Neural Networks Solving Free and Fixed Final Time Optimal Control Problems

2014 ◽  
Vol 24 (02) ◽  
pp. 1440002
Author(s):  
Tibor Kmet
Keyword(s):  
Neural Network ◽  
Optimal Control ◽  
State Constraints ◽  
Optimal Control Problems ◽  
Time Optimal Control ◽  
Control Problems ◽  
Final Time ◽  
Adaptive Critic ◽  
Time Optimal ◽  
Control And State Constraints

In this paper, the neural network based optimal control synthesis is presented for solving free and fixed final time optimal control problems with the control and state constraints. The optimal control problem is transcribed into a nonlinear programming problem, which is implemented with the adaptive critic neural network. The proposed simulation methods are illustrated by the optimal control problem of photosynthetic production and the nitrogen transformation cycle model. The results show that the adaptive critic based systematic approach is promising in obtaining free and fixed final time optimal control with the control and state constraints.

scholarly journals The Adjoint Method for Time-Optimal Control Problems

2020 ◽  
Vol 16 (2) ◽  
Author(s):  
Philipp Eichmeir ◽  
Thomas Lauß ◽  
Stefan Oberpeilsteiner ◽  
Karin Nachbagauer ◽  
Wolfgang Steiner
Keyword(s):  
Optimal Control ◽  
Time Domain ◽  
Adjoint Method ◽  
Optimal Control Problems ◽  
Hybrid Approach ◽  
Time Optimal Control ◽  
Adjoint Equations ◽  
Control Problems ◽  
Final Time ◽  
Time Optimal

Abstract In this article, we discuss a special class of time-optimal control problems for dynamic systems, where the final state of a system lies on a hyper-surface. In time domain, this endpoint constraint may be given by a scalar equation, which we call transversality condition. It is well known that such problems can be transformed to a two-point boundary value problem, which is usually hard to solve, and requires an initial guess close to the optimal solution. Hence, we propose a new gradient-based iterative solution strategy instead, where the gradient of the cost functional, i.e., of the final time, is computed with the adjoint method. Two formulations of the adjoint method are presented in order to solve such control problems. First, we consider a hybrid approach, where the state equations and the adjoint equations are formulated in time domain but the controls and the gradient formula are transformed to a spatial variable with fixed boundaries. Second, we introduce an alternative approach, in which we carry out a complete elimination of the time coordinate and utilize a formulation in the space domain. Both approaches are robust with respect to poor initial controls and yield a shorter final time and, hence, an improved control after every iteration. The presented method is tested with two classical examples from satellite and vehicle dynamics. However, it can also be extended to more complex systems, which are used in industrial applications.

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