scholarly journals Tensor method for optimal control problems constrained by fractional three‐dimensional elliptic operator with variable coefficients

2021 ◽  
Author(s):  
Britta Schmitt ◽  
Boris N. Khoromskij ◽  
Venera Khoromskaia ◽  
Volker Schulz
Keyword(s):  
Optimal Control ◽  
Elliptic Operator ◽  
Optimal Control Problems ◽  
Three Dimensional ◽  
Variable Coefficients ◽  
Control Problems ◽  
Tensor Method

scholarly journals On the structure of the singular set of solutions in one class of 3D time-optimal control problems

2021 ◽  
Vol 31 (3) ◽  
pp. 471-486
Author(s):  
A.A. Uspenskii ◽  
P.D. Lebedev
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Extreme Points ◽  
Time Optimal Control ◽  
Control Problems ◽  
Singular Set ◽  
Time Optimal ◽  
Characteristic Points

A class of time-optimal control problems in terms of speed in three-dimensional space with a spherical velocity vector is considered. A smooth regular curve $\Gamma$ was chosen as the target set. Pseudo-vertices — characteristic points on $\Gamma,$ responsible for the appearance of a singularity in the optimal result function, are selected. The characteristic features of the structure of a singular set belonging to the family of bisectors are revealed. An analytical representation is found for the extreme points of the bisector corresponding to a fixed pseudo-vertex. As an illustration of the effectiveness of the developed methods for solving nonsmooth dynamic problems, an example of the numerical-analytical construction of resolving structures of a control problem in terms of speed is given.

scholarly journals Optimal Control of a Formula One Car on a Three-Dimensional Track—Part 1: Track Modeling and Identification

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
Giacomo Perantoni ◽  
David J. N. Limebeer
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Three Dimensional ◽  
Curvilinear Coordinates ◽  
Gps Data ◽  
Control Problems ◽  
Formula One ◽  
Control Techniques ◽  
Optimal Smoothing ◽  
Race Track

The identification of three-dimensional (3D) race track models from noisy measured GPS data is treated as a problem in the differential geometry of curves and surfaces. Curvilinear coordinates are adopted to facilitate the use of the track model in the solution of vehicular optimal control problems. Our proposal is to model race tracks using a generalized Frenet–Serret apparatus, so that the track is specified in terms of three displacement-dependent curvatures and two edge variables. The optimal smoothing of the curvature and edge variables is achieved using numerical optimal control techniques. Track closure is enforced through the boundary conditions associated with the optimal control problem. The Barcelona formula one track is used as an illustrative example.

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.

Sweep Algorithm for Solving Discrete Optimal Control Problems with Three-point Boundary Conditions

2008 ◽  
Vol 40 (7) ◽  
pp. 48-58 ◽  
Author(s):  
Fikret Akhmed Ali Ogly Aliev ◽  
Rena Takhir kyzy Zulfugarova ◽  
Mutallim Mirzaakhmed ogly Mutallimov
Keyword(s):  
Optimal Control ◽  
Boundary Conditions ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Point Boundary ◽  
Discrete Optimal Control ◽  
Sweep Algorithm
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