In this manuscript, we address discrete-time state and error feedback output regulator designs for a class of linear distributed parameter systems (DPS) with bounded input and output operators. By utilising the Cayley...
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In this manuscript, we address discrete-time state and error feedback output regulator designs for a class of linear distributed parameter systems (DPS) with bounded input and output operators. By utilising the Cayley-Tustin bilinear transform, a linear infinite-dimensional discrete-time system is obtained without model spatial approximation or model order reduction. Based on the internal model principle, discrete state and error feedback regulators are designed. In particular, discrete Sylvester regulator equations are formulated, and their solvability is proved and linked to the continuous counterparts. To ensure the stability of the closed-loop system, the design of stabilising feedback gain and its dual problem of stabilising output injection gain design are provided in the discrete-time setting. Finally, three simulation examples including a first-order hyperbolic partial differential equation model and a 1-D heat equation with considerations of step-like, ramp-like and harmonic exogenous signals are shown to demonstrate the effectiveness of the proposed method.
In this article, we address the constrained output estimation of discrete-time linear distributed parameter systems in the presence of plant and measurement disturbances. Sufficient conditions are proposed for the str...
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In this article, we address the constrained output estimation of discrete-time linear distributed parameter systems in the presence of plant and measurement disturbances. Sufficient conditions are proposed for the strong stability of the proposed moving horizon estimator. We further show that the discrete-time estimation results can be linked to continuous-time infinite-dimensional systems described by partial differential equations with unbounded disturbance and output operators by using the Cayley-Tustin transformation. The theoretical results are illustrated with numerical examples on a 1-D wave equation and a 1-D diffusion equation.
In this paper we propose definitions for strong stabilizability and strong detectability of infinite-dimensional control systems. We show that these definitions are appropriate by showing that they can be used to give...
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In this paper we propose definitions for strong stabilizability and strong detectability of infinite-dimensional control systems. We show that these definitions are appropriate by showing that they can be used to give necessary and sufficient conditions for the strong stability of a system in terms of its input-output stability. As an application, we discuss the strong stability of the feedback interconnection of two strongly stabilizable and strongly detectable systems. (C) 1999 Elsevier Science B.V. All rights reserved.
In this paper, we consider the unknown trajectory tracking problem for stable distributed parameter systems. The main assumptions are that trajectory signals are generated by an unknown finite-dimensional exosystem th...
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In this paper, we consider the unknown trajectory tracking problem for stable distributed parameter systems. The main assumptions are that trajectory signals are generated by an unknown finite-dimensional exosystem that is a marginally stable system and the tracking error is available for measurement. In order to achieve perfect error regulation, a frequency estimator scheme is proposed to estimate unknown exosystem parameters, and the control law that is designed based on geometric output regulation theory is revisited. The success of the proposed method is demonstrated on a parabolic heat equation and a first-order hyperbolic partial differential equation.
In this note, the use of linear time-invariant distributed parameter systems (LTIDPS) as models of physical processes is considered from a control viewpoint. Specifically, classes of LTIDPS exhibiting properties which...
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In this note, the use of linear time-invariant distributed parameter systems (LTIDPS) as models of physical processes is considered from a control viewpoint. Specifically, classes of LTIDPS exhibiting properties which potentially limit their usefulness in feedback design are defined and termed ill-posed. The structure of these classes is investigated within a general mathematical framework which encompasses many distributed parameter systems of engineering interest. Within this framework necessary and sufficient conditions are derived which completely characterize these classes and establish their equivalence.
We give conditions on a controlled, observed distributedparameter system under which external stability, also known as input-output stability, implies internal stability, which is the exponential stability of the und...
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We give conditions on a controlled, observed distributedparameter system under which external stability, also known as input-output stability, implies internal stability, which is the exponential stability of the underlying semigroup generator. We show that when the system satisfies a general definition of stabilizability and detectability, external stability is equivalent to internal stability. Unlike previous definitions of stabilizability and detectability, a system which satisfies these does not necessarily have a spectrum decomposition. Therefore, in order to check internal stability, it is often sufficient to check the boundedness of the transfer function in the right-half complex plane. We illustrate this with a simple example.
The aim of this paper is to apply an algebraic test such as the Routh algorithm, Hurwitz determinant, or any similar method to a certain class of distributed parameter systems with multiple delays. As a first step, an...
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The aim of this paper is to apply an algebraic test such as the Routh algorithm, Hurwitz determinant, or any similar method to a certain class of distributed parameter systems with multiple delays. As a first step, an auxiliary system is generated, and then two auxiliary polynomials are formed by using only the coefficients of the characteristic equation of the auxiliary system. The input-output stability of the original system is determined on the basis of the zero distribution of two auxiliary polynomials. An illustrative example is included.
In this note, various connections are established between linear time-invariant distributedparameter continuous-time systems and their zero-order hold discrete-time equivalents. These connections are established in b...
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In this note, various connections are established between linear time-invariant distributedparameter continuous-time systems and their zero-order hold discrete-time equivalents. These connections are established in both the time and frequency domains. The time-domain connections relate various growth constants and norm bounds of the continuous-time systems considered to those of their zero-order hold discrete-time equivalents. The frequency-domain connection provides an upper bound on the difference between the frequency response of a continuous-time system and that of its zero-order hold discrete-time equivalent.
The problem of boundary output feedback for fixed-time stabilization of parabolic distributed parameter systems with space and time dependent reactivity is considered by utilizing the backstepping method. An observer ...
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The problem of boundary output feedback for fixed-time stabilization of parabolic distributed parameter systems with space and time dependent reactivity is considered by utilizing the backstepping method. An observer is constructed by applying the time-varying observer gain and boundary measurements, where the gain is unbounded as time approaches the terminal time. However, the fixed-time stability of error system is guaranteed by comparing the time growth rate of the observer gain with the decay rate of target error system state. Then, an observer-based output feedback boundary controller is established to achieve the fixed-time stabilization of the closed-loop system by combining the fixed-time stabilizing state feedback boundary controller and the fixed-time observer based on separation principle. Finally, a numerical simulation is shown to illustrate the effectiveness of the theoretical results.
This paper presents an iterative learning identification scheme for a class of parabolic distributed parameter systems with unknown curved surfaces. The identification design method is proposed on the basis of the ite...
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This paper presents an iterative learning identification scheme for a class of parabolic distributed parameter systems with unknown curved surfaces. The identification design method is proposed on the basis of the iterative learning concept. Initially, a new nonlinear learning identification law based on vector-plot analysis is developed to estimate the curved surface with spatial-temporal varying iteratively. Subsequently, through theoretical analysis, the sufficient convergence conditions for identification error in the sense of norm is manifested. Furthermore, a high-order P-type learning law is applied to identifying the curved surface in order to compare the convergent rate with the aforesaid identification law. Finally, simulation results on a specific numerical example and the temperature profile of a catalytic rod confirm that the proposed learning identification laws is effective.
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