A near-optimal decentralized control approach for polynomial nonlinear interconnected systems. (April 2021)

• Record Type: Journal Article
• Authors: Attia, Mohamed Sadok; Bouafoura, Mohamed Karim; Benhadj Braiek, Naceur
• Is Part Of: Transactions of the Institute of Measurement and Control. Volume 43:Number 6(2021)
• Page Start: 1363
• Page End: 1375
• Publication Date: 2021-04
• Subjects: Decentralized control -- optimal control -- nonlinear systems -- Kronecker product -- stability analysis -- shifted Legendre polynomials; Automatic control -- Periodicals; Measuring instruments -- Periodicals; Commande automatique -- Périodiques; Mesure -- Instruments -- Périodiques; 681.2
• DOI: 10.1177/0142331220977433
• Languages: English
• ISSNs: 0142-3312

Abstract

This article tackles the decentralized near-optimal control problem for the class of nonlinear polynomial interconnected system based on a shifted Legendre polynomials direct approach. The proposed method converts the interconnected optimal control problems into a nonlinear programming one with multiple constraints. In light of the formulated NLP optimization, state and control coefficients are used to design a nonlinear decentralized state feedback controller. Overall closed-loop system stability sufficient conditions are investigated with the help of Grönwall lemma. The triple inverted pendulum case is considered for simulation. Satisfactory results are obtained in both open-loop and closed-loop schemes with comparison to collocation and state-dependent Riccati equation techniques.