In this study, the iterative learning control (ILC) method is considered for tracking control of a class of distributed parameter systems (DPSs) based on sensor-actuator networks (SANs) with the unknown exogenous inpu...
详细信息
In this study, the iterative learning control (ILC) method is considered for tracking control of a class of distributed parameter systems (DPSs) based on sensor-actuator networks (SANs) with the unknown exogenous input and the measurement noise, which are described by a semi-linear parabolic partial differential equation. The D-type ILC algorithm is presented to control DPSs with non-collocated SANs. When the unknown exogenous input and the measurement noise are bounded, the upper bounds of output errors are obtained via the Bellman-Gronwall lemma and semi-group theory, respectively. The authors prove that the output errors converge to zero in the absence of the unknown exogenous input and the measurement noise. Two examples are given to show the effectiveness of the proposed D-type ILC scheme.
The present work addresses continuous-time approximation of distributed parameter systems governed by linear one-dimensional partial differential equations. While approximation is usually realized by lumped systems, t...
详细信息
The present work addresses continuous-time approximation of distributed parameter systems governed by linear one-dimensional partial differential equations. While approximation is usually realized by lumped systems, that is finite dimensional systems, we propose to approximate the plant by a time-delay system. Within the graph topology, we prove that, if the plant admits a coprime factorization in the algebra of BIBO-stable systems, any linear distributedparameter plant can be approximated by a time-delay system, governed by coupled differential-difference equations. Considerations on stabilization and state space realization are carried out. A numerical method for constructive approximation is also proposed and illustrated. (C) 2016 Elsevier Ltd. All rights reserved.
Control and estimation of second-order distributed parameter systems are of importance in mechanical systems. In particular, flexible structures can be modeled as second-order distributed parameter systems. This paper...
详细信息
Control and estimation of second-order distributed parameter systems are of importance in mechanical systems. In particular, flexible structures can be modeled as second-order distributed parameter systems. This paper investigates adaptive consensus filtering for a class of second-order distributed parameter systems under an abstract framework. We propose an adaptive consensus mechanism to minimize the disagreement among all local filters consisting of different sensor nodes and written in the natural setting of a second-order formulation with an additional coupling. A parameter-dependent Lyapunov function is presented to analyze the stability of the collective dynamics, that is, all filters agree with each other and converge to the true state of the second-order system. The performance is demonstrated on a numerical example of a second-order partial differential equation with point measurements.
In this paper, we introduce a new approach, zero dynamics inverse (ZDI) design, for designing a feedback compensation scheme achieving asymptotic regulation for a linear or nonlinear distributedparameter system in th...
详细信息
In this paper, we introduce a new approach, zero dynamics inverse (ZDI) design, for designing a feedback compensation scheme achieving asymptotic regulation for a linear or nonlinear distributedparameter system in the case when the value w(t) at time t of the signal w to be tracked or rejected is a measured variable. Following the nonequilibrium formulation of output regulation, we formulate the problem of asymptotic regulation by requiring zero steady-state error together with ultimate boundedness of the state of the system and the controller(s), with a bound determined by bounds on the norms of the initial data and w. Because a controller solving this problem depends only on a bound on the norm of w not on the particular choice of w, this formulation is in sharp contrast to both exact tracking, asymptotic tracking or dynamic inversion of a completely known trajectory and to output regulation with a known exosystem. The ZDI design consists of the interconnection, via a memoryless filter, of a stabilizing feedback compensator and a cascade controller, designed in a simple, universal way from the zero dynamics of the closed-loop feedback system. This design philosophy is illustrated with a problem of asymptotic regulation for a boundary controlled viscous Burgers' equation, for which we prove that the ZDI is input-to-state stable. In infinite dimensions, however, input-to-state stable compactness arguments are supplanted by smoothing arguments to accommodate crucial technical details, including the global existence, uniqueness, and regularity of solutions to the interconnected systems. Copyright (C) 2011 John Wiley & Sons, Ltd.
In this paper, a fuzzy feedback control design problem with a mixed H-2/H-infinity performance is addressed by using the distributed proportional-spatial integral (P-sI) control approach for a class of nonlinear distr...
