Tracking Control Design for Discrete-time Polynomial Systems: A Sum-of-Squares Approach

In this paper, tracking control synthesis problem for nonlinear polynomial discrete-time systems are studied. Proposed controller drives the plant such that the state vector of the plant follows those of a stable reference model. The objective is to design a controller such that the energy gains from the exogenous signals that are the reference signal and the state vector of the reference model, to the tracking error to be less or equal to prescribe thresholds. The main difficulty in the problem of designing tracking nonlinear discrete-time control law for the polynomial discrete time systems is that in general this problem may not be formulated as a convex problem. With proper selection of Lyapunov function and based on Lyapunov theory and by using sum of square approach, sufficient conditions for existence of controller are presented in terms of a feasibility SOS programming problem that can be solved using numerical solvers such as SOSTOOLS. Finally, the performance of proposed approach will be shown using the simulation of several examples.