A convex optimization-based method is proposed to numerically solve dynamic programs in continuous state and action spaces. This approach using a discretization of the state space has the following salient features. First, by introducing an auxiliary optimization variable that assigns the contribution of each grid point, it does not require an interpolation in solving an associated Bellman equation and constructing a control policy. Second, the proposed method allows us to solve the Bellman equation with a desired level of precision via convex programming in the case of linear systems and convex costs. We can also construct a control policy of which performance converges to the optimum as the grid resolution becomes finer in this case. Third, when a nonlinear control-affine system is considered, the convex optimization approach provides an approximate control policy with a provable suboptimality bound. Fourth, for general cases, the proposed convex formulation of dynamic programming op 查看全文>>