Discrete Time Predictive Control with Dual State System Around Unstable Origin Case Study

Abstract

Fulfilling asymptotic stability of Model Predictive Control formulation is not an easy task. Concepts like terminal cost and terminal region are often required. Previously developed approaches provide lesser options for the terminal region computation. Current work presents an approach based on linear quadratic regulator with a explanatory case study. The approach involves finding solution in the steady state to Lyapunov equations and later simulating the discrete time con-troller. A standard dual state mathematically complex system is chosen for demonstration. Larger terminal regions assist in making some otherwise infeasible initial conditions feasible with prediction and control horizon length of 1. Area of terminal region computed using LQR based approach is approximately 9.5 times bigger than the area of the terminal region computed using the literature approach.