Abstract:
A terminal control problem with linear dynamics and a boundary condition given implicitly in the form of a solution of a variational inequality is considered. In the general control theory, this problem belongs to the class of stabilization problems. A saddle-point method of the extragradient type is proposed for its solution. The method is proved to converge with respect to all components of the solution, i.e., with respect to controls, phase and adjoint trajectories, and the finite-dimensional variables of the terminal problem.
Key words:
linear dynamics, control, boundary value problem, variational inequality, saddle-point method, convergence.
This publication is cited in the following 12 articles:
Kubra Sanaullah, Saleem Ullah, Najla M. Aloraini, “A Self Adaptive Three-Step Numerical Scheme for Variational Inequalities”, Axioms, 13:1 (2024), 57
A. S. Antipin, E. V. Khoroshilova, “Synthesis of a Regulator for a Linear-Quadratic Optimal Control Problem”, Comput. Math. and Math. Phys., 64:9 (2024), 1921
Anatoly Antipin, Elena Khoroshilova, Lecture Notes in Computer Science, 13781, Optimization and Applications, 2022, 108
Kubra Sanaullah, Saleem Ullah, Muhammad Shoaib Arif, Kamaleldin Abodayeh, Rabia Fayyaz, Nawab Hussain, “Self-Adaptive Predictor-Corrector Approach for General Variational Inequalities Using a Fixed-Point Formulation”, Journal of Function Spaces, 2022 (2022), 1
Anatoly Antipin, Elena Khoroshilova, Lecture Notes in Computer Science, 13078, Optimization and Applications, 2021, 151
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F. S. Stonyakin, “On the Adaptive Proximal Method for a Class of Variational Inequalities and Related Problems”, Proc. Steklov Inst. Math. (Suppl.), 309, suppl. 1 (2020), S139–S150
A. V. Gasnikov, P. E. Dvurechenskii, F. S. Stonyakin, A. A. Titov, “An adaptive proximal method for variational inequalities”, Comput. Math. Math. Phys., 59:5 (2019), 836–841
A. S. Antipin, E. V. Khoroshilova, “Feedback synthesis for a terminal control problem”, Comput. Math. Math. Phys., 58:12 (2018), 1903–1918
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