On the estimation of systems with discontinuities using continuous-discrete unscented Kalman filter

Discontinuous systems have been increasingly paid attention since it can be found in various physical and biological systems. In this paper we consider an effective estimation algorithm for system with multiple discontinuities. We propose that a discontinuous-right-hand-side of state equation is approximated as multiplication of known discontinuous basis function and parameter that evolves in time. The basis function is selected in such a way that stability of estimation is guaranteed. Computational behavior (chattering) on sliding surface is investigated. We use continuous-discrete unscented Kalman filter to estimate the proposed model. A particular feature is included to the algorithm i. e. when system state orbits along sliding surface, estimation is switched to computation of deterministic model as it is shown unobservable by using Filippov´s convex method. Extension of the Filippov´s convex method is also used in order to obtain accurate computation (avoiding chattering) along sliding surface. Simulation results of two application examples are provided to show the robustness of the algorithm.