Dynam Waldburgstr 17-19 D-70563 Stuttgart Germany

Bioreactors are used for commercial manufacturing of products or as a simplified representation of wastewater treatment plants. If it is taken into account that individual organisms from the population in the bioreactor behave differently, an additional structure such as age can be added to the population. This leads to a nonlinear, hyperbolic, integro-partial differential equation (IPDE) with non-local integral boundary conditions (BC) in the modeling. The steady-states of this system can be uniquely determined by a substitution due to the non-local BC. Using the asymptotic properties of the system, the IPDE is split into finite-dimensional dynamics and infinite dimensional internal dynamics. The internal dynamics are globally exponentially stable. Therefore, a feedforward control based on the finite dimensional dynamics is designed, augmented with a feedback control to compensate for the remaining influence of the internal dynamics on the output. Finally, the control concept is supplemented by an observer. Global exponential attractiveness of certain reference trajectories is proven. The overall control concept is validated experimentally with a bioreactor. A system parameter is identified and it is shown that by applying the control concept, the biomass can track various reference trajectories with small errors.(c) 2023 Elsevier Ltd. All rights reserved.

关键词： distributed parameter systems Biocybernetics Partial differential equations Exponentially stable

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Robust boundary tracking control of wave PDE: Insight on forcing slow-aseismic response

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systems & CONTROL LETTERS 2023年第1期178卷

作者： Gutierrez-Oribio, Diego Orlov, Yury Stefanou, Ioannis Plestan, Franck Nantes Univ Ecole Cent Nantes CNRS GeMUMR 6183 F-44000 Nantes France CICESE Res Ctr Ensenada 22860 Mexico Nantes Univ Ecole Cent Nantes CNRS LS2NUMR 6004 F-44000 Nantes France

The output boundary tracking problem is addressed for a wave partial differential equation (PDE) with uncertain multiplicative parameters and additive boundary and in-domain terms. To solve this problem, a homogeneous boundary feedback controller is designed using collocated boundary measurements only. Global exponential Input-to-State Stability (eISS) of the closed-loop system and its insensitivity to matched disturbances are additionally achieved. The ultimate bound estimate is diminished by tuning of the controller gains and/or by an appropriate pre-selection of a reference signal to follow. The proposed homogeneity-based strategy is further evaluated in a simplified earthquake model for controlled dissipation of its stored energy and producing slow-aseismic response. Such a case study possesses important applications in earthquake prevention, renewable energy production and storage. Numerical simulations are additionally conducted to support the robustness and the smoothness of the resulting closed-loop system depending on the homogeneous control parameter selection. & COPY;2023 Elsevier B.V. All rights reserved.

关键词： distributed parameter systems Boundary tracking Disturbance attenuation Sliding-mode control Earthquake prevention

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Synchronization Analysis of Networks of Linear Parabolic Partial Differential Equations

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IEEE CONTROL systems LETTERS 2021年第2期5卷 475-480页

作者： Xia, Tian Scardovi, Luca Univ Toronto Edward S Rogers Sr Dept Elect & Comp Engn Toronto ON M5S 3G4 Canada

It is known that synchronization of (identical) coupled finite-dimensional linear systems is characterized by the spectrum of the Laplacian matrix and stability properties of the isolated systems. This characterization, in general, fails for infinite-dimensional linear systems. This letter identifies a class of systems for which this characterization remains valid. As an illustration, the theoretical results are used to study synchronization of coupled heat equations.

关键词： Synchronization Mathematical model Linear systems Stability analysis Heating systems Couplings Hilbert space Network analysis and control linear systems distributed parameter systems

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Global stabilization of a 1D semilinear heat equation via modal decomposition and direct Lyapunov approach

