Nonlinearly constrained optimal control problems

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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LIPSCHITZ CONTINUITY OF THE MEASURE LAGRANGE MULTIPLIER FROM THE MAXIMUM PRINCIPLE FOR OPTIMAL CONTROL PROBLEMS WITH STATE CONSTRAINTS OF EQUALITY AND INEQUALITY TYPE

Tambov University Reports Series Natural and Technical Sciences ◽

10.20310/1810-0198-2017-22-3-508-516 ◽

2017 ◽

Vol 22 (3) ◽

pp. 508-516

Author(s):

A.V. Gorbacheva ◽

◽

D.Yu. Karamzin ◽

Keyword(s):

Optimal Control ◽

Maximum Principle ◽

Lagrange Multiplier ◽

State Constraints ◽

Optimal Control Problems ◽

Lipschitz Continuity ◽

Control Problems ◽

The Maximum Principle ◽

Inequality Type

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Primal-Dual Active Set Strategy for a General Class of Constrained Optimal Control Problems

SIAM Journal on Optimization ◽

10.1137/s1052623499358008 ◽

2002 ◽

Vol 13 (2) ◽

pp. 321-334 ◽

Cited By ~ 60

Author(s):

K. Kunisch ◽

A. Rösch

Keyword(s):

Optimal Control ◽

General Class ◽

Optimal Control Problems ◽

Control Problems ◽

Active Set ◽

Constrained Optimal Control ◽

Active Set Strategy ◽

Primal Dual

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On a Fully Adaptive SQP Method for PDAE-Constrained Optimal Control Problems with Control and State Constraints

International Series of Numerical Mathematics - Trends in PDE Constrained Optimization ◽

10.1007/978-3-319-05083-6_7 ◽

2014 ◽

pp. 85-108

Author(s):

Stefanie Bott ◽

Debora Clever ◽

Jens Lang ◽

Stefan Ulbrich ◽

Jan Carsten Ziems ◽

...

Keyword(s):

Optimal Control ◽

State Constraints ◽

Optimal Control Problems ◽

Control Problems ◽

Sqp Method ◽

Constrained Optimal Control ◽

Fully Adaptive ◽

Control And State Constraints

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Nonlinearly constrained optimal control problems involving piecewise smooth controls

The Journal of the Australian Mathematical Society Series B Applied Mathematics ◽

10.1017/s0334270000008407 ◽

1990 ◽

Vol 32 (2) ◽

pp. 151-179 ◽

Cited By ~ 1

Author(s):

K. L. Teo ◽

K. K. Leong ◽

G. J. Goh

Keyword(s):

Optimal Control ◽

Optimal Control Problems ◽

Optimal Parameter ◽

Numerical Approach ◽

Piecewise Smooth ◽

Control Problems ◽

Dynamic Optimisation ◽

Constrained Optimal Control ◽

Continuous State ◽

Smooth Controls

AbstractIn this paper, we consider a class of optimal control problems involving inequality continuous-state constraints in which the control is piecewise smooth. The requirement for this type of control is more stringent than that for the control considered in standard optimal control problems in which the controls are usually taken as bounded measurable functions. In this paper, we shall show that this class of optimal control problems can easily be transformed into an equivalent class of combined optimal parameter selection and optimal control problems. We shall then use the control parametrisation technique to devise a computational algorithm for solving this equivalent dynamic optimisation problem. Furthermore, convergence analysis will be given to support this numerical approach. For illustration, two nontrivial optimal control problems involving transferring cargo via a container crane will be solved using the proposed approach.

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