Distributed Truncated Predictive Control for Networked Systems under Uncertainty: Stability and Near-Optimality Guarantee

We study the problem of distributed online control of networked systems with time-varying cost functions and disturbances, where each node only has local information of the states and forecasts of the costs and disturbances. We develop a distributed truncated predictive control (DTPC) algorithm, where each node solves a ``truncated'' predictive optimal control problem with horizon $k$, but only involving nodes in a $\kappa$-hop neighborhood (ignoring nodes outside). We show that the DTPC algorithm satisfies input-to-state stability (ISS) bounds and has regret decaying exponentially in $k$ and $\kappa$, meaning a short predictive horizon $k$ and a small truncation radius $\kappa$ is sufficient to achieve near-optimal performance. Furthermore, we show that when the future costs and disturbances are not exactly known, the regret has exponentially decaying sensitivity to the forecast errors in terms of predictive horizon, meaning near-term forecast errors play a much more important role than longer-term forecasts.