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

Authors: Amirhossein Ahadi; Afshin Rahimi; Reza Khoshrooz Azad; Sogol Bandehali

Addresses: Mechanical and Industrial Engineering Department, Ryerson University, Toronto, EPH-413, 87 Gerrard St East, Ontario, M5B 2K3, Canada ' Aerospace Engineering Department, Ryerson University, Toronto, Ontario, M5B2K3, Canada ' Aerospace Engineering Department, Sharif University, 1392, Tehran, Iran ' Civil Engineering Department, Ryerson University, M5B2K3, Toronto, Ontario, Canada

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.

Keywords: nonlinear systems; near-optimal tuning; evolutionary algorithms; attitude control; flexible satellites; genetic algorithms; particle swarm optimisation; PSO; ant colony optimisation; ACO; linear quadratic regulator; LQR; optimal control theory; sliding mode control; SMC; PID control; micro-satellites; numerical simulation; hardware-in-the-loop; HITL.

DOI: 10.1504/IJSPACESE.2015.072346

International Journal of Space Science and Engineering, 2015 Vol.3 No.2, pp.171 - 198

Received: 26 May 2015
Accepted: 06 Jul 2015
Published online: 09 Oct 2015 *

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