Observer-based optimal output tracking for discrete-time systems with multiple state and input delays

Abstract

The optimal output tracking control (OOTC) problem for a class of discrete-time systems with state and input delays is addressed. An augmented system is constructed such that the OOTC problem can be transformed into a two-point boundary value (TPBV) problem with both advance and delay terms from the necessary optimality conditions. The successive approximating method recently developed is extended to obtain an approximate solution of the TPBV problem, which is then used to obtain a feedforward and feedback tracking controller. An observer is designed for the uncertain reference input such that the feedforward controller is physically realizable. Simulations show the results are effective even with long time-delays.

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

“…By comparing parameters of (19) and (21), we can get the Riccati matrix equation (14) and Stein matrix equation (15).…”

“…is completely observable, according to the optimal control theory, P is the unique positive definite solution of Riccati matrix equation (14). Because discrete-time system (9) …”

“…However, mostly the state of the exosystem is unmeasurable and most of systems with time-delays do not include the physical realizable problem of the designed controller [14].…”

Optimal tracking control for discrete-time systems with multiple input delays under sinusoidal disturbances

“…Virtually most of the studies on optimal control for discrete-time system with multiple input delays consider only approximate optimal control. For example, [28] proposed a successive approximation approach (SAA) to design a suboptimal control for discrete linear systems with time delay, in which an iterative procedure is introduced to solve the TPBV problem with time-delay items; after that, [29] designed an approximate tracking controller for discrete-time systems with multiple state and input delays based on SAA and an augmented system; [30] deals with the control of SISO linear time-delayed systems, when there are different delays in the output/input transfer function.…”

“…Different from the previous works on optimal control for multiply delay systems by using SAA and the augmented method, such as those in [28] and [29], the motivation for this work is to design an optimal tracking control law for discrete-time systems with multiply input delays under sinusoidal disturbances based on a discrete variable transformation. To solve the difficulty of control problem caused by sinusoidal disturbance and multiple input delays, an exosystem is introduced to estimate the sinusoidal disturbance, a non-delayed system is transformed based on the discrete variable transformation, an augmented model is constructed, and the quadratic performance index of the original system is simplified.…”