Event-driven observer-based control for distributed parameter systems using mobile sensor and actuator

This paper concerns a second-order P-type iterative learning control (ILC) scheme for a class of fractional order linear distributed parameter systems. First, by analyzing of the control and learning processes, a discrete system for P-type ILC is established and the ILC design problem is then converted to a stability problem for such a discrete system. Next, a sufficient condition for the convergence of the control input and the tracking errors is obtained by using generalized Gronwall inequality, which is less conservative than the existing one. By incorporating the convergent condition obtained into the original system, the ILC scheme is derived. Finally, the validity of the proposed method is verified by a numerical example.

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“…where > 0, Π is the same as in Lemma 7, then for all (x, t) ∈ Ω × [0, T], the second-order P-type ILC updating law (9) guarantees that…”

Section: Lemma 8 Denote Thatmentioning

confidence: 99%

Iterative Learning Control for a Class of Fractional Order Distributed Parameter Systems

Lan

Liu

Luo

2018

Asian Journal of Control

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“…Distributed parameter systems are a class of complicated infinite-dimensional systems, whose states depend on both spatial position and time [8][9][10][11]. In recent years, the application of ILC to distributed parameter systems has become a new topic [12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

ILC with Initial State Learning for Fractional Order Linear Distributed Parameter Systems

Lan

Cui

2018

Algorithms

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This paper presents a second order P-type iterative learning control (ILC) scheme with initial state learning for a class of fractional order linear distributed parameter systems. First, by analyzing the control and learning processes, a discrete system for P-type ILC is established, and the ILC design problem is then converted to a stability problem for such a discrete system. Next, a sufficient condition for the convergence of the control input and the tracking errors is obtained by introducing a new norm and using the generalized Gronwall inequality, which is less conservative than the existing one. Finally, the validity of the proposed method is verified by a numerical example.

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“…The derivation of the adaptive control scheme does not require the knowledge of a Lyapunov functional for the parabolic PDE.It should be noted that the closed-loop system under the proposed adaptive control scheme is a hybrid infinite-dimensional system. The study of hybrid (event-triggered) distributed-parameter systems has attracted the interest of many researchers during the last decade: see the works [13,30] for parabolic PDEs, the works [14,15,24,29] for hyperbolic PDEs and the works [16,26] for abstract infinite-dimensional systems.The structure of the present work is as follows: Section 2 describes the adaptive boundary control scheme in detail and explains the intuitive ideas behind the event-trigger and the regulation-based, least-squares identifier. The main result (Theorem 2.2) is stated in Section 2 and its consequences are discussed in detail.…”

mentioning

confidence: 99%

“…It should be noted that the closed-loop system under the proposed adaptive control scheme is a hybrid infinite-dimensional system. The study of hybrid (event-triggered) distributed-parameter systems has attracted the interest of many researchers during the last decade: see the works [13,30] for parabolic PDEs, the works [14,15,24,29] for hyperbolic PDEs and the works [16,26] for abstract infinite-dimensional systems.…”

mentioning

confidence: 99%

Adaptive boundary control of constant-parameter reaction–diffusion PDEs using regulation-triggered finite-time identification

2019

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For parabolic PDEs, we present a new certainty equivalence-based adaptive boundary control scheme with a least-squares identifier of an event-triggering type, where the triggering is based on the size of the regulation error (as opposed to the identifier updates being triggered by the estimation error, or the control changes being triggered by the regulation error). The scheme guarantees exponential convergence of the state to zero in the 2 L norm and a finite-time convergence of the parameter estimates to the true values of the unknown parameters. The scheme is developed for a specific benchmark problem with Dirichlet actuation, where the only unknown parameters are the reaction coefficient and the high-frequency gain. For this specific problem, no existing adaptive scheme can handle the unknown high-frequency gain. An illustrative example allows the comparison with other adaptive control design methodologies.Keywords: parabolic PDEs, boundary feedback, backstepping, adaptive control. Recently, the scope of adaptive controllers has been extended to more complicated cases: parabolic PDEs with input delays (see [11]) and parabolic PDEs with distributed parameters and inputs (see [27]). Moreover, adaptive controllers have been used extensively for hyperbolic PDEs: see [1][2][3][4][5][6][7][8][9][10]20].The purpose of the present work is the development of a novel adaptive boundary control scheme for parabolic PDEs. The proposed methodology is based on the extension to the parabolic infinite-2 dimensional case of the recently proposed adaptive control scheme in [17] for finite-dimensional systems. It is a certainty-equivalence adaptive scheme with a least-squares, regulation-based identifier. The proposed adaptive boundary control scheme guarantees exponential convergence of the state to zero in the 2 L norm. Moreover, the scheme guarantees a finite-time convergence of the parameter estimates to the true values of the unknown parameters. The adaptive scheme is developed for a specific benchmark problem with Dirichlet actuation, where the only unknown parameters are the reaction coefficient and the high-frequency gain. For this specific problem, no other adaptive scheme can handle the unknown high-frequency gain. It should be noticed that the proposed adaptive design can be extended to more complicated cases as well as to systems of parabolic PDEs.An advantage of the certainty-equivalence adaptive boundary control scheme with regulationbased, least-squares identifier is that it can be combined with all methodologies of static boundary feedback design for parabolic PDEs. More specifically, the proposed scheme can be combined with: i) the backstepping design (see [22,31]), and ii) the reduced model design (see [12,25]). The derivation of the adaptive control scheme does not require the knowledge of a Lyapunov functional for the parabolic PDE.It should be noted that the closed-loop system under the proposed adaptive control scheme is a hybrid infinite-dimensional system. The study of hybrid (event-triggered) distributed...

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Event-driven observer-based control for distributed parameter systems using mobile sensor and actuator

Cited by 38 publications

References 31 publications

Iterative Learning Control for a Class of Fractional Order Distributed Parameter Systems

Iterative Learning Control for a Class of Fractional Order Distributed Parameter Systems

ILC with Initial State Learning for Fractional Order Linear Distributed Parameter Systems

Adaptive boundary control of constant-parameter reaction–diffusion PDEs using regulation-triggered finite-time identification

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