Complexity reduction of Robust Model Predictive Controller for uncertain Piecewise Affine Systems

Abstract

This paper considers discrete-time, uncertain Piecewise Affine (PWA) systems affected by both polytopic parameter variations and bounded disturbances. We are interested in the Robust Model Predictive Control (RMPC) for uncertain PWA systems where the uncertainty can be presented in polytopes framework. RMPC is known as a complex problem and indeed for PWA systems, the on-line computation becomes computationally burdensome and inapplicable. In this paper we develop a new algorithm that consists of three different phases, based on the system states location. The proposed algorithm gives a simple and fast sub-optimal solution which considerably reduces the on-line computation and guarantee to drive the system states to the target region in spite of the considered uncertainties. The proposed algorithm is applied in simulation to a two tanks example.

An efficient application of particle swarm optimization in model predictive control of constrained two-tank system

“…The two-tank [28] shown in Figure 1 is a basic benchmark model to investigate and analyze the control issues for PWA system. The tanks are filled by pump acting on tank 1, continuously manipulated from 0 up to a maximum flow Q1.…”

“…This model can be defined as a piecewise affine system of the shape (1), with four modes, depicted as takes after [28]: For example, the first mode of the system matrices is:…”