Discrete-time systems: control and tracking

The design of controllers for linear discrete-time systems using the Lyapunov stability theory and Hamilton-Jacobi framework, numerical optimization and other viable methods, has been thoroughly studied. However, for nonlinear discrete-time systems, the tracking problem has not been rigorously approached to ensure desirable results. Motion control and tracking are important problems, and these issues are emphasized and studied in this paper using the Hamilton-Jacobi theory. The optimal state-feedback nonlinear tracking problem is formulated and solved using necessary conditions for optimality, and a nonquadratic performance index is minimized. It is shown that the proposed procedure extends the available analytical tools and provides a viable avenue to solve a wide spectrum of nonlinear design problems. The reported concept is applied to design a nonlinear digital controller for a ground vehicle driven by an advanced turbocharged diesel. The synthesized controller is verified, and the nonlinear simulation results carried out using high-fidelity mathematical model are reported and discussed.