The Matrix Dynamic Programming Property and Its Implications

The dynamic programming (DP) technique rests on a very simple idea, the principle of optimality due to Bellman. This principle is instrumental in solving numerous problems of optimal control. The control law minimizes a cost functional and is determined by using the optimality principle. However, applicability of the optimality principle requires that the cost functional satisfies the property called "matrix dynamic programming (MDP) property." A simple definition of this property will be provided and functionals having it will be considered.

[1]  I. Olkin,et al.  Inequalities: Theory of Majorization and Its Applications , 1980 .

[2]  K. Gong,et al.  Fundamental properties and performance of conventional bearings-only target motion analysis , 1984 .

[3]  J. Le Cadre,et al.  Discrete-time observability and estimability analysis for bearings-only target motion analysis , 1997, IEEE Transactions on Aerospace and Electronic Systems.

[4]  Ingram Olkin,et al.  Inequalities: Theory of Majorization and Its Application , 1979 .

[5]  P. T. Liu,et al.  An optimum approach in target tracking with bearing measurements , 1988 .

[6]  Jean-Pierre Le Cadre,et al.  Optimization of the observer motion using dynamic programming , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.

[7]  Thomas Kailath,et al.  Estimability and regulability of linear systems , 1987, 26th IEEE Conference on Decision and Control.

[8]  E. Weinstein,et al.  A new method for evaluating the log-likelihood gradient, the Hessian, and the Fisher information matrix for linear dynamic systems , 1989, IEEE Trans. Inf. Theory.

[9]  Józef Korbicz,et al.  Parameter identification of two-dimensional distributed systems , 1990 .

[10]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[11]  D.S.G. Pollock,et al.  Tensor products and matrix differential calculus , 1985 .

[12]  Sherry Hammel,et al.  Observability Requirements for Three-Dimensional Tracking via Angle Measurements , 1985, IEEE Transactions on Aerospace and Electronic Systems.

[13]  M. Marcus.  Finite dimensional multilinear algebra , 1973 .

[14]  H. Vincent Poor,et al.  An Introduction to Signal Detection and Estimation , 1994, Springer Texts in Electrical Engineering.

[15]  J. G. Gander,et al.  An introduction to signal detection and estimation , 1990 .

[16]  Dimitri P. Bertsekas,et al.  Dynamic Programming: Deterministic and Stochastic Models , 1987 .