Feedback optimization (FO) is a control paradigm that is gaining popularity for the optimal steady-state operation of complex systems through the use of optimization algorithms in closed-loop control. FO controllers are capable of addressing control objectives beyond simply regulating setpoints and are often used to track solution trajectories of time-varying optimization problems that are not known in advance. Previous research in this area has typically utilized simplified control dynamics, ignored model uncertainties, and has not adequately addressed constraints or transient performance. Additionally, traditional optimal control approaches often require prior knowledge of the desired equilibrium point.
In this thesis, we approach the FO problem from an optimal control and model predictive control (MPC) perspective. Specifically, we propose MPC schemes that can steer the steady-state of a linear dynamical system to the solution of a defined static optimization problem without numerically solving the problem or relying on external setpoints. We accomplish this by formulating the cost functional in MPC to embed an optimization algorithm for the steady-state optimization problem, which is driven to convergence by the implicit feedback inherent in MPC. This allows for the system to be driven to an optimal equilibrium point following a disturbance, without explicit knowledge of the disturbance or setpoints, while also achieving improved transient performance.
Compared to direct online economic optimization (e.g., economic MPC), our approach offers improved computational efficiency, and robustness to model uncertainty and unmeasured disturbances. Additionally, the algorithms we develop are only slightly more complex than conventional linear tracking MPC, so theoretical guarantees of stability and performance can be readily derived from standard tracking MPC results without additional assumptions.
To demonstrate the effectiveness of the proposed MPC schemes, we present several numerical examples and an application to the challenging problem of real-time economic dispatch in load-frequency control of power system networks. The results obtained show that our proposed MPC schemes are indeed feedback optimizing, with good robustness properties and optimal transient performance.
