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 Optimal Control of Mechanical Systems

2007 ◽  
Vol 2007 ◽  
pp. 1-16 ◽  
Author(s):  
Vadim Azhmyakov
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimization Problem ◽  
Multiobjective Programming ◽  
Optimal Control Problems ◽  
Auxiliary Problem ◽  
Control Problems ◽  
Hamilton Equations ◽  
Variational Structure

In the present work, we consider a class of nonlinear optimal control problems, which can be called “optimal control problems in mechanics.” We deal with control systems whose dynamics can be described by a system of Euler-Lagrange or Hamilton equations. Using the variational structure of the solution of the corresponding boundary-value problems, we reduce the initial optimal control problem to an auxiliary problem of multiobjective programming. This technique makes it possible to apply some consistent numerical approximations of a multiobjective optimization problem to the initial optimal control problem. For solving the auxiliary problem, we propose an implementable numerical algorithm.

OPTIMAL CONTROL OF A HYSTERESIS SYSTEM BY MEANS OF CO-OPERATIVE CO-EVOLUTION

2004 ◽  
Vol 04 (04) ◽  
pp. 321-336 ◽  
Author(s):  
KITTIPONG BOONLONG ◽  
NACHOL CHAIYARATANA ◽  
SUWAT KUNTANAPREEDA
Keyword(s):  
Genetic Algorithm ◽  
Optimal Control ◽  
Energy Cost ◽  
Optimal Control Problems ◽  
Hybrid Control ◽  
Space Representation ◽  
Control Problems ◽  
Programming Technique ◽  
Efficient Manner ◽  
State Space Representation

This paper presents the use of a co-operative co-evolutionary genetic algorithm (CCGA) for solving optimal control problems in a hysteresis system. The hysteresis system is a hybrid control system which can be described by a continuous multivalued state-space representation that can switch between two possible discrete modes. The problems investigated cover the optimal control of the hysteresis system with fixed and free final state/time requirements. With the use of the Pontryagin maximum principle, the optimal control problems can be formulated as optimisation problems. In this case, the decision variables consist of the value of control signal when a switch between discrete modes occurs while the objective value is calculated from an energy cost function. The simulation results indicate that the use of the CCGA is proven to be highly efficient in terms of the minimal energy cost obtained in comparison to the results given by the searches using a standard genetic algorithm and a dynamic programming technique. This helps to confirm that the CCGA can handle complex optimal control problems by exploiting a co-evolutionary effect in an efficient manner.

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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