Decentralized dynamic output feedback for robust stabilization of a class of nonlinear interconnected systems (original) (raw)
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Robust stabilization of nonlinear interconnected systems by decentralized dynamic output feedback
Systems & Control Letters, 2009
The objective of this note is to propose a dynamic output control scheme within the LMI framework for robust decentralized stabilization of systems composed of linear dynamic subsystems coupled by static nonlinear interconnections satisfying quadratic constraints. The procedure utilizes the general linear dynamic feedback structure, and consists of two steps, the first giving a block-diagonal Lyapunov matrix together with the robustness degree, and the second the controller parameters. A numerical example illustrates the applicability of the method.
Decentralized Observers for Optimal Stabilization of Large Class of Nonlinear Interconnected Systems
International Journal of Computer Applications, 2016
This paper focuses on the design of decentralized state observers based on optimal guaranteed cost control for a class of systems which are composed of linear subsystems coupled by nonlinear time-varying interconnections. One of the main contributions lies in the use of the differential mean value theorem (DMVT) to simplify the design of estimation and control matrices gains. This has the advantage of introducing a general condition on the nonlinear time-varying interconnections functions. To ensure asymptotic stability, sufficient conditions expressed in terms of linear matrix inequalities (LMIs) are established to compute the control and the observation gains of the overall system. High performances are shown through numerical simulation of a power system with three interconnected machines.
On decentralized stabilization of interconnected systems
Automatica, 1980
A decentralized control scheme is proposed for stabilization of interconnected systems consisting of arbitrarily connected, linear, time-invariant multivariable subsystems. Sufficient conditions are given for an interconnected system to be stabilized using only local state feedback. The obtained results are illustrated by an example.
The focus of this paper is on the design of a H 1 decentralized observation and control approach for a class of nonlinear disturbed interconnected systems. The proposed scheme is formulated as an optimization problem in terms of linear matrix inequality (LMI) to compute the robust observation and control gain matrices simultaneously, to maximize the bounds on the nonlinearity which the system can tolerate without going unstable, to improve the performance of the proposed control strategy by minimizing the H 1 criterion and to ensure the stability of the closed loop system in the Lyapunov framework despite the exogenous disturbances applied to the subsystems. A simulation is provided on a 3-machine power system, which generators are strongly nonlinear interconnected, to show the efficiency of the designed approach. .tn (A.S. Tlili), naceur.benhadj@ept.rnu.tn (N. Benhadj Braiek). reference tracking have been developed in the literature such as the nonlinear , the robust , the adaptive and the fuzzy decentralized control .
Robust decentralized control of large-scale interconnected systems: general interconnections
Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251), 1999
In this paper, a new decentralized control scheme is developed for a large-scale interconnected nonlinear systems with uncertain but bounded nonlinear interconnections. The interconnections are assumed to be bounded by polynomial type nonlinearities in states. If the interconnections are bounded by a pth-order polynomial in states, then the proposed controller has terms involving pth-order or less. This is in sharp contrast to the existing literature, which use a ( 2 p -1)thorder terms in the controller. We develop robust designs if the coefficients of the bounded polynomial are known, and adaptive designs if the coefficients are not known. We show global exponential convergence of the states for the robust case and global asymptotic convergence of the states for the adaptive case. First, we consider systems that satisfy matching conditions and then extend the designs for systems that do not satisfy matching conditions. We give several examples to illustrate the design methodology. Further, we show how our designs can be extended to interconnections that cannot be bounded by finite length polynomials.
We consider the problem of designing decentralized PI observer-based controller for nonlinear interconnected systems using linear matrix inequalities (LMIs). The overall system is composed of linear subsystems and nonlinear time-varying interconnections depending on both time and state. We take advantage of additional degrees of freedom in PI observer to maximize the bound on nonlinear interconnection terms. Also we extend the original problem of robust stabilization by including a disturbance term and provide a sufficient condition for connective stability with disturbance attenuation in the L 2 gain sense. An example is included to validate the theoretical results.
A generic approach to the design of decentralized linear output- feedback controllers
Systems & Control Letters, 2006
A sufficient condition for failure-tolerant performance stabilization in a desirable performance region under decentralized linear output feedback is established. To exploit the flexibility in decentralized control beyond multivariable pole assignment, and to address the subsystem design objectives along with those of the overall system, a generic problem on decentralized linear output feedback is then defined. The problem is reformulated in terms of a constrained nonlinear optimization problem. The proposed methodology results in the optimal reconciliation of failure-tolerant robust performance of the overall system, and (maximal) robustness, disturbance rejection, noninteractive performance, reliability and low actuator gains in the isolated subsystems in the face of unstructured perturbations in the controller and plant parameters. The effectiveness of the proposed approach is demonstrated by an example.
A generalized approach to stabilization of linear interconnected time-delay systems
Asian Journal of Control, 2012
The objective of this paper is to propose a generalized approach to stabilization of systems which are composed of linear time-delay subsystems coupled by linear time-varying interconnections. The proposed algorithms, which are formulated within the convex optimization framework, provide decentralized solutions to the problem of delay-dependent asymptotic stability with strict dissipativity. It is established that the new methodology can reproduce earlier results on passivity, positive realness and disturbance attenuation. Then a decentralized structure of dissipative statefeedback controllers is designed to render the closed-loop interconnected system delay-dependent asymptotically stable with strict dissipativity. Numerical examples are presented to illustrate the applicability of the design method.
Decentralized control of nonlinear large-scale systems using dynamic output feedback
Journal of Optimization Theory and Applications, 2000
In this paper, a class of nonlinear large-scale systems with similar subsystems is studied. Both matched and unmatched uncertainties are considered by utilizing their bounding functions, and the interconnections take a more general form than considered previously. Based on a constrained Lyapunov equation, a nonlinear dynamic output feedback decentralized controller is presented. Unlike existing results, matched uncertainties are considered in the control design; by using a decomposition of the interconnections, the known and uncertain interconnections are treated separately; thus, the robustness is improved and conservativeness is reduced significantly. The computation effort for solving the Lyapunov equation is greatly reduced by taking into account the similar subsystem structure. Finally, simulation is used to illustrate the effectiveness of our results.
Nonlinear decentralized control of large-scale systems with strong interconnections
This paper addresses the problem of nonlinear decentralized state feedback stabilization for a class of large-scale systems with strong interconnections. The interconnections and their bounds are general functions of all the states. By developing a new recursive design method, a decentralized state feedback controller is successfully constructed for the large-scale system. The novelty of the proposed method is that a Lyapunov function in an appropriate product integral form is introduced at each step so that the recur-sive design can be carried out. A numerical example is given to illustrate the effectiveness of the proposed method.