Consistent Approximations for Optimal Control Problems Based on Runge--Kutta Integration

Authors:
A. Schwartz;E. Polak
Affiliations:
-;-
Venue:
SIAM Journal on Control and Optimization
Year:
1996

Citing 0
Cited 11

Photo, Biography and Selected Publications of Professor Elijah Polak

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Approximate Gradient Projection Method with Runge-Kutta Schemes for Optimal Control Problems

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Discretization methods for optimal control problems with state constraints

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Brief paper: Optimal soft landing control for moon lander

Automatica (Journal of IFAC)
Convergence rates for direct transcription of optimal control problems using collocation at Radau points

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Discretization methods for optimal control problems with state constraints

Journal of Computational and Applied Mathematics
Discretization-optimization methods for optimal control problems

SMO'05 Proceedings of the 5th WSEAS international conference on Simulation, modelling and optimization
Approximate gradient/penalty methods with general discretization schemes for optimal control problems

LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
Approximations with error estimates for optimal control problems for linear systems

LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
Fast, accurate, and small-scale direct trajectory optimization using a Gegenbauer transcription method

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On sample size control in sample average approximations for solving smooth stochastic programs

Computational Optimization and Applications

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Abstract

This paper explores the use of Runge--Kutta integration methods in the construction of families of finite-dimensional, consistent approximations to nonsmooth, control and state constrained optimal control problems. Consistency is defined in terms of epiconvergence of the approximating problems and hypoconvergence of their optimality functions. A significant consequence of this concept of consistency is that stationary points and global solutions of the approximating discrete-time optimal control problems can only converge to stationary points and global solutions of the original optimal control problem. The construction of consistent approximations requires the introduction of appropriate finite-dimensional subspaces of the space of controls and the extension of the standard Runge--Kutta methods to piecewise-continuous functions.It is shown that in solving discrete-time optimal control problems that result from Runge--Kutta integration, a non-Euclidean inner product and norm must be used on the control space to avoid potentially serious ill-conditioning effects.