Stochastic optimal control of jump diffusion excited energy harvesters

A finite horizon stochastic optimal control problem is considered for an energy harvester driven by the jump-diffusion excitation. The dynamics of the harvester include a constant time-delay and a retardation (distributed delay) term. The jump component accounts for abrupt changes in the excitation signal. The optimal control is characterized based on the dynamic programming. In the delay-free and retardation term-free cases, constructing the optimal control reduces to solving a system of ordinary differential equations backward-in-time. Thus the inclusion of the jump terms in the model does not significantly complicate the optimal control and optimal cost construction. With delay and/or retardation terms present, it is demonstrated that a set of appropriately formulated Partial Differential Equations need to be solved. The approach enables the quantification of limits on achievable performance by the energy harvester in terms of amounts of energy that can be extracted when jump-diffusion input excitation is present. A computational example for a delay free case is reported.