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

Shi, Kanghong; Vladimirov, Igor G.; Petersen, Ian R.

doi:10.1016/j.ifacol.2021.06.081

Cited by 18 publications

(8 citation statements)

References 17 publications

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“…This paper extends the investigation of the output feedback consensus problem for networked heterogeneous linear NI systems in [15] to nonlinear NI systems by using the results in [11] and [14]. Output feedback consensus of networked heterogeneous nonlinear NI systems is proved by analysing the stability of the closed-loop interconnection of a network of heterogeneous nonlinear NI plants and a network of heterogeneous nonlinear OSNI controllers.…”

Section: Introductionmentioning

confidence: 92%

“…where f : R p × R m → R p is a Lipschitz continuous function and h : R p → R m is a class C 1 function. Definition 1: [14] The system (1), ( 2) is said to be a nonlinear negative-imaginary system if there exists a positive definite storage function V : R p → R of class C 1 such that…”

Section: Preliminariesmentioning

confidence: 99%

“…for all t ≥ 0. Definition 2: [14] The system (1), ( 2) is said to be a nonlinear output strictly negative-imaginary system if there exists a positive definite storage function V : R p → R of class C 1 and a constant ǫ > 0 such that…”

Section: Preliminariesmentioning

confidence: 99%

“…A class of NI systems called output strictly negativeimaginary (OSNI) systems was introduced in [12] and [13] for linear systems and was recently extended to nonlinear systems in [14]. A nonlinear system is said to be nonlinear OSNI if it is dissipative with the supply rate w(u, ẏ) = u T ẏ − ǫ | ẏ| 2 , where u, x and y are the input, state and output of the system, respectively.…”

Section: Introductionmentioning

confidence: 99%

“…Here, ǫ > 0 is an index that quantifies the level of output strictness of the system. It is proved in [14] that the closed-loop interconnection of a nonlinear NI system and a nonlinear OSNI system is asymptotically stable under certain conditions.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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

Shi,

Vladimirov,

Petersen

2020

Preprint

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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.

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Section: Introductionmentioning

confidence: 92%

Section: Preliminariesmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Shi,

Vladimirov,

Petersen

2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Modelling and control of nonlinear negative imaginary systems

Choudhary

Shreesha

Sudhakara

2022

Int. J. Dynam. Control

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This article investigates mathematical modelling and control of a nonlinear negative imaginary system using an illustrative benchmark physical example of a quadrotor dynamic model. A generalized methodology based on Euler–Lagrange equation is applied to obtain nonlinear negative imaginary dynamic model for the quadrotor. In this method, the Kronecker product is employed to formulate the Coriolis matrix, which is then used to construct a mathematical model of a quadrotor. This article further presents nonlinear negative imaginary systems theory-based analysis and synthesis framework to find the control solution for quadrotor’s attitude stability problem while hovering. The multi-loop control scheme is applied to the quadrotor that directly uses the Euler angles (angular positions) instead of angular velocity measurements. Numerical simulation results of this paper show that the investigated control strategy ensures the asymptotic stabilization of quadrotor attitude system model in the presence of external disturbance.

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Dynamic output feedback control strategy for a satellite orbital model within negative-imaginary systems theory framework

Choudhary,

Chokkadi

2024

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This article presents the synthesis of a dynamic output feedback controller for a satellite orbital system confronted with uncertainties. The investigated method transforms the closed-loop system, synthesized by the controller, into an $$\alpha $$ α -strictly negative-imaginary system. It utilizes the DC-loop gain condition associated with negative-imaginary systems theory to demonstrate robust stability of the satellite orbital system in the presence of uncertainties. Furthermore, the synthesized negative-imaginary closed-loop system exhibits notable time-domain performance. The numerical simulation outcomes presented in this article validate the investigated synthesis method.

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

Cited by 18 publications

References 17 publications

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

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

Modelling and control of nonlinear negative imaginary systems

Dynamic output feedback control strategy for a satellite orbital model within negative-imaginary systems theory framework

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