Hybrid Functions Direct Approach and State Feedback Optimal Solutions for a Class of Nonlinear Polynomial Time Delay Systems

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...

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Bibliographic Details
Published in:Complexity (New York, N.Y.) N.Y.), 2019-01, Vol.2019 (2019), p.1-14
Main Authors: Bouafoura, Mohamed Karim, Benhadj Braiek, Naceur
Format: Article
Language:English
Subjects:
Computer simulation
Control systems
Feedback control
Functions (mathematics)
Nonlinear control
Nonlinear feedback
Nonlinear programming
Nonlinear systems
Optimization
Polynomials
Solvers
State feedback
Tensors
Time delay systems
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Summary: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.
ISSN:1076-2787
1099-0526
DOI:10.1155/2019/9596253