Hybrid Functions Direct Approach and State Feedback Optimal Solutions for a Class of Nonlinear Polynomial Time Delay Systems. (2nd April 2019)

• Record Type: Journal Article
• Authors: Bouafoura, Mohamed Karim; Benhadj Braiek, Naceur
• Other Names: Aguirre-Hernandez Baltazar Guest Editor.
• Is Part Of: Complexity. Volume 2019(2019)
• Publication Date: 2019-04-02
• Subjects: Chaotic behavior in systems -- Periodicals; Complexity (Philosophy) -- Periodicals; 003
• DOI: 10.1155/2019/9596253
• Languages: English
• ISSNs: 1076-2787

Abstract

Abstract : The aim of this paper is to determine the optimal open loop solution and a nonlinear delay-dependent state feedback suboptimal control for a class of nonlinear polynomial time delay systems. The proposed method uses a hybrid of block pulse functions and Legendre polynomials as an orthogonal base for system's states and input expansion. Hence, the complex dynamic optimization problem is then reduced, with the help of operational properties of the hybrid basis and Kronecker tensor product lemmas, to a nonlinear programming problem that could be solved with available NLP solvers. A practical nonlinear feedback controller gains are deduced with respect to a least square formalism based on the optimal open loop control results. Simulation results show efficiency of the proposed numerical optimal approach.