Moving horizon observer-based control

Two topics are explored. First, a new approach to the problem of obtaining an estimate of the state of a nonlinear system is proposed. The moving horizon observer produces an estimate of the state of the nonlinear system at time t either by minimizing, or approximately minimizing, a cost function over the preceding interval (horizon) [t-T,t]; as t advances, so does the horizon. Convergence of the estimator is established under the assumption that the corresponding optimization problem can be (approximately) solved and a uniform observability condition is satisfied; the latter condition is automatically satisfied for linear (time-varying) systems. Second, the utility of the estimator for receding horizon control is explored. In particular, the stability of a composite moving horizon system, comprising a moving horizon regulator and a moving horizon observer, is established