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.

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numerical optimal approach hybrid basis nonlinear delaydependent state feedback suboptimal control systems states and input optimal open loop solution nlp legendre polynomials complex dynamic optimization problem kronecker tensor product nonlinear polynomial time delay systems nonlinear programming problem orthogonal base least square formalism hybrid of block pulse functions

Mohamed Karim Bouafoura,Naceur Benhadj Braiek,.Hybrid Functions Direct Approach and State Feedback Optimal Solutions for a Class of Nonlinear Polynomial Time Delay Systems. 2019 (),.

Mohamed Karim Bouafoura,Naceur Benhadj Braiek,"Hybrid Functions Direct Approach and State Feedback Optimal Solutions for a Class of Nonlinear Polynomial Time Delay Systems" 2019

Mohamed Karim Bouafoura,Naceur Benhadj Braiek,"Hybrid Functions Direct Approach and State Feedback Optimal Solutions for a Class of Nonlinear Polynomial Time Delay Systems"