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Numerical solution of optimal control problems by direct collocation. (English) Zbl 0790.49024
Bulirsch, R. (ed.) et al., Optimal control. Calculus of variations, optimal control theory and numerical methods. Basel: Birkhäuser. ISNM, Int. Ser. Numer. Math. 111, 129-143 (1993).
Summary: By an appropriate discretization of control and state variables, a constrained optimal control problem is transformed into a finite- dimensional nonlinear program which can be solved by standard SQP- methods. Convergence properties of the discretization are derived. From a solution of this method known as direct collocation, these properties are used to obtain reliable estimates of adjoint variables. In the presence of active state constraints, these estimates can be significantly improved by including the switching structure of the state constraint into the optimization procedure. Two numerical examples are presented.
For the entire collection see [Zbl 0780.00018].

MSC:
49K15 Optimality conditions for problems involving ordinary differential equations
Software:
NPSOL; OTIS
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