Numerical Solution of Optimal Control Problems by Direct Collocation

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 [10]. Convergence properties of the discretization are derived. Prom 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.

[1]  J. Breakwell.  The Optimization of Trajectories , 1959 .

[2]  Arthur E. Bryson,et al.  OPTIMAL PROGRAMMING PROBLEMS WITH INEQUALITY CONSTRAINTS , 1963 .

[3]  Arthur E. Bryson,et al.  Applied Optimal Control , 1969 .

[4]  D. Jacobson,et al.  New necessary conditions of optimality for control problems with state-variable inequality constraints , 1971 .

[5]  U. Heidemann,et al.  Optimale Steuerprozesse mit Zustandsbeschränkungen , 1975 .

[6]  H. Bock,et al.  A Multiple Shooting Algorithm for Direct Solution of Optimal Control Problems , 1984 .

[7]  Dieter Kraft,et al.  On Converting Optimal Control Problems into Nonlinear Programming Problems , 1985 .

[8]  C. Hargraves,et al.  DIRECT TRAJECTORY OPTIMIZATION USING NONLINEAR PROGRAMMING AND COLLOCATION , 1987 .

[9]  R. Fletcher.  Practical Methods of Optimization , 1988 .

[10]  Bruce A. Conway,et al.  Discrete approximations to optimal trajectories using direct transcription and nonlinear programming , 1992 .

[11]  O. V. Stryk.  Ein direktes Verfahren zur Bahnoptimierung von Luft- und Raumfahrzeugen unter Berücksichtigung von Beschränkungen , 1991 .

[12]  Hans Josef Pesch,et al.  Abort landing in the presence of windshear as a minimax optimal control problem, part 1: Necessary conditions , 1991 .

[13]  Oskar von Stryk,et al.  Direct and indirect methods for trajectory optimization , 1992, Ann. Oper. Res..

[14]  P. Berck,et al.  Calculus of variations and optimal control theory , 1993 .

[15]  H. J. Pesch,et al.  Combining Direct and Indirect Methods in Optimal Control: Range Maximization of a Hang Glider , 1993 .

[16]  Kurt Chudej,et al.  Optimal Ascent of a Hypersonic Space Vehicle , 1993 .