The HJB Approach and State Estimation for Control Systems with Uncertainty

Abstract

This paper deals with the comparison principle for the first-order ODEs of the Hamilton - Jacobi - Bellman (HJB) type which describe solutions of the dynamical control system with a special structure, with combined nonlinearity of quadratic and bilinear kinds and with uncertainty in initial states and in system parameters. The uncertainty studied here is of set-membership type when only the bounding set for unknown items is given. The ellipsoidal estimates of reachable sets are derived using the special structure of studied control system. The techniques of generalized solutions of Hamilton - Jacobi - Bellman inequalities together with previously established results of ellipsoidal calculus are applied to find the external set-valued estimates of reachable sets as the level sets of a related cost functional. © 2018