State estimation for a class of nonlinear dynamic systems through HJB technique
The paper deals with the state estimation problem for dynamical control systems 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 control system assuming that initial system states are unknown but bounded. For this purpose we use the comparison principle for the first-order ODEs of the Hamilton - Jacobi - Bellman (HJB) type and the generalized solutions of HJB inequalities which allow finding the set-valued estimates
of reachable sets as the level sets of a related cost functional.
The motivations to consider set-membership approach in state estimation problems for dynamical systems with uncertainty may be found in many applied areas ranged from engineering problems in physics to economics as well as to biological and ecological modeling.
CYBERNETICS AND PHYSICS, Vol. 2, No. 3, 127-132..