State Estimation for a Class of Nonlinear Dynamic Systems with Uncertainty through Dynamic Programming Technique
The paper deals with the comparison principle for the first-order ODEs of the Hamilton - Jacobi - Bellman type which describe solutions of the dynamical control system with a special structure, in which the nonlinear terms in the right-hand sides of related
differential equations are quadratic in state coordinates. We construct external ellipsoidal estimates of reachable sets of the system assuming that initial system states are unknown but bounded. We apply the techniques of generalized solutions of Hamilton - Jacobi - Bellman inequalities to find the external set-valued estimates of reachable sets as the level sets of a related cost functional.