Approximate Optimal Distributed Control of Nonlinear Interconnected Systems using Event-Triggered Nonzero-Sum Games


In this paper, approximate optimal distributed control schemes for a class of nonlinear interconnected systems with strong interconnections are presented using continuous and event-sampled feedback information. The optimal control design is formulated as an N-player nonzero-sum game where the control policies of the subsystems act as players. An approximate Nash equilibrium solution to the game, which is the solution to the coupled Hamilton-Jacobi equation, is obtained using the approximate dynamic programming-based approach. A critic neural network (NN) at each subsystem is utilized to approximate the Nash solution and novel event-sampling conditions, that are decentralized, are designed to asynchronously orchestrate the sampling and transmission of state vector at each subsystem. To ensure the local ultimate boundedness of the closed-loop system state and NN parameter estimation errors, a hybrid-learning scheme is introduced and the stability is guaranteed using Lyapunov-based stability analysis. Finally, implementation of the proposed event-based distributed control scheme for linear interconnected systems is discussed. For completeness, Zeno-free behavior of the event-sampled system is shown analytically and a numerical example is included to support the analytical results.


Electrical and Computer Engineering

Research Center/Lab(s)

Intelligent Systems Center


This work was supported in part by the Intelligent Systems Center, Missouri University of Science and Technology, Rolla, MO, USA, in part by NSF ECCS under Grant 1406533, in part by CMMI under Grant 1547042, and in part by the start-up fund Oklahoma State University, Stillwater, OK 74078 USA.

Keywords and Phrases

Closed loop systems; Cost functions; Decentralized control; Distributed parameter control systems; Dynamic programming; Large scale systems; Adaptive dynamic programming (ADP); Event-triggered controls; Games; Nonzero sum (NZS) game; Optimal controls; Performance analysis; Adaptive control systems; Interconnected systems

International Standard Serial Number (ISSN)

2162-237X; 2162-2388

Document Type

Article - Journal

Document Version


File Type





© 2019 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 May 2019