scholarly journals Optimal Control of Evolution Macro-Hybrid Mixed Variational Inclusions

2017 ◽  
Vol 9 (6) ◽  
pp. 124 ◽  
Author(s):  
Gonzalo Alduncin
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Conjugate Duality ◽  
Control Problems ◽  
Reflexive Banach Spaces ◽  
Duality Method ◽  
Constrained Problems ◽  
Primal And Dual ◽  
Dual Evolution ◽  
Appl Math

Optimal control problems governed by primal and dual evolution macro-hybrid mixed variational state inclusions, in reflexive Banach spaces, are studied. This is a spatially localized macro-hybrid variational version of our mixed optimal control theory published in Appl. Math. Optim. 68, 2013, 445-473, where the solvability analysis of the state systems is given in terms of duality principles, and the mixed optimality analysis is performed via a perturbation conjugate duality method. Applications to nonlinear constrained problems from mechanics exemplify the theory.

scholarly journals Conjugate duality in stochastic controls with delay

2017 ◽  
Vol 49 (4) ◽  
pp. 1011-1036
Author(s):  
Zimeng Wang ◽  
David J. Hodge ◽  
Huiling Le
Keyword(s):  
Optimal Control ◽  
Stochastic Optimal Control ◽  
Optimal Control Problems ◽  
Maximum Principles ◽  
Conjugate Duality ◽  
Control Problems ◽  
Convex Problem ◽  
Stochastic Controls ◽  
The Relationship ◽  
Equations With Delay

AbstractIn this paper we use the method of conjugate duality to investigate a class of stochastic optimal control problems where state systems are described by stochastic differential equations with delay. For this, we first analyse a stochastic convex problem with delay and derive the expression for the corresponding dual problem. This enables us to obtain the relationship between the optimalities for the two problems. Then, by linking stochastic optimal control problems with delay with a particular type of stochastic convex problem, the result for the latter leads to sufficient maximum principles for the former.

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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