Optimal tracking control for discrete-time systems with delayed state and input

Abstract

The optimal tracking control for discrete-time systems with delayed state and input is addressed. By introducing a function-based transformation, the discrete time-delay system is transformed into a non-delayed system. The optimal tracking controller is constructed by the solution of a Riccati matrix equation and a Stein matrix equation. A reduced-order observer is constructed to solve the physically realizable problem of the feedforward compensator. Simulation results demonstrate the effectiveness of the optimal tracking control law.

Dual Heuristic dynamic Programming for nonlinear discrete-time uncertain systems with state delay

“…Then the next value function V 1 (x(k)) can be computed as in (9). The next state vector can be obtained by (10)…”

“…[9] used the T-S fuzzy model to represent the state-space model of nonlinear discrete-time systems with time delays and a stable fuzzy H∞ filter was designed for signal estimation. In [10] the discrete time delay system is transformed into a non-delayed system by a function-based transformation; an optimal tracking controller is constructed by solving Riccati matrix equation and Stein matrix equations. A simultaneous state and disturbance estimation technique is developed for time delay systems and applied to fault estimation and signal compensation in [11].…”