A Generalized Control Paradigm for Storage Systems: Optimal Energy Management and Stability Certificates

In this brief, we propose a suboptimal control update for lossless storage systems that operates based on the instantaneous value of the load power and generalizes previously suggested solutions for energy management problems. The proposed control update performs under uncertain conditions and does not require statistical information about the load profile. We leverage tools from Pontryagin's minimum principle and stochastic dynamic programming methods to derive the control strategy and then investigate its stability properties using the Lyapunov analysis. However, the analysis of this control paradigm presents significant challenges, among which the key difficulty arises due to the presence of nonlinear feedback terms. To address this challenge, we first introduce a coordinate transformation, which transforms the original problem into an equivalent stabilization problem, and then verify its stability properties using the Lyapunov function theory and LaSalle's invariance principle. We show that the proposed control policy works for both continuous-time and stochastic load profiles, and it keeps the stored energy within the capacity bounds by following the optimal path.