Discrete-time linear quadratic stochastic control with equality-constrained inputs: Application to energy demand response
This work addresses energy demand response in renewable systems by enabling exact power tracking with constraints, but it is incremental as it applies known methods to a specific domain.
The paper tackles the discrete-time stochastic linear quadratic control problem for cooperative agents under hard equality constraints on total inputs, motivated by energy demand response, and derives an optimal control law using dynamic programming and KKT conditions, achieving exact power tracking in applications like coordinating residential battery charging.
We investigate the discrete-time stochastic linear quadratic control problem for a population of cooperative agents under the hard equality constraint on total control inputs, motivated by demand response in renewable energy systems. We establish the optimal solution that respects hard equality constraints for systems with additive noise in the dynamics. The optimal control law is derived using dynamic programming and Karush-Kuhn-Tucker (KKT) conditions, and the resulting control solution depends on a discrete-time Riccati-like recursive equation. Application examples of coordinating the charging of a network of residential batteries to absorb excess solar power generation are demonstrated, and the proposed control is shown to achieve exact power tracking while considering individual State-of-Charge (SoC) objectives