scholarly journals On the discontinuity of the costates for optimal control problems with Coulomb friction

2001 ◽  
Vol 22 (4) ◽  
pp. 197-200 ◽  
Author(s):  
Brian J. Driessen ◽  
Nader Sadegh
Keyword(s):  
Optimal Control ◽  
Coulomb Friction ◽  
Optimal Control Problems ◽  
Control Problems

scholarly journals On the Discontinuity of the Costates for Optimal Control Problems With Coulomb Friction

2000 ◽  
Author(s):  
Brian J. Driessen ◽  
Nader Sadegh
Keyword(s):  
Optimal Control ◽  
Coulomb Friction ◽  
Optimal Control Problems ◽  
Minimum Time ◽  
Control Problems ◽  
Time Points ◽  
Discontinuous Functions ◽  
Time Problem ◽  
Switching Functions ◽  
Minimum Time Problem

Abstract This work points out that the costates are actually discontinuous functions of time for optimal control problems with Coulomb friction. In particular these discontinuities occur at the time points where the velocity of the system changes sign. To our knowledge, this has not been noted before. This phenomenon is demonstrated on a minimum-time problem with Coulomb friction and the consistency of discontinuous costates and switching functions with respect to the input switches is shown.

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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