Linear quadratic tracking problem for discrete‐time systems with multiple delays in single input channel

Abstract

SUMMARYThe linear quadratic tracking problem for discrete-time systems with multiple delays in single input channel is considered. In this paper, we provide an approach without resorting to system state augmentation. The optimal tracking control is given in terms of the current state, the previous inputs, and the output of an auxiliary backward deterministic delay system which is formulated for the first time in this paper. The solution relies on a Riccati difference equation of the same dimension as the plant (ignoring the delays). The key to our development is the establishment of a duality between the optimal tracking control and the optimal smoothing estimation of an associated stochastic backward system as well as the introduction of the auxiliary backward deterministic delay system. An analysis of the computational complexity of the proposed approach and its comparison with that of the augmentation method, which is to incorporate the delayed inputs into the augmented state, are provided. An example is given to demonstrate the effectiveness of the results.

Control of input/output delayed and disturbed unstable plants

“…In most cases, the input signal acts on the state through several terms related with delayed inputs. The control goal refers to the dynamic behavior of the state and ad hoc control design procedures are proposed, such as the linear quadratic regulator (LQR) [45], [40].…”

State feedback control for stochastic regular linear quadratic tracking problem with input time delay

“…For some recent works on problem of LQT, we refer the reader to the references 20‐27 . To be specific, polynomial input–output models have been employed in Reference 22 to present a new solution for the LQT problem for linear discrete‐time multivariable systems.…”

“…Based on the cost function, they have extracted a Bellman equation and an algebraic Riccati equation (ARE) to deal with the LQT problem. In Reference 24, the duality between the LQT problem and the optimal smoothing of the states and the noise for a stochastic backward delay system has been utilized to solve the LQT problem for multidelay discrete‐time systems in an individual input channel. The optimal control input has been expressed as a function of the present state, the past control input signals and the auxiliary backward delay system output.…”

NN-adaptive predictive control for a class of discrete-time nonlinear systems with input-delay

“…In the last decades, predictive control has been implemented successfully in many industrial control, and shows good performance (e.g., see [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]). In [16,17], the NN predictive control problems for nonlinear systems were investigated.…”