Optimal Sliding Mode Tracking Control For A Class Of Affine Nonlinear Systems

The optimal tracking problem has been received great growing attention owing to its wide practical applications. The linear optimal tracking problem could be solved by directly using the solution of optimal regulation problem. However, the nonlinear optimal tracking problem often leads to a nonlinear two-point boundary-value problem (TPBV) and an analytical solution generally does not exist except some simplest cases. Exact linearization, which is usually used to realize nonlinear system transformation, could avoid nonlinear TPBV problem and effectively simplify the optimal regulator design. The real plants inevitably contain system uncertainty. This may degrade the dynamic performance of the optimal controller which is usually designed based on precise mathematical modes, even make it unstable. The outstanding advantage of sliding mode control (SMC) is that sliding mode can provide complete robustness to system uncertainty. Therefore, SMC can be employed to robustify the optimal regulator, in order to achieve the'optimal invariance'.The design of optimal sliding mode tracking controller is studied for a class of affine nonlinear systems in this thesis. The main works are summarized as follows:1. The optimal sliding mode tracking control is studied for uncertain linear systems. An augmented system, composed of the original system and the exosystem, is constructed to transform the optimal output tracking problem into an optimal regulation problem. Considering system uncertainty, the optimal sliding manifold is constructed, based on the optimal control law of nominal system of the augmented system. Sliding mode satisfies requirement of given optimal performance criterion and exhibits complete robustness to system uncertainty. A reference input observer is constructed to guarantee the control law physically realizable. Simulation results illustrate the effectiveness of the proposed method.2. The optimal sliding mode tracking controller is designed for a class of uncertain nonlinear Single-Input-Single-Output (SISO) systems, with reference signal given by an exosystem. Firstly feedback linearization is adopted to transform the nonlinear model into an equivalent linear one. Considering the reference exosystem, the tracking error state equation is established and the optimal tracking problem is transformed into an optimal regulation problem. Then an optimal regulator is designed based on the nominal error system. SMC is employed to robustify the regulator, in order to guarantee system optimal dynamic performance obtained and provide robustness to uncertainties. A robot dynamic control system is considered to demonstrate effectiveness and superiority of the proposed algorithm.3. The design of optimal sliding mode tracking controller is studied for a class of uncertain nonlinear Multiple-Input-Multiple-Output (MIMO) systems, with an exosignal. Exact linearization is employed to decouple the original MIMO system, in order to simplify the design process. Based on the decoupled system and the exosystem, an error equation is constructed. Therefore, the optimal tracking problem of original system is transferred into an optimal regulation problem about the error system. Based on the nonlinear optimal control law, an integral sliding mode surface is constructed, which can remove the reaching phase of SMC and guarantee the global sliding mode. To reduce chattering, the reaching law is used to design the optimal sliding mode tracking control law. As a result, not only the optimal performance can be obtained but the system robustness to uncertainties is guaranteed also. The proposed algorithm is applied to two-link robot system, and simulation results show its effectiveness.