scholarly journals Constants within Error Estimates for Legendre-Galerkin Spectral Approximations of Control-Constrained Optimal Control Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Jianwei Zhou
Keyword(s):  
Optimal Control ◽  
Error Estimate ◽  
Optimal Control Problems ◽  
Control Variable ◽  
Control Problems ◽  
Constrained Optimal Control ◽  
One Dimensional ◽  
Error Indicator ◽  
Spectral Approximations ◽  
Explicit Formulae

Explicit formulae of constants within the aposteriorierror estimate for optimal control problems are investigated with Legendre-Galerkin spectral methods. The constrained set is put on the control variable. For simpleness, one-dimensional bounded domain is taken. Meanwhile, the corresponding aposteriorierror indicator is established with explicit constants.

A Constraining Hyperplane Technique for State Variable Constrained Optimal Control Problems

1973 ◽  
Vol 95 (4) ◽  
pp. 380-389 ◽  
Author(s):  
K. Martensson
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Control Variable ◽  
Dynamic Programming Algorithm ◽  
Inequality Constraints ◽  
Programming Algorithm ◽  
Control Problems ◽  
State Control ◽  
Constrained Optimal Control ◽  
State Variable

A new approach to the numerical solution of optimal control problems with state-variable inequality constraints is presented. It is shown that the concept of constraining hyperplanes may be used to approximate the original problem with a problem where the constraints are of a mixed state-control variable type. The efficiency and the accuracy of the combination of constraining hyperplanes and a second-order differential dynamic programming algorithm are investigated on problems of different complexity, and comparisons are made with the slack-variable and the penalty-function techniques.

scholarly journals The Constants in A Posteriori Error Indicator for State-Constrained Optimal Control Problems with Spectral Methods

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Jianwei Zhou
Keyword(s):  
Optimal Control ◽  
Spectral Methods ◽  
Optimal Control Problems ◽  
Posteriori Error ◽  
Control Problems ◽  
A Posteriori ◽  
A Posteriori Error ◽  
Constrained Optimal Control ◽  
Error Indicator ◽  
State Variable

We employ Legendre-Galerkin spectral methods to solve state-constrained optimal control problems. The constraint on the state variable is an integration form. We choose one-dimensional case to illustrate the techniques. Meanwhile, we investigate the explicit formulae of constants within a posteriori error indicator.

scholarly journals Nonlinearly constrained optimal control problems

1992 ◽  
Vol 33 (4) ◽  
pp. 517-530 ◽  
Author(s):  
K. L. Teo ◽  
K. H. Wong
Keyword(s):  
Optimal Control ◽  
General Class ◽  
State Constraints ◽  
Computational Algorithm ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Constrained Optimal Control ◽  
Continuous State ◽  
Constraint Transcription ◽  
Inequality Type

AbstractIn a paper by Teo and Jennings, a constraint transcription is used together with the concept of control parametrisation to devise a computational algorithm for solving a class of optimal control problems involving terminal and continuous state constraints of inequality type. The aim of this paper is to extend the results to a more general class of constrained optimal control problems, where the problem is also subject to terminal equality state constraints. For illustration, a numerical example is included.

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