scholarly journals Maxwell Points of Dynamical Control Systems Based on Vertical Rolling Disc—Numerical Solutions

Robotics ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 88
Author(s):  
Marek Stodola ◽  
Matej Rajchl ◽  
Martin Brablc ◽  
Stanislav Frolík ◽  
Václav Křivánek
Keyword(s):  
Optimal Control ◽  
Control Systems ◽  
Optimal Control Problems ◽  
Numerical Solutions ◽  
Control Problems ◽  
Affine Control Systems ◽  
Dynamical Control ◽  
And Control ◽  
Analytical Approaches ◽  
Maxwell Points

We study two nilpotent affine control systems derived from the dynamic and control of a vertical rolling disc that is a simplification of a differential drive wheeled mobile robot. For both systems, their controllable Lie algebras are calculated and optimal control problems are formulated, and their Hamiltonian systems of ODEs are derived using the Pontryagin maximum principle. These optimal control problems completely determine the energetically optimal trajectories between two states. Then, a novel numerical algorithm based on optimisation for finding the Maxwell points is presented and tested on these control systems. The results show that the use of such numerical methods can be beneficial in cases where common analytical approaches fail or are impractical.

scholarly journals OPTIMAL CONTROL REALIZATIONS OF LAGRANGIAN SYSTEMS WITH SYMMETRY

2011 ◽  
Vol 08 (07) ◽  
pp. 1627-1651 ◽  
Author(s):  
M. DELGADO-TÉLLEZ ◽  
A. IBORT ◽  
T. RODRÍGUEZ DE LA PEÑA
Keyword(s):  
Optimal Control ◽  
Control Systems ◽  
Optimal Control Problems ◽  
Lagrangian System ◽  
Control Problems ◽  
Lagrangian Systems ◽  
Explicit Realization ◽  
Control Equation ◽  
And Control

A new relation among a class of optimal control systems and Lagrangian systems with symmetry is discussed. It will be shown that a family of solutions of optimal control systems whose control equation are obtained by means of a group action are in correspondence with the solutions of a mechanical Lagrangian system with symmetry. This result also explains the equivalence of the class of Lagrangian systems with symmetry and optimal control problems discussed in [1, 2]. The explicit realization of this correspondence is obtained by a judicious use of Clebsch variables and Lin constraints, a technique originally developed to provide simple realizations of Lagrangian systems with symmetry. It is noteworthy to point out that this correspondence exchanges the role of state and control variables for control systems with the configuration and Clebsch variables for the corresponding Lagrangian system. These results are illustrated with various simple applications.

scholarly journals Optimal control of affine connection control systems from the point of view of Lie algebroids

2014 ◽  
Vol 11 (09) ◽  
pp. 1450038 ◽  
Author(s):  
Lígia Abrunheiro ◽  
Margarida Camarinha
Keyword(s):  
Optimal Control ◽  
Vector Field ◽  
Control Systems ◽  
Lie Groups ◽  
Optimal Control Problems ◽  
Affine Connection ◽  
Point Of View ◽  
Lie Algebroids ◽  
Control Problems ◽  
Hamiltonian Vector Field

The purpose of this paper is to use the framework of Lie algebroids to study optimal control problems (OCPs) for affine connection control systems (ACCSs) on Lie groups. In this context, the equations for critical trajectories of the problem are geometrically characterized as a Hamiltonian vector field.

scholarly journals A global method for some class of optimization and control problems

2000 ◽  
Vol 23 (9) ◽  
pp. 605-616 ◽  
Author(s):  
R. Enkhbat
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Convex Function ◽  
Control Problem ◽  
Optimality Condition ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Global Method ◽  
Optimization And Control ◽  
And Control

The problem of maximizing a nonsmooth convex function over an arbitrary set is considered. Based on the optimality condition obtained by Strekalovsky in 1987 an algorithm for solving the problem is proposed. We show that the algorithm can be applied to the nonconvex optimal control problem as well. We illustrate the method by describing some computational experiments performed on a few nonconvex optimal control problems.

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