Direct and Indirect M ' Ethods for Trajectory Optimization

This paper gives a brief list of commonly used direct and indirect efficient methods for the numerical solution of optimal control problems. To improve the low accuracy of the direct methods and to increase the convergence areas of the indirect methods we suggest a hybrid approach. For this a special direct collocation method is presented. In a hybrid approach this direct method can be used in combination with multiple shooting. Numerical examples illustrate the direct method and the hybrid approach.

[1]  Arnold Neumaier,et al.  Introduction to Numerical Analysis , 2001 .

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

[3]  R. Bulirsch,et al.  Optimal ascent and staging of a two-stage space vehicle system , 1990 .

[4]  Hans Bock,et al.  Time optimal trajectories of elbow robots by direct methods , 1989 .

[5]  M. K. Horn.  Solution of the Optimal Control Problem Using the Software Package Stomp , 1989 .

[6]  H. J. Pesch.  Real-time computation of feedback controls for constrained optimal control problems. Part 2: A correction method based on multiple shooting , 1989 .

[7]  R. V. Dooren,et al.  A Chebyshev technique for solving nonlinear optimal control problems , 1988 .

[8]  G. Feichtinger,et al.  Planning the unusual: Applications of control theory to nonstandard problems , 1986 .

[9]  C. R. Hargraves,et al.  DIRECT TRAJECTORY OPTIMIZATION USING NONLINEAR PROGRAMMING AND COLLOCATION , 1986 .

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

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

[12]  A. Miele.  Gradient Algorithms for the Optimization of Dynamic Systems. , 1978 .

[13]  Klaus H. Well,et al.  Approximate Solution of Optimal Control Problems Using Third Order Hermite Polynomial Functions , 1974, Optimization Techniques.

[14]  J. Meditch,et al.  Applied optimal control , 1972, IEEE Transactions on Automatic Control.

[15]  W. Williamson.  Use of Polynomial Approximations to Calculate Suboptimal Controls , 1971 .

[16]  R. Gottlieb.  Rapid convergence to optimum solutions using Min-H Strategy , 1966 .