Modified ADMM algorithm for solving proximal bound formulation of multi-delay optimal control problem with bounded control

Document Type : Research Article

Author

• K.A. Dawodu

Department of Mathematical Sciences, The Federal University of technology Akure, Ondo-State, Nigeria.

10.22067/ijnao.2021.69185.1020

Abstract

 This study presents an algorithm for solving optimal control problems with the objective function of the Lagrange-type and multiple delays on both the state and control variables of the constraints, with bounds on the control variable. The full discretization of the objective functional and the multiple delay constraints is carried out by using the Simpson numerical scheme. The discrete recurrence relations generated from the discretization of both the objective functional and constraints are used to develop the matrix operators, which satisfy the basic spectral properties. The primal-dual residuals of the algorithm are derived in order to ascertain the rate of convergence of the algorithm, which performs faster when relaxed with an accelerator variant in the sense of Nesterov. The direct numerical approach for handling the multi-delay control problem is observed to obtain an accurate result at a faster rate of convergence when over-relaxed with an accelerator variant. This research problem is limited to linear constraints and objective functional of the Lagrange-type and can address real-life models with multiple delays as applicable to quadratic optimization of intensity modulated radiation theory planning. The novelty of this research paper lies in the method of discretization and its adaptation to handle linearly and proximal bound-constrained program formulated from the multiple delay optimal control problems.

Keywords

• Multi-delay
• ADMM
• Primal-dual
• Proximal operator

20.1001.1.24236977.2022.12.1.1.5

Main Subjects

• Optimal Control

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