LQR for Generalized Systems Using Metaheuristic Algorithms Based on Disturbance Observer

Abstract

In this paper, the linear quadratic regulator (LQR) optimal control of constrained dynamic systems for generalized systems with external disturbances is designed. At first, a generalized system is given, this model includes some ordinary differential equations (ODEs) and some algebraic equations as a constraint on dynamics. In this paper, we address the optimal LQR control for continuous linear generalized systems in which the system has only finite dynamic modes. In the LQR problem, we derive a Riccati equation in each case. Then a linear disturbance observer is proposed to estimate the disturbance. Then, we propose four types of metaheuristic algorithms such as grasshopper optimization algorithm (GOA), grey wolf optimizer (GWO), genetic algorithm (GA), and particle swarm optimization (PSO) with a suitable structure for solving Riccati equation. In each case, the solution obtained by GOA, GWO, GA, and PSO. Simulation results demonstrate the good performance of the proposed methods.