An extension of linear-quadratic regulator trend to determine near optimal performance of nonlinear systems using evolutionary algorithms

Abstract

The optimal control theory is focused on operating dynamic systems at minimum cost where cost would be defined as a function of time, the control effort, or a combination of both. Linear-quadratic regulator (LQR), as one of the well-known methods in this field, deals with obtaining an optimum control input for linear systems. In this study, we have proposed a novel method to employ the linear-quadratic regulator solution of a linearised system towards determining near-optimal performance for the corresponding nonlinear system. The LQR solution is used in this method to determine either the starting point or boundaries of the search domain. Next, an optimisation technique such as particle swarm optimisation (PSO), genetic algorithm (GA) or ant colony optimisation (ACO) can be used to find the near-optimal parameters for the employed controller unit. It should be noted that the controller unit can operate based on any modern control concept such as sliding mode control (SMC) or primitive partial-integral-derivative (PID) control commonly used in industrial applications for the ease-of-use and reliability it provides. Performance of the proposed technique is evaluated for the attitude control of a flexible micro-satellite. Numerical simulations are employed in conjunction with experimental results from a hardware-in-the-loop (HITL) test-bed. Results show superior performance of the proposed methodology compared to existing literature.