Robust Output Feedback Consensus for Networked Heterogeneous Nonlinear Negative-Imaginary Systems

Abstract

This paper provides a control protocol for the robust output feedback consensus of networked heterogeneous nonlinear negative-imaginary (NI) systems. Heterogeneous nonlinear output strictly negative-imaginary (OSNI) controllers are applied in positive feedback according to the network topology to achieve output feedback consensus. The main contribution of this paper is extending the previous studies of the robust output feedback consensus problem for networked heterogeneous linear NI systems to nonlinear NI systems. Output feedback consensus is proved by investigating the internal stability of the closed-loop interconnection of the network of heterogeneous nonlinear NI plants and the network of heterogeneous nonlinear OSNI controllers through the network topology. The network of heterogeneous nonlinear NI systems is proved to be also a nonlinear NI system, and the network of heterogeneous nonlinear OSNI systems is proved to be a nonlinear NI system. Under suitable conditions, the nonlinear OSNI controllers lead to the convergence of the outputs of all nonlinear NI plants to a common limit trajectory, regardless of the system model of each plant. Hence, the protocol is robust with respect to uncertainty in the system models of the heterogeneous nonlinear NI plants in the network. This paper also describes some typical firstorder and second-order nonlinear OSNI systems that can be used as controllers for the robust output feedback consensus of heterogeneous nonlinear NI plants.

Output Feedback Consensus for Networked Heterogeneous Nonlinear Negative-Imaginary Systems with Free Body Motion

“…The control framework in Fig. 5 is very similar to the framework used in [33]. The connections between the plants and controllers can be best visualised using the undirected graph, as shown in the example in Fig.…”

“…The contribution of this paper involves establishing a stability result and providing a control framework to achieve robust output feedback consensus for nonlinear NI systems with free body motion, which can be regarded as a complement to the nonlinear NI system results in [19], [20] and [33]. This paper can also be considered as an extension of the previous studies in [18] and [8] from linear systems to nonlinear systems.…”

“…However, the result in [8] is restricted to linear systems only and cannot solve cooperative control problems for nonlinear systems. Motivated by nonlinear NI systems theory, the result in [8] has been recently extended in [33] to provide a method for robust output feedback consensus for networked heterogeneous nonlinear NI systems without free body motion.…”

“…The input feedthrough term in an OSNI controller makes it possible for a Lyapunov function for the closed-loop interconnection of a nonlinear NI system with free body motion and a nonlinear OSNI system to be positive definite. Robust output feedback consensus is achieved for multiple heterogeneous nonlinear NI systems with possible free body motion using a control framework similar to that in [33]. However, the control framework is refined and a new proof is given due to the new definition for nonlinear NI systems.…”