Decentralized Observers for Optimal Stabilization of Large Class of Nonlinear Interconnected Systems (original) (raw)
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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 .
The objective of this paper is to propose an approach to robust stabilization of systems which are composed of linear subsystems coupled by nonlinear time-varying interconnections satisfying quadratic constraints. The proposed algorithms, which are formulated within the convex optimization framework, employ linear dynamic feedback structure involving local Luenberger-type observers. It is also shown how the new methodology can produce improved results if interconnections have linear parts that are known a priori. Examples of output stabilization of inverted pendulums and decentralized control of a platoon of vehicles are used to illustrate the applicability of the design method. ᭧ He published numerous scientific papers from diverse fields, including estimation and identification, adaptive systems, digital signal processing, processing of medical images, large-scale systems and neural networks. He was also leader of numerous scientific projects for government and industry. His research interests include currently large-scale systems, multiagent systems, vehicle formation control and statistical learning applied to biomedicine. Dušan M. Stipanović received the B.S. degree in electrical engineering from the University of Belgrade, Belgrade, Serbia, in 1994, and the M.S.E.E. and Ph.D. degrees (under supervision of Professor Dragoslav Šiljak) in electrical engineering
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.
On decentralized stabilization of interconnected systems
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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.
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.
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.
Decentralized robust guaranteed cost control for multimachine power systems
14th International Conference on Sciences and Techniques of Automatic Control & Computer Engineering - STA'2013, 2013
In this paper, we investigate the problem of the decentralized robust stabilizing control approach and mainly the decentralized robust guaranteed cost control for robust stabilization of interconnected multimachine power systems. The proposed feedback control schemes are developed to ensure the asymptotic stability of the nonlinear uncertain large scale system and formulated in a minimization problem within the framework of linear matrix inequalities (LMIs) which resolution yields the decentralized control gain matrices. The effectiveness of the proposed control techniques are demonstrated through numerical simulations on a nonlinear uncertain power system with three interconnected machines, for different cases of perturbations. Index Terms-Decentralized control; Robust control; Guaranteed cost control; Interconnected power systems; LMI;
Transactions of the Institute of Measurement and Control, 2018
This paper presents a new robust decentralized control of nonlinear interconnected systems, which is applied and validated on a large scale power system. Our work is performed in three steps. Firstly, we have developed the polynomial description of the nonlinear uncertain and interconnected system using odd Kronecker power of state vectors, which is an easy-manipulation model for such complex systems. Then we applied Lyapunov’s direct method of stability analysis, associated with a quadratic function, in order to determine a sufficient condition for global asymptotic stability by applying a nonlinear, decentralized and optimal polynomial control. Finally, we carried out a simulation study on a nonlinear uncertain power system with three interconnected machines. We considered different cases of perturbations on its state variables as well as different cases of fault locations. We prove via advanced simulations, the effectiveness of the proposed control technique which is able to miti...
Decentralised control of multimachine power systems with guaranteed performance
IEE Proceedings - Control Theory and Applications, 2000
The paper focuses on a robust dcccntralised excitation control of inultimachine power systems. The authors are concerned with the design of a decentralised state feedback controller for the powcr system to enhance its transient stability and ensure a guaranteed level of performance when there exist variations of generator parameters due to changing load and/or network topology. It is shown that the power system can be modelled as a class of interconnected systems with uncertain parameters and interconnections. The authors develop a guaranteed cost control technique for the interconnected system using a linear matrix inequality (LMI) approach. A procedure is given for the minimisation of the cost by employing the powerful LMI tool. The proposed controller design is simulated for a three-machine power system example. Simulation results show that the decentralised guaranteed cost control greatly enhances thc transient stability of the power system in the face of various operating points, faults in different locations or changing network parameters.
IEEE Transactions on Automatic Control, 2009
This note presents a broad LMI condition that can ascertain the stability of uncertain systems under decentralized feedback in the presence of interconnection and feedback delays. Based on the Lyapunov's direct approach with a four-term energy functional and a three-term quadratic formulation of the given state dynamics, this method has a larger search space than used so far. Numerical examples corroborate the superiority of this method vis-à-vis the existing ones for several subsets of the general problem. Index Terms-Decentralized control, linear matrix inequality (LMI), uncertain time-delay systems.