scholarly journals A computational method for free time optimal control problems, with application to maximizing the range of an aircraft-like projectile

1987 ◽  
Vol 28 (3) ◽  
pp. 393-413 ◽  
Author(s):  
K. L. Teo ◽  
G. Jepps ◽  
E. J. Moore ◽  
S. Hayes
Keyword(s):  
Optimal Control ◽  
Computational Algorithm ◽  
Optimal Control Problems ◽  
Computational Method ◽  
Control Problems ◽  
Control Parametrization ◽  
Final Time ◽  
Final State ◽  
Method Of Solution ◽  
Time Optimal

AbstractA class of non-standard optimal control problems is considered. The non-standard feature of these optimal control problems is that they are of neither fixed final time nor of fixed final state. A method of solution is devised which employs a computational algorithm based on control parametrization techniques. The method is applied to the problem of maximizing the range of an aircraft-like gliding projectile with angle of attack control.

scholarly journals ON DIFFERENTIATION OF FUNCTIONALS OF APPROXIMATING PROBLEMS IN THE FRAME OF SOLUTION OF FREE TIME OPTIMAL CONTROL PROBLEMS BY THE SLIDING NODES METHOD

2018 ◽  
pp. 861-876
Author(s):  
Andrei Vladimirovich Chernov
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Free Time ◽  
Time Optimal Control ◽  
Control Problems ◽  
Control Parametrization ◽  
Derivative Formulas ◽  
Control Parametrization Technique ◽  
Time Optimal ◽  
And Control

We give strict justification for derivative formulas of functionals in problems approximating free time optimal control problems in the frame of sliding nodes method and control parametrization technique. As example we present results of numerical solution for landing on the Moon problem.

scholarly journals On a computational algorithm for time-laǵ optimal control problems with restricted phase coordinates

1980 ◽  
Vol 21 (4) ◽  
pp. 385-397 ◽  
Author(s):  
K. L. Teo ◽  
B. D. Craven
Keyword(s):  
Optimal Control ◽  
Computational Algorithm ◽  
Optimal Control Problems ◽  
Time Lag ◽  
Computational Method ◽  
Control Problems ◽  
Phase Coordinates

AbstractIn this paper we present a computational method for solving a class of time-lag optimal control problems with restricted phase coordinates.

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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