Should controls be eliminated while solving optimal control problems via direct methods?

1995 ◽  
Author(s):  
Renjith Kumar ◽  
Hans Seywald
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Direct Methods ◽  
Control Problems

Direct methods with maximal lower bound for mixed-integer optimal control problems

2007 ◽  
Vol 118 (1) ◽  
pp. 109-149 ◽  
Author(s):  
Sebastian Sager ◽  
Hans Georg Bock ◽  
Gerhard Reinelt
Keyword(s):  
Optimal Control ◽  
Lower Bound ◽  
Optimal Control Problems ◽  
Direct Methods ◽  
Mixed Integer ◽  
Control Problems

scholarly journals Feedback Control Method Using Haar Wavelet Operational Matrices for Solving Optimal Control Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Waleeda Swaidan ◽  
Amran Hussin
Keyword(s):  
Optimal Control ◽  
Feedback Control ◽  
Optimal Control Problems ◽  
Control Method ◽  
Numerical Technique ◽  
Direct Methods ◽  
Haar Wavelet ◽  
Control Problems ◽  
Operational Matrices ◽  
Feedback Control Method

Most of the direct methods solve optimal control problems with nonlinear programming solver. In this paper we propose a novel feedback control method for solving for solving affine control system, with quadratic cost functional, which makes use of only linear systems. This method is a numerical technique, which is based on the combination of Haar wavelet collocation method and successive Generalized Hamilton-Jacobi-Bellman equation. We formulate some new Haar wavelet operational matrices in order to manipulate Haar wavelet series. The proposed method has been applied to solve linear and nonlinear optimal control problems with infinite time horizon. The simulation results indicate that the accuracy of the control and cost can be improved by increasing the wavelet resolution.

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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