Research On Robust Adaptive Control For Nonlinear Uncertain Systems

This dissertation mainly studies the robust adaptive control problem for nonlinear uncertain systems . The main topics are:(1) A backstepping design procedure is proposed for a class of SISO cascaded nonlinear systems with dynamics uncertainties and zero dynamics. A robust adaptive control law is proposed. The derived robust adaptive controller guarantees the global stability of the closed system and the uniformly ultimate boundedness property for all the states of the closed-loop system.(2) A robust adaptive controller with L 2 -gain is derived for a class of SISO cascaded nonlinear uncertain systems with zero dynamics. The state feedback controller guarantees that the closed-loop system is input-to-state stable and the L 2 -gain from the disturbance input to the controlled output is not larger than a prescribed value for all admissible parameter uncertainties. A recursive Lyapunov-based design approach is developed to construct the controller explicitly. The paper addresses the design approach of H adaptive controller without the need of solving HJI inequality for a class of SISO nonlinear uncertain systems.(3) We propose a new recursive design method for robust adaptive control of a class of SISO cascaded nonlinear systems with parametric uncertainties and disturbances. The method is called dynamic surface control . Traditional backstepping algorithm requires repeated differentiations of the modeled nonlinearities. The addition of n first order low pass filters allows the algorithm to be implemented without differentiating any model nonlinearities, thus ending the complexity arising due to the "explosion of terms" that has made other methods difficult to implement in practice. The controller designed guarantees the semiglobal stability of the closed-loop system and the semiglobal output tracking of given desired trajectory.(4) The problem of robust decentralized dissipative control for a class of nonlinear interconnected systems with uncertainties and disturbances is addressed. The interconnection between the nonlinear robust dissipative control and the nonlinear robust decentralized dissipative control is established. A sufficient condition for the existence of a solution to robust decentralized dissipative control via state feedback and via output feedback is derived in term of a set of Hamilton-Jacobi-Issacs(HJI) inequalities. The sufficient condition is that the robust decentralized dissipative control problem can be resovled for all admissible uncertainties, if there exists a scaling C1 storage function such that HJI inequalities have nonnegative solution. The controllers constructed make the nonlinearsystem robust dissipative with respect to the quadratic supply rate.(5) An adaptive controller specially designed is proposed to solve the problem of making a MIMO nonlinear system, with explicit linear parametric uncertainty, equivalent to a passive system. The controller designed guarantees that the closed-loop system is stable and the parameter estimates converge to some constants. The simulation results also demonstrate the controller's effectiveness and feasibility.(6) An adaptive H tracking control equipped with a VSC algorithm is proposed for a class of MIMO nonlinear systems with parametric uncertainties, unmodeled perturbations and external disturbances. In order to counteract the effect due to the unmodeled perturbation, the H tracking control requires to solve a modified algebraic Riccati-like matrix equation. The derived hybrid adaptive-robust tracking control scheme guarantees that all the signals and states are bounded, the tracking error is uniformly ultimately bounded and H tracking performance is achieved.(7) An adaptive robust iterative learning control method is presented for the control of MIMO nonlinear uncertain systems The scheme ceases both learning and adaptation whenever the previous iteration error enters a pre-specified error bound, in the sequel enhances the robustness of the control system and meanwhile achieves arbitrary tracking accuracy. For...