Robust H_∞ Control For Uncertain Nonlinear Systems

This paper studies mainly the problem of robust control for uncertain nonlinear systems. Firstly, the robust regulation problem is discussed for iionholonomic chained form with parametric and structural uncertainties.Based on a combined application of the discontinuous state-scaling coordinates transformation method and backstepping procedure, we propose a robust nonlinear controller which makes the closed-loop systems (1.2), (1.53) and (1.54) global robust stable (Theorem 1.1).Secondly, we consider the problem of robust output feedback disturbance attenuation control for mismatched nonlinear uncertain system whose nominal system is passiveUsing passivity techniques, the problem of adaptive regulation disturbance attenuation is solved by constructing a dynamic adaptive output feedback controller (Theorem 2.1 and Corollary 2.1), meanwhile, we design a static-state robust output feedback control law which ensures the closed-loop systems (2.10) and (2.24) disturbance attenuation with internal stability (Theorem 2.2). Further, this paper extends and improves the results of the related references.Finally, this paper deals with the almost disturbance decoupling problem and robust H control problem respectively for high-order cascade systems with uncertainties.In this paper, the problem of almost disturbance decoupling is investigated for minimum-phase high-order uncertain nonlinear cascade systemsCombining the adding one power integrator technique and improved essentially Lemma 3.1, in terms of L2m - L2mp (m ?1,2, ???, we construct explicitly a robust feedback control law which attenuates the disturbance's effect on the output to an arbitrary degree of accuracy with internal stability. (Theorem 3.1).Aagin, this paper addresses the robust adaptive H^ control problem for high-order uncertain nonlinear systemsand the robust adaptive almost disturbance decouph'ng problem for minimum-phase high-order uncertain nonlinear systems.Utilizing the adding one power integrator technique and recursive algorithm which are improved essentially in this paper, the problem of robust adaptive almost disturbance decoupling is solved via smooth robust dynamic controller for high-order nonlinear systems with unknown parameter (Theorem 4.1 and Theorem 5.1).