Terminal Cost Distribution in Discrete-Time Controlled System with Disturbance and Noise-Corrupted State Information

Recursive formula for the terminal cost distribution in a scalar linear discrete-time system with disturbance and noise corrupted measurements is obtained. The system is subject to a linear saturated control strategy. The distributions of the initial state and the estimator error are assumed to be known. The disturbance is independent of the state/control and its distribution is known. The general result is applied to an interception problem with different types of disturbance. An illustrative numerical example confirms that the analytical method can replace extensive Monte Carlo simulations.