Real-Time Minimization of Average Error in the Presence of Uncertainty and Convexification of Feasible Sets
For researchers in real-time control systems, this work offers a theoretical framework to handle prediction errors and convexification mismatches, though it is incremental in extending error diffusion to this context.
This paper addresses real-time control under uncertainty where local controllers may not exactly implement setpoints from a central controller. It proposes an error diffusion algorithm to compensate for mismatches and provides conditions for bounded minimal invariant sets, ensuring average error converges to zero.
We consider a two-level discrete-time control framework with real-time constraints where a central controller issues setpoints to be implemented by local controllers. The local controllers implement the setpoints with some approximation and advertize a prediction of their constraints to the central controller. The local controllers might not be able to implement the setpoint exactly, due to prediction errors or because the central controller convexifies the problem for tractability. In this paper, we propose to compensate for these mismatches at the level of the local controller by using a variant of the error diffusion algorithm. We give conditions under which the minimal (convex) invariant set for the accumulated-error dynamics is bounded, and give a computational method to construct this set. This can be used to compute a bound on the accumulated error and hence establish convergence of the average error to zero. We illustrate the approach in the context of real-time control of electrical grids.