Design bounded robust controller using HJB solution for the nonlinear hybrid dynamical systems

This paper deals with the bounded robust controller design for event wise multiple models of the nonlinear hybrid dynamical systems (NHDS) with matched and unmatched uncertainties. The Hamilton-Jacobi-Bellman (HJB) equation based bounded robust control problem is proposed using a suitable non-quadratic term in the objective function of event wise local linearized model. The families of local bounded control laws are designed, to enforce stability using Lyapunov theorem for the individual events with the knowledge of the maximum bound of uncertainty. Using direct method of Lyapunov stability, the local bounded control law is shown to be optimal with respect to the objective function of the system under uncertainty. The new generalized Lyapunov function is proposed with crisp logic variables to establish the stability around the equilibrium points using bounded robust control law. Simulation and experimental results are presented, which validates the proposed bounded robust control approach.