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Direct Collocation Method

The basis of the direct collocation approach is a finite dimensional approximation of control and state variables, i. e., a discretization. Here, we choose a continuous, piecewise linear control approximation and a continuously differentiable, piecewise cubic state approximation, cf. Hargraves, Paris [11] and [25], [26], [28]. The differential equations, the state and control constraints are only pointwise fulfilled in this approach. The discretization results in a nonlinear optimization problem subject to nonlinear constraints. Convergence properties of the method and details of an efficient implementation are discussed in [26], [27]. Here, we used the code DIRCOL [27] where the resulting nonlinear programming problems are solved by the Sequential Quadratic Programming method NPSOL due to Gill, Murray, Saunders, and Wright [9]. The direct collocation method has a large domain of convergence and is easy to handle as the user has not to be concerned with adjoint variables or necessary conditions of optimality.

Oskar von Stryk
Fri Apr 5 21:57:02 MET DST 1996