Converse Optimality for Discrete-Time Systems

Given an optimal value function for a discrete-time infinite-horizon optimal control problem, how does one derive a nonlinear system dynamics model, which satisfies this optimal value function? This problem is called converse optimality and was successfully addressed in the continuous-time case. There is, however, no similar derivation in the discrete-time case, and this is the purpose of this paper. A class of discrete-time systems satisfying the given optimality condition is constructed, and its properties are analyzed.