Robust Fuzzy Control for a Class of Uncertain Discrete Fuzzy Bilinear Systems
ABSTRACT The main theme of this paper is to present robust fuzzy controllers for a class of discrete fuzzy bilinear systems. First, the parallel distributed compensation method is utilized to design a fuzzy controller, which ensures the robust asymptotic stability of the closed-loop system and guarantees an Hinfin norm-bound constraint on disturbance attenuation for all admissible uncertainties. Second, based on the Schur complement and some variable transformations, the stability conditions of the overall fuzzy control system are formulated by linear matrix inequalities. Finally, the validity and applicability of the proposed schemes are demonstrated by a numerical simulation and the Van de Vusse example.
- [show abstract] [hide abstract]
ABSTRACT: This paper presents the closed-loop composite control of singularly perturbed bilinear systems with a quadratic performance criterion, using the successive Galerkin approximation (SGA). The singularly perturbed bilinear system is decomposed into two subsystems of a slow-time and fast-time scale by the singular perturbation theory, and we obtain feedback control laws from each subsystem using the SGA. We design the composite control law that consists of two optimal control laws for each subsystem. This paper attempts to design the closed-loop composite controller of singularly perturbed bilinear systems with the SGA method, and to reduce the disadvantages of the SGA methodControl Applications, 2001. (CCA '01). Proceedings of the 2001 IEEE International Conference on; 02/2001 · 1.05 Impact Factor
Conference Proceeding: On Nonlinear Systems with Poorly Behaved Zero Dynamics[show abstract] [hide abstract]
ABSTRACT: The design of controllers for nonlinear, nonminimum-phase systems is very challenging and is currently considered to be one of the most difficult theoretical control problems. Most control algorithms for nonlinear processes perform a linearization making use of an inverse of the system. In the linear case, the system can be factored into the minimum-phase and the nonminimum-phase parts and only the first one is inverted for purpose of control design. A similar scheme for nonlinear systems is still under investigation. The present work adresses the problem of synthesizing nonlinear state feedback controllers for nonlinear, nonminimum-phase processes in three different ways. The first approach consists of a partial linearization which preserves stability by using an approximate stable/anti-stable factorization. The second technique can be viewed as an inner-outer factorization based approach. And, finally, in the single-output case, it is shown (through an example) that stabilization of the internal dynamics of a nonmininum-phase system can be achieved by using an additional input if this is feasible in practice. In this case, the manipulated variables have different roles, i.e., one is chosen such as to input/output feedback linearize the system and the second is used to locally stabilize the resulting nonminimum-phase internal dynamics.American Control Conference, 1992; 07/1992
- [show abstract] [hide abstract]
ABSTRACT: This paper investigates the effectiveness of a passive tuned mass damper (TMD) and fuzzy controller in reducing the structural responses subject to the external force. In general, TMD is good for linear systems. We proposed here an approach of Takagi-Sugeno (T-S) fuzzy controller to deal with the nonlinear system. To overcome the effect of modeling error between nonlinear multiple time-delay systems and T-S fuzzy models, a robustness design of fuzzy control via model-based approach is proposed in this paper. A stability criterion in terms of Lyapunov's direct method is derived to guarantee the stability of nonlinear multiple time-delay interconnected systems. Based on the decentralized control scheme and this criterion, a set of model-based fuzzy controllers is then synthesized via the technique of parallel distributed compensation (PDC) to stabilize the nonlinear multiple time-delay interconnected system and the H<sup>∞</sup> control performance is achieved at the same time. Finally, the proposed methodology is illustrated by an example of a nonlinear TMD system.Circuits and Systems I: Regular Papers, IEEE Transactions on 10/2005; · 2.24 Impact Factor