Turnpike solutions in optimal control problems for quantum-mechanical systems

2011 ◽  
Vol 72 (6) ◽  
pp. 1248-1257 ◽  
Author(s):  
V. I. Gurman
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Mechanical Systems ◽  
Quantum Mechanical ◽  
Control Problems ◽  
Quantum Mechanical Systems

scholarly journals On a Variational Approach to Optimization of Hybrid Mechanical Systems

2010 ◽  
Vol 2010 ◽  
pp. 1-13 ◽  
Author(s):  
Vadim Azhmyakov ◽  
Ruben Velazquez
Keyword(s):  
Optimal Control ◽  
Multiobjective Optimization ◽  
Optimal Control Problems ◽  
Hybrid Control ◽  
Mechanical Systems ◽  
Optimization Techniques ◽  
Control Problems ◽  
Variational Structure ◽  
Dynamical Optimization ◽  
Hybrid Control Systems

This paper deals with multiobjective optimization techniques for a class of hybrid optimal control problems in mechanical systems. We deal with general nonlinear hybrid control systems described by boundary-value problems associated with hybrid-type Euler-Lagrange or Hamilton equations. The variational structure of the corresponding solutions makes it possible to reduce the original “mechanical” problem to an auxiliary multiobjective programming reformulation. This approach motivates possible applications of theoretical and computational results from multiobjective optimization related to the original dynamical optimization problem. We consider first order optimality conditions for optimal control problems governed by hybrid mechanical systems and also discuss some conceptual algorithms.

scholarly journals A Dissipativity Characterization of Velocity Turnpikes in Optimal Control Problems for Mechanical Systems

2021 ◽  
Vol 54 (9) ◽  
pp. 624-629
Author(s):  
Timm Faulwasser ◽  
Kathrin Flaßkamp ◽  
Sina Ober-Blöbaum ◽  
Karl Worthmann
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Mechanical Systems ◽  
Control Problems

On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems

2020 ◽  
Vol 26 ◽  
pp. 41
Author(s):  
Tianxiao Wang
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Open Loop ◽  
Time Inconsistency ◽  
Control Problems ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Equilibrium Strategies

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.

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