State Estimation In Control Systems Research Articles

The HJB Approach and State Estimation for Control Systems with Uncertainty

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.

State-space least mean square

In this paper, we present a generalized form of the well-known least mean square (LMS) filter. The proposed filter incorporates linear time-varying state-space model of the underlying environment and hence is termed as state-space LMS (SSLMS). This attribute results in marked improvement in its tracking performance over the standard LMS. Furthermore, the use of SSLMS in state estimation in control systems is straightforward. Overall performance of SSLMS, however, depends on factors like model uncertainty and time-varying nature of the problem. SSLMS with adaptive memory, having time-varying step-size parameter, provides solutions to such cases. The step-size parameter is iteratively tuned by stochastic gradient method so as to minimize the mean square value of the prediction error. Different computer simulations demonstrate the ability of the algorithms suggested in this paper. A detailed study of computational complexities of the proposed algorithms is carried out at the end.