Sliding mode estimation and optimization methods in nonlinear control problems.

摘要

In this thesis, several sliding mode estimation and optimization methods are developed and their usage in nonlinear control problems are investigated in a Lyapunov stability framework. We first present ideal illustrative designs for both the equivalent control based disturbance estimation and state observation problems and then perform an ultimate boundedness analysis by tracing the propagation of possible low-pass filtering approximation errors through the sequential derivation. Utilizing the proof on the approximability of the equivalent control by a low-pass filter at each step, we demonstrate a relation between the estimation accuracy and the selection of the filter time constants. Second, these estimation methods are utilized in several nonlinear control design methods so as to provide a nominal design with robustness while keeping the conservatism at an acceptable level. The basic control idea is simply to estimate the perturbation of a nominal system from its actual and to use the estimated quantities in the specification of the control law. The robustness of the closed loop system then needs to be guaranteed against the estimation errors which would relatively be an easier task since the estimated values are already compensated throughout the design. Specifically, this idea is studied on the tracking control problems of an uncertain nonlinear system in strict feedback form and an uncertain feedback linearizable system via backstepping and feedback linearization design methods. The on-line optimization of a closed loop system is also studied in this thesis. A two-time scale sliding mode optimization method where an on-line performance criterion is to be maximized while a regulative control is in the loop is developed. The proposed method assumes a regulative control which creates an equilibria as a function of a free control parameter and then this parameter is adapted in a slower time scale so as to increase the performance of the overall system. Finally, the estimation and the optimization tools developed in this dissertation are used in an application example from automotive industry where the tire force is to be kept in the vicinity of its maximum during an acceleration transient.