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ABSTRACT
Optimal control theory analyzes how to optimize dynamical systems with various criteria: reaching a target in minimal time or with minimal energy, maximizing the efficiency of an industrial process, etc. This involves the optimization of both time-independent parameters and of the control variables that are a function of time. This article analyzes the first- and second-order optimality conditions, and how to solve them by time discretization, the shooting algorithm, or dynamic programming.
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-
J. Frédéric BONNANS: INRIA Research Director - INRIA and Center for Applied Mathematics, Ecole Polytechnique, Palaiseau
INTRODUCTION
A dynamic system is said to be controlled if it can be acted upon by time-dependent variables, known as commands. Let's illustrate this concept in the case of a spacecraft, described by position and velocity variables (in
) h and V, and a mass m > 0, i.e. 7 state variables. The dynamics are, omitting the time argument,
,
and
. Here c is a positive constant and F (h, V) corresponds to the forces of gravity and (where applicable) aerodynamics. The control is the applied force, whose Euclidean norm is denoted by
, subjected to a constraint of the type
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KEYWORDS
dynamical systems | path following | minimal time | shooting algorithm | dynamical programming
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