Differential dynamic programming and separable programs

This paper deals with differential dynamic programming for solving nonlinear separable programs. The present algorithm and its derivation are rather different from differential dynamic programming algorithms and their derivations by Mayne and Jacobson, who have not proved the convergence of their algorithms. The local convergence of the present algorithm is proved, and numerical examples are given.

[1]  R. E. Kalman,et al.  Control System Analysis and Design Via the “Second Method” of Lyapunov: II—Discrete-Time Systems , 1960 .

[2]  E. M. L. Beale,et al.  Nonlinear and Dynamic Programming , 1965 .

[3]  D. Mayne.  A Second-order Gradient Method for Determining Optimal Trajectories of Non-linear Discrete-time Systems , 1966 .

[4]  On the Singularity of a Certain Bordered Matrix , 1967 .

[5]  D. Jacobson,et al.  A discrete-time differential dynamic programming algorithm with application to optimal orbit transfer , 1970 .

[6]  A. V. Levy,et al.  Modified quasilinearization and optimal initial choice of the multipliers part 1—Mathematical programming problems , 1970 .

[7]  H. Mine,et al.  Decomposition of mathematical programming problems by dynamic programming and its application to block-diagonal geometric programs , 1970 .

[8]  Stephen R. McReynolds,et al.  The computation and theory of optimal control , 1970 .

[9]  Leon S. Lasdon,et al.  Optimization Theory of Large Systems , 1970 .

[10]  James M. Ortega,et al.  Iterative solution of nonlinear equations in several variables , 2014, Computer science and applied mathematics.

[11]  David Q. Mayne,et al.  Differential dynamic programming , 1972, The Mathematical Gazette.

[12]  R. Havira,et al.  Computation of quantized controls using differential dynamic programming , 1972 .

[13]  David Q. Mayne,et al.  Differential Dynamic Programming–A Unified Approach to the Optimization of Dynamic Systems , 1973 .

[14]  Richard P. O'Neill,et al.  Technical Note - Computational Experience with Normed and Nonnormed Column-Generation Procedures in Nonlinear Programming , 1975, Oper. Res..

[15]  D. Mayne,et al.  First-order strong variation algorithms for optimal control , 1975 .

[16]  R. Tapia.  A stable approach to Newton's method for general mathematical programming problems inRn , 1975 .

[17]  D. Mayne,et al.  First-order strong variation algorithms for optimal control problems with terminal inequality constraints , 1975 .

[18]  Masao Fukushima,et al.  Multilevel decomposition of nonlinear programming problems by dynamic programming , 1976 .