An Improved Memory State Feedback RMPC for Uncertain Constrained Linear Systems with Multiple Uncertain Delays

Bing He,Gang Liu,Pengtao Zhao,Weiwei Qin

doi:10.1155/2015/659176

Bing He, Gang Liu + Show 2 more

Open Access

https://doi.org/10.1155/2015/659176

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Abstract

The problem of robust asymptotic stabilization is considered for a class of discrete-time uncertain linear systems with multiple uncertain time-delayed states and input constraints. Compared with other works in the literature, the proposed approach takes the information of the delayed states with the estimated time-delays indices into full consideration. Based on the predictive control principle of receding horizon optimization and Lyapunov stability theory combined with linear matrix inequalities (LMIs) techniques, a time-delayed state dependent quadratic function is considered for incorporating MPC problem formulation. The robust MPC problem is formulated to minimize the upper bound of infinite horizon cost that satisfies the sufficient conditions. The proposed approach allows for the synthesis of robust memory state feedback controllers with respect to uncertainties on the implemented delay. Since developing the improved memory state feedback controller, the novel improved method is much less conservative and more general. Finally, the numerical simulation results prove availability of the proposed method.

Highlights

Model predictive control (MPC), known as receding horizon control, is a mature technology and has become the standard approach for implementing constrained, multivariable control in the process industries today
MPC provides an integrated solution for controlling systems with interacting variables, complex dynamics, and constraints [1,2,3]
We propose a new MPC algorithm for a multiple uncertain state delayed system (1), in which the gain matrices K(k) and Kd1(k), . . . , Kdl(k) of the memory state feedback controller (7) are determined from the new sufficient condition for cost monotonicity

Summary

Introduction

Model predictive control (MPC), known as receding horizon control, is a mature technology and has become the standard approach for implementing constrained, multivariable control in the process industries today. A memory state feedback RMPC for uncertain linear systems with multiple known time-delayed states was proposed in [7]. An MPC algorithm for uncertain timevarying systems with input constraints and state-delay was proposed in [8], and the delay was assumed unknown but with a known upper bound. A robust MPC algorithm for a class of uncertain multiple state and input time-delay systems with nonlinear disturbance was proposed in [17]. We propose a novel delay-dependent RMPC algorithm for a class of linear uncertain systems with multiple uncertain time-delayed states and input constraints, by taking the information of the multiple delayed states with estimated time-delay indices into full consideration.

Problem Statement

Delay-Dependent Robust Model Predictive Controller

Main Result

Numerical Example

Conclusions

Conflict of Interests