Explicit Agent-Level Optimal Cooperative Controllers for Dynamically Decoupled Systems with Output Feedback

TL;DR

This work provides generically minimal agent-level implementations of the local controllers along with intuitive interpretations of their states and the information that should be transmitted between controllers.

Abstract

We consider a dynamically decoupled network of agents each with a local output-feedback controller. We assume each agent is a node in a directed acyclic graph and the controllers share information along the edges in order to cooperatively optimize a global objective. We develop explicit state-space formulations for the jointly optimal networked controllers that highlight the role of the graph structure. Specifically, we provide generically minimal agent-level implementations of the local controllers along with intuitive interpretations of their states and the information that should be transmitted between controllers.

Figures (3)

• Figure 1: Example of a dynamically decoupled system. The plants $\mathcal{G}_i$ each have controllers $\mathcal{K}_i$ that share information instantaneously along a directed acyclic graph. The edge $\mathcal{K}_1 \rightarrow \mathcal{K}_5$ is implied but not shown.
• Figure 2: Block diagram representation of the global plant $\mathcal{G}$ and global controller $\mathcal{K}$ from Theorem \ref{['thm:2']}. Here, the (block-diagonal) estimator dynamics are contained in $\bar{\mathcal{T}} \defeq (sI-\bar{A}-\bar{L}\bar{C})^{-1}$ and the remaining blocks of $\mathcal{K}$ are static.
• Figure 3: Block diagram representation of a local plant $\mathcal{G}_i$ and associated controller $\mathcal{K}_i$ (left) and the Observer-Regulator structure of $\mathcal{K}_i$ (right) from \ref{['agent:all']}. Agent $i$ updates its local state $\xi_{i,\underline i}$ and computes its local input $u_i$ using the local measurement $y_i$ and the states $\xi_{k,\underline k}$ and partial inputs $\tilde{v}_{k,\underline k}$ from strict ancestors $k\in \bar{\bar{i}}$. For simplicity, we used the following notation for the estimator dynamics: $\mathcal{T}_{\underline{ii}} \defeq (sI-A_{\underline{ii}}-E_{n_{\underline{i}}}^{\tp} E_{n_i} L^i C_{2_{ii}} E_{n_{i}}^{\tp} E_{n_{\underline{i}}})^{-1}$.

Theorems & Definitions (1)

• proof