Title: An analytical approach to optimal control of nonlinear systems with input constraints

Authors: Reza Mojed Gharamaleki; Mehdi Mirzaei; Sadra Rafatnia; Behrooz Alizadeh

Addresses: Department of Mechanical Engineering, Sahand University of Technology, Tabriz, Iran ' Department of Mechanical Engineering, Sahand University of Technology, Tabriz, Iran ' Department of Mechanical Engineering, Sahand University of Technology, Tabriz, Iran ' Department of Applied Mathematics, Sahand University of Technology, Tabriz, Iran

Abstract: In this paper, a novel optimal control method with the analytical solution strategy is developed for a wide class of nonlinear systems with input constraints. First, an equivalent constrained optimisation problem is formulated by performing a quadratic performance index including the control inputs and the predicted tracking errors. Then, the problem is analytically solved by using the Kerush-Kuhn-Tucker (KKT) theorem to find the optimal control law. For comparison, a computational technique based on calling the genetic algorithm (GA) is also provided to online solving the developed optimisation problem. The proposed control method with two solutions is applied on a mathematical example and a chemical reactor which is a multi-input multi-output (MIMO) system. The results show that the proposed KKT-based predictive controller is effective from different aspects. Importantly, it is very fast, easy to solve and suitable for online implementation compared with the conventional nonlinear model predictive control (NMPC) method.

Keywords: constrained optimal control; nonlinear systems; prediction; optimisation; analytical solution.

DOI: 10.1504/IJAAC.2020.105519

International Journal of Automation and Control, 2020 Vol.14 No.2, pp.213 - 238

Received: 24 Feb 2018
Accepted: 14 Jul 2018
Published online: 03 Mar 2020 *

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