详细信息
In this paper, a fuzzy feedback control design problem with a mixed H-2/H-infinity performance is addressed by using the distributed proportional-spatial integral (P-sI) control approach for a class of nonlinear distributed parameter systems represented by semi linear parabolic partial differential-integral equations (PDIEs). The objective of this paper is to develop a fuzzy distributed P-sI controller with a mixed H-2/H-infinity performance index for the semi-linear parabolic PDIE system. To do this, the semi-linear parabolic PDIE system is first assumed to be exactly represented by a Takagi-Sugeno (T-S) fuzzy parabolic PDIE model in a given local domain of Hilbert space. Then, based on the T-S fuzzy PDIE model, a distributed fuzzy P-sI state feedback controller is proposed such that the closed-loop PDIE system is locally exponentially stable with a mixed H-2/H-infinity performance. The sufficient condition on the existence of the fuzzy controller is given by using the Lyapunov's direct method, the technique of integration by parts, and vector-valued Wirtinger's inequalities, and presented in terms of standard linear matrix inequalities (LMIs). Moreover, by using the existing LMI optimization techniques, a suboptimal H-infinity fuzzy controller is derived in the sense of minimizing an upper bound of a given H-2 performance function. Finally, the developed design methodology is successfully applied to feedback control of a semi-linear reaction diffusion system with spatial integral terms. (C) 2016 Elsevier B.V. All rights reserved.
This work extends the geometric theory of output regulation to linear distributed parameter systems with bounded input and output operator, in the case when the reference signal and disturbances are generated by a fin...
详细信息
This work extends the geometric theory of output regulation to linear distributed parameter systems with bounded input and output operator, in the case when the reference signal and disturbances are generated by a finite dimensional exogenous system. In particular, it is shown that the full state feedback and error feedback regulator problems are solvable, under the standard assumptions of stabilizability and detectability, if and only if a pair of regulator equations is solvable. For linear distributed parameter systems this represents an extension of the geometric theory of output regulation developed in [10] and [4], We also provide simple criteria for solvability of the regulator equations based on the eigenvalues of the exosystem and the system transfer function. Examples are given of periodic tracking, set point control, and disturbance attenuation for parabolic systems and periodic tracking for a damped hyperbolic system.
A collocation method is adopted as a numerical framework to develop approximate inertial manifolds (AIMs) in the case of partial differential problems (e.g. reaction/diffusion models) containing non-polynomial nonline...
详细信息
A collocation method is adopted as a numerical framework to develop approximate inertial manifolds (AIMs) in the case of partial differential problems (e.g. reaction/diffusion models) containing non-polynomial nonlinearities. The spatial discretization, based on the collocation approach, is the starting point for the alternative construction of AIMs by means of a renormalization/decimation approach naturally derived from the incremental unknown method developed by Temam in a finite difference framework. (C) 2002 Elsevier Science Ltd. All rights reserved.
We present an estimate for a class of unbounded perturbations of the generator of an exponentially stable semigroup. When this estimate is satisfied then the perturbed operator still generates an exponentially stable ...
详细信息
We present an estimate for a class of unbounded perturbations of the generator of an exponentially stable semigroup. When this estimate is satisfied then the perturbed operator still generates an exponentially stable semigroup. For generators of holomorhic semigroups the class of allowed perturbations contains unbounded operators of the form HA-alpha, with alpha < 1/2. The estimate is given in terms of the norm of the solution of the Lyapunov equation which corresponds to the unperturbed system.
The aim of this manuscript is to present an alternative method for designing state observers for second-order distributed parameter systems without resorting to a first-order formulation. This method has the advantage...
详细信息
The aim of this manuscript is to present an alternative method for designing state observers for second-order distributed parameter systems without resorting to a first-order formulation. This method has the advantage of utilizing the algebraic structure that second-order systems enjoy with the obvious computational savings in observer gain calculations. The proposed scheme ensures that the derivative of the estimated position is indeed the estimate of the velocity component and to achieve such a result, a parameter-dependent Lyapunov function was utilized to ensure the asymptotic convergence of the state estimation error. (C) 2003 Elsevier B.V. All rights reserved.
暂无评论