Predictive control for a class of distributed delay systems using Chebyshev polynomials

Abstract

In this paper, the model predictive control (MPC) is developed for linear time-varying systems with distributed time delay in state. The Chebyshev operational matrices of product, integration and delay are utilized to transform the solution of distributed delay differential equation to the solution of algebraic equations. The Chebyshev functions are also applied to derive approximate solution of finite horizon optimal control problem involved in MPC. The proposed method is simple and computationally advantageous. Illustrative example demonstrates the validity and applicability of the technique.

Keywords:

• distributed delay system
• model predictive control
• Chebyshev polynomials

2000 AMS Subject Classification :

• 49J25