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

Abstract

A robust output feedback consensus problem for networked identical nonlinear negative-imaginary (NI) systems is investigated in this paper. Output consensus is achieved by applying identical linear output strictly negative-imaginary (OSNI) controllers to all the nonlinear NI plants in positive feedback through the network topology. First, we extend the definition of nonlinear NI systems from single-input single-output (SISO) systems to multipleinput multiple-output (MIMO) systems and also extend the definition of OSNI systems to nonlinear scenarios. Asymptotic stability is proved for the closed-loop interconnection of a nonlinear NI system and a nonlinear OSNI system under reasonable assumptions. Then, an NI property and an OSNI-like property are proved for networked identical nonlinear NI systems and networked identical linear OSNI systems, respectively. Output feedback consensus is proved for a network of identical nonlinear NI plants by investigating the stability of its closed-loop interconnection with a network of linear OSNI controllers. This closed-loop interconnection is proposed as a protocol to deal with the output consensus problem for networked identical nonlinear NI systems and is robust against uncertainty in the individual system's model.

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

“…In this section, new definitions of nonlinear NI and nonlinear OSNI systems are provided and a new stability result is established for the interconnection of a single nonlinear NI system and a single nonlinear OSNI system. The new stability result is applicable to nonlinear NI systems with free body motion, which are excluded in the previous stability result given in [20].…”

“…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.…”

“…Systems with free body motion such as single integrators and double integrators were included in this new definition and the new robust stability result for NI systems in [18]. The original definition of NI systems has also been recently extended to include nonlinear systems [19] and some stability results were established for nonlinear NI systems in [19] and [20]. However, systems with free body motion are excluded in the nonlinear NI definition in [19].…”

“…In particular, this paper provides a new definition for nonlinear NI systems, which includes systems with free body motion. Nonlinear OSNI systems are also defined to allow a direct feedthrough from their inputs to their outputs, which is in contrast to the previous definition in [20]. 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.…”

Mean Square Optimal Control by Interconnection for Linear Stochastic Hamiltonian Systems

“…The energy conservation and dissipation play an important role in the dynamics of Hamiltonian systems and their open versions, port-Hamiltonian systems [10], [11], [19], which interact between themselves and with the surroundings. The energy transfer mechanisms are employed in the control-by-interconnection approach to achieving performance specifications for networks of such systems, whose analysis uses dissipation inequalities with storage and supply rate functions [15], [20], [24].…”