Estimation of systems with multiple sliding surfaces

With increasing attention to discontinuous systems, in this paper we consider an effective estimation algorithm for system with multiple sliding surfaces. We propose that a discontinuous-right-hand-side of state equation is approximated as multiplication of discontinuous arbitrary basis function and parameter that evolves in time. The problem becomes how to estimate join state and model parameters. We use continuous-discrete unscented Kalman filter to estimate the proposed model as it is compatible with discontinuous system and can accommodate model uncertainty. A particular feature of our algorithm is that when system state orbits along discontinuity surface, estimation is switched to computation of deterministic model as it becomes unobservable. Filippov's convex method, then, takes part in order to obtain accurate computation. Simulation results of two application examples are provided to show the robustness of the algorithm.