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AUTOMATICA 2023年第1期149卷

作者： Katz, Rami Fridman, Emilia Tel Aviv Univ Sch Elect Engn Tel Aviv Israel

In this paper we consider state-feedback global stabilization of a semilinear 1D heat equation with a nonlinearity exhibiting a linear growth bound. We study both non-local and boundary control via a modal decomposition approach. For both cases, we suggest a direct Lyapunov method applied to the full-order closed-loop system. The nonlinear terms are compensated by using Parseval's inequality, leading to efficient and constructive linear matrix inequality (LMI) conditions for obtaining the controller dimension and gain. For non-local control we provide sufficient conditions that guarantee global stabilization for any linear growth bound via either linear or nonlinear controller, provided the number of actuators is large enough. We prove that the nonlinear controller achieves at least the same performance as the linear one. For the case of boundary control, we employ a multi-dimensional dynamic extension, whereas in the numerical example we manage with a larger linear growth bound. The introduced direct Lyapunov approach gives tools for a variety of robust control problems for semilinear parabolic PDEs.(c) 2022 Elsevier Ltd. All rights reserved.

关键词： distributed parameter systems Nonlinear systems Parabolic PDEs Global stabilization Lyapunov method

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Strict Dissipativity for LQ Problem with Left-invertible Underlying Semigroups

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IFAC-PapersOnLine 2023年第2期56卷 8946-8951页

作者： Roberto Guglielmi Zhuqing Li University of Waterloo Waterloo Canada

The paper analyzes the strict dissipativity property of generalized linear-quadratic infinite dimensional optimal control systems. For dynamics described by left-invertible semigroups, we first characterize exponential detectability of the system in terms of an analytic condition. Then, under a stabilizability assumption, we establish the equivalence between strict dissipativity and exponential detectability of the system.

关键词： distributed parameter systems dissipativity left-invertible semigroup exponential detectability linear-quadratic problem

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Approximate moving horizon estimation for switching conservative linear infinite-dimensional systems

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AUTOMATICA 2023年 158卷

作者： Xie, Junyao Humaloja, Jukka-Pekka Koch, Charles Robert Dubljevic, Stevan Univ Alberta Dept Chem & Mat Engn Edmonton AB T6G 2V4 Canada Univ Alberta Dept Mech Engn Edmonton AB T6G 2V4 Canada

This work addresses moving horizon estimation for switching conservative linear infinite-dimensional systems described by partial differential equations (PDE), where the plant and measurement equations are corrupted with bounded disturbances, and the system mode is regarded as an unknown and unpredictable discrete state to be estimated. To address the issues associated with unbounded opera-tors (induced by boundary or point observation and disturbance) and facilitate discrete-time moving horizon estimator design, the Cayley-Tustin transformation is deployed for model time-discretization without any spatial discretization or model reduction while preserving model essential properties. A series of observability concepts along with corresponding properties are proposed and analyzed for the switching linear infinite-dimensional discrete-time systems. A moving horizon estimation algorithm that accounts for state/output and mode estimation and constraint handling is proposed. Based on the proposed observability properties, we prove the stability of the proposed moving horizon estimator. The derived results are demonstrated by an undamped Schrodinger equation with switching group-velocity dispersion. (c) 2023 Elsevier Ltd. All rights reserved.

关键词： Infinite-dimensional systems distributed parameter systems Conservative linear systems Switching systems Observability Moving horizon estimation Cayley-Tustin transformation

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Stability Analysis of the Observer Error of an In-Domain Actuated Vibrating String

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IEEE CONTROL systems LETTERS 2021年第4期5卷 1237-1242页

作者： Malzer, Tobias Rams, Hubert Kolar, Bernd Schoberl, Markus Johannes Kepler Univ Linz Inst Automat Control & Control Syst Technol A-4040 Linz Austria B&R Ind Automat GmbH Dept Technol Software A-5142 Eggelsberg Austria

In this letter, the behaviour of the observer error of an in-domain actuated vibrating string, where the observer system has been designed based on energy considerations exploiting a port-Hamiltonian system representation for infinite-dimensional systems, is analysed. Thus, the observer-error dynamics are reformulated as an abstract Cauchy problem, which enables to draw conclusions regarding the well-posedness of the observer-error system. Furthermore, we show that the observer error is asymptotically stable by applying LaSalle's invariance principle.

关键词： Observers Asymptotic stability Boundary conditions Stability criteria Manifolds Actuators distributed parameter systems stability of linear systems observers for linear systems

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