The Matrix Dynamic Programming Property and Its Implications
J.-P. Le Cadre, O. Trémois · SIAM Journal on Matrix Analysis and Applications · 1997
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.