Sequential Linear-Dynamic Programming for Reliability Control in Wind Energy Conversion Systems

This paper addresses the problem of reliability control to promote power balance in energy systems with wind generation. Reliability control is reformulated as a trajectory optimization or optimal control problem for a hybrid stochastic differential system. Accordingly, in theory, the dynamic programming principle provides the only closed form exact solution to the problem of reliability control. But in practice, its complexity resides in the resolution of the Hamilton-Jacobi-Bellman equation. In most cases, indeed, Bellman's equation cannot be solved analytically. This paper explores a feasible alternative: successive approximations of the exact solution that could be referred to as sequential linear-dynamic programming or SLDP in abridged notation. On the one hand, these successive approximations stipulate by construction a stochastic optimal control of the feedback type, and on the other hand, they enjoy the properties of cost convergence and strict monotonicity over the course of the iterations. Significant result has been achieved in the implementation of the SLDP approach.