Adaptive State Feedback Control for Lipschitz Nonlinear Singular Systems

Singular systems behave more powerfully in terms of dynamical system modeling than ordinary state space systems. Since the algebraic equations in singular models can describe the systems constraints, nonlinear singular systems can present a general method for modeling and controlling constrained dynamical systems. This paper discusses an adaptive control for nonlinear singular systems which satisfy Lipschitz condition. Adaptive methods for singular systems are hardly ever investigated in literatures; however they are very useful methods in practice because the adaptive mechanism during the adaptive control can adjust the controller for a system with the unknown structures and parameters to improve the system performance. The presented controller is composed of a state feedback approach with adaptive gains and a mechanism to adjust the gains based on the Lyapunov stability theorem. First the controller is designed to stabilize the system, as a result, it is extended for the tracking problem. A simulation on a mobile robot singular model is provided to illustrate the effectiveness of the proposed control approach