10 The Calculus of Variations, Functional Analysis, and Optimal Control Problems

1967 ◽  
pp. 417-461 ◽  
Author(s):  
E.K. Blum
Keyword(s):  
Optimal Control ◽  
Functional Analysis ◽  
Calculus Of Variations ◽  
Optimal Control Problems ◽  
Control Problems

Suboptimal control of fractional-order dynamic systems with delay argument

2017 ◽  
Vol 24 (12) ◽  
pp. 2430-2446 ◽  
Author(s):  
Amin Jajarmi ◽  
Dumitru Baleanu
Keyword(s):  
Optimal Control ◽  
Linear Programming ◽  
Calculus Of Variations ◽  
Fractional Order ◽  
Optimal Control Problems ◽  
Fractional Integration ◽  
Suboptimal Control ◽  
Control Problems ◽  
Lagrange Equations ◽  
Delay Argument

In this paper, an efficient linear programming formulation is proposed for a class of fractional-order optimal control problems with delay argument. By means of the Lagrange multiplier in the calculus of variations and using the formula for fractional integration by parts, the Euler–Lagrange equations are derived in terms of a two-point fractional boundary value problem including an advance term as well as the delay argument. The derived equations are then reduced into a linear programming problem by using a Grünwald–Letnikov approximation for the fractional derivatives and introducing a new transformation in the calculus of variations. The new scheme is also effective for the delay fractional optimal control problems influenced by the external persistent disturbances. Numerical simulations and comparative results verify that the proposed approach is efficient and easy to implement.

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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