Tunable Passivity Control for Centralized Multiport Networked Systems

TL;DR

This work addresses stability challenges in Centralized Multiport Networked Dynamic (CMND) systems under non-ideal networks, proposing Tunable Centralized Optimal Passivity Control (TCoPC) that combines a centralized passivity observer with a distributed passivity controller. The method computes adaptive dissipation gains by solving a constrained optimization that enforces passivity while respecting a designer-defined priority matrix $Q$, enabling targeted stabilization even with time-varying delays and nonpassive or non-minimum phase nodes. Theoretical formulation, along with simulations on a three-node network, demonstrates that TCoPC guarantees $L_2$ stability, achieves flexible energy allocation across nodes, and remains robust to delays and network uncertainties. The approach offers practical impact for scalable, flexible stabilization in multi-agent control, multilateral telerobotics, and complex epidemic-network dynamics by enabling precise dissipation distribution without strict passive assumptions on remote nodes.

Abstract

Centralized Multiport Networked Dynamic (CMND) systems have emerged as a key architecture with applications in several complex network systems, such as multilateral telerobotics and multi-agent control. These systems consist of a hub node/subsystem connecting with multiple remote nodes/subsystems via a networked architecture. One challenge for this system is stability, which can be affected by non-ideal network artifacts. Conventional passivity-based approaches can stabilize the system under specialized applications like small-scale networked systems. However, those conventional passive stabilizers have several restrictions, such as distributing compensation across subsystems in a decentralized manner, limiting flexibility, and, at the same time, relying on the restrictive assumptions of node passivity. This paper synthesizes a centralized optimal passivity-based stabilization framework for CMND systems. It consists of a centralized passivity observer monitoring overall energy flow and an optimal passivity controller that distributes the just-needed dissipation among various nodes, guaranteeing strict passivity and, thus, L2 stability. The proposed data-driven model-free approach, i.e., Tunable Centralized Optimal Passivity Control (TCoPC), optimizes total performance based on the prescribed dissipation distribution strategy while ensuring stability. The controller can put high dissipation loads on some sub-networks while relaxing the dissipation on other nodes. Simulation results demonstrate the proposed frameworks performance in a complex task under different time-varying delay scenarios while relaxing the remote nodes minimum phase and passivity assumption, enhancing the scalability and generalizability.

Figures (7)

• Figure 1: Example network robotic teleoperation architecture of local node communicating with multiple remote nodes.
• Figure 2: Overall schematic of local hub interconnection with multiple remote nodes in addition to the distributed adaptive dissipative gains of $\alpha_i$.
• Figure 3: Impulse response for the system with (bottom) and without (top) the proposed stabilizer. (a) states' (velocity and position) trajectories over time for each node without a stabilizer. (b) Energy vs. Power over Time for each node without stabilizer. (c) states' (velocity and position) trajectories over time for each node in the presence of the stabilizer. (d) Energy vs. Power vs. Time plot for each node in the presence of the stabilizer.
• Figure 4: Case 1 ($Q=\text{Diag}(1,1,1)$): (a) Force modification (before and after the controller) for each node; (b) the $\alpha$ plots (showing the activations of the controller).
• Figure 5: Case 2 ($Q=\text{Diag}(1,0.0001,1)$): (a) Force modification (before and after the controller) for each node; (b) the $\alpha$ plots (showing the the activations of the controller).