Optimal Discrete-Time Energy Harvesting From Infinite-Dimensional Stochastic Systems

This paper considers the optimization of discrete-time control systems for power generation from stochastically-excited linear dynamical systems, characterized by infinite-dimensional dynamics. Weiner-Hopf theory is used to determine the physical upper bound on stationary power generation. The resultant expressions for power generation do not require a finite-dimensional state-space model to be specified at any point in the analysis. However, the constraint that the controller be causal leads to the need to perform spectral factorizations on two associated power spectra. In many cases, analytical solutions to these factorizations are intractable, and approximate numerical techniques must be used. This paper makes use of subspace identification techniques for approximate spectral factorization. The concepts are illustrated in a wave energy conversion example.