The Lagrange-Newton method for nonlinear optimal control problems

We investigate local convergence of the Lagrange-Newton method for nonlinear optimal control problems subject to control constraints including the situation where the terminal state is fixed. Sufficient conditions for local quadratic convergence of the method based on stability results for the solutions of nonlinear control problems are discussed.

[1]  Brian D. O. Anderson,et al.  Singular Optimal Control: The Linear-Quadratic Problem , 1978 .

[2]  W. Alt.  The lagrange-newton method for infinite-dimensional optimization problems , 1990 .

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

[4]  Stephen M. Robinson,et al.  Perturbed Kuhn-Tucker points and rates of convergence for a class of nonlinear-programming algorithms , 1974, Math. Program..

[5]  H. Maurer.  First and second order sufficient optimality conditions in mathematical programming and optimal control , 1981 .

[6]  Hans Josef Pesch,et al.  Solution Differentiability for Nonlinear Parametric Control Problems , 1994 .

[7]  W. Hager.  Lipschitz Continuity for Constrained Processes , 1979 .

[8]  Stephen M. Robinson,et al.  Regularity and Stability for Convex Multivalued Functions , 1976, Math. Oper. Res..

[9]  S. M. Robinson.  Local structure of feasible sets in nonlinear programming, Part III: Stability and sensitivity , 1987 .

[10]  Stephen M. Robinson,et al.  Strongly Regular Generalized Equations , 1980, Math. Oper. Res..

[11]  K. C. P. Machielsen,et al.  Numerical Solution of Optimal Control Problems with State Constraints by Sequential Quadratic Programming in Function Space. , 1993 .

[12]  J. Stoer.  Principles of Sequential Quadratic Programming Methods for Solving Nonlinear Programs , 1985 .

[13]  B. T. Poljak,et al.  Lectures on mathematical theory of extremum problems , 1972 .

[14]  W. Hager.  Multiplier methods for nonlinear optimal control , 1990 .

[15]  K. Malanowski.  Second-order conditions and constraint qualifications in stability and sensitivity analysis of solutions to optimization problems in Hilbert spaces , 1992 .