Lyapunov-Based Online Optimal Control of a Class of Cascaded Systems with an Infinite Horizon Time-Average Performance Guarantee

In this paper, we investigate the optimal control of a class of cascaded systems, where mass and/or energy flow through subsystems connected in series. In a stochastic setting, model predictive control (MPC) is a widely adopted approach for tackling this problem. However, it can be computationally intensive and, perhaps more importantly, relies on the characterization of uncertainty. To overcome these potential limitations, we propose a Lyapunov-based online optimal control method, which operates in real time without requiring prior characterization of the uncertainty. By relaxing time-coupling constraints, the proposed online method becomes suboptimal compared to offline optimization with perfect foresight, i.e., the ideal solution to the optimal control problem. Our main result establishes an infinite horizon time-average performance guarantee, demonstrating bounded suboptimality of the proposed method. We apply the Lyapunov-based online optimal control method to the economic dispatch of cascaded hydropower plants, and show that it can outperform both greedy online control and popular MPC.