An iterative method for suboptimal control of a class of nonlinear time-delayed systems |
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Authors: | Seyed Mehdi Mirhosseini-Alizamini |
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Affiliation: | Department of Mathematics, Payame Noor University (PNU)
, Tehran, Iran |
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Abstract: | This work presents an approximate solution method for the infinite-horizon nonlinear time-delay optimal control problem. A variational iteration method (VIM) is applied to design feedforward and feedback optimal controllers. By using the VIM, the original optimal control is transformed into a sequence of nonhomogeneous linear two-point boundary value problems (TPBVPs). The existence and uniqueness of the optimal control law are proved. The optimal control law obtained consists of an accurate linear feedback term and a nonlinear compensation term which is the limit of an adjoint vector sequence. The feedback term is determined by solving Riccati matrix differential equation. By using the finite-step iteration of a nonlinear compensation sequence, we can obtain a suboptimal control law. Simulation results demonstrate the validity and applicability of the VIM. |
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Keywords: | Delay optimal control problems Pontryagin's maximum principle Riccati differential equation variational iteration method Lyapunov function converse optimal control method |
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