Reduced-order observer-based synchronization and output tracking in chain network of a class of nonlinear systems using contraction framework

• Published in: International journal of dynamics and control 2023-10, Vol.11 (5), p.2523-2537
• Main Authors: Ranjan, Ravi Kumar, Sharma, Bharat Bhushan
• Format: Article
• Language: English
• Subjects: Complexity; Control; Control and Systems Theory; Dynamical Systems; Engineering; Nonlinear systems; Subsystems; Synchronism; Tracking problem; Vibration
• ISSN: 2195-268X; 2195-2698
• DOI: 10.1007/s40435-023-01147-z

Synchronization of complex networks can easily be seen in nature around us and is an integral part of many real-world applications. Synchronization of a network is a phenomenon to achieve a common goal through cooperative interaction between systems at each node. The work presented here deals with the synchronization of a class of nonlinear systems connected in a chain network with each subsystem in network unidirectionally coupled through available output states only. To achieve synchronization, reduced-order observer-based scheme is utilized in contraction theory framework. System at a particular node is considered as an observer for the previous system which exponentially converges to actual system states using the proposed observer structure, ultimately leading to synchronization of overall network. The synchronizing gains for observer-based approach are obtained indirectly with proper selection of virtual system. An application of proposed synchronization procedure is further used for output tracking problem for the network. Representative numerical validation is shown further for chain network of chaotic Chua systems as an example. Simulation results justify the efficacy of the proposed synchronization as well as the combined output tracking scheme.