Symmetries in left-invariant optimal control problems

Quasi-Invariant Optimal Control Problems

Quasi-Invariant Optimal Control Problems

We study in optimal control the important relation between invariance of the problem under a family of transformations, and the existence of preserved quantities along the Pontryagin extremals. Several extensions of Noether theorem are provided, in the direction which enlarges the scope of its application. We formulate a more general version of Noether’s theorem for optimal control problems, wh...

Solving optimal control problems by PSO-SVM

The optimal control of problem is about finding a control law for a given system such that a certain optimality criterion is achieved. Methods of solving the optimal control problems are divided into direct methods and mediated methods (through other equations). In this paper, the PSO- SVM indirect method is used to solve a class of optimal control problems. In this paper, we try to determine t...

A New Optimal Solution Concept for Fuzzy Optimal Control Problems

In this paper, we propose the new concept of optimal solution for fuzzy variational problems based on the possibility and necessity measures. Inspired by the well–known embedding theorem, we can transform the fuzzy variational problem into a bi–objective variational problem. Then the optimal solutions of fuzzy variational problem can be obtained by solving its corresponding biobjective variatio...

Self-Invariant Contact Symmetries

Every smooth second-order scalar ordinary differential equation (ODE) that is solved for the highest derivative has an infinite-dimensional Lie group of contact symmetries. However, symmetries other than point symmetries are generally difficult to find and use. This paper deals with a class of one-parameter Lie groups of contact symmetries that can be found and used. These symmetry groups have ...