Event-Triggered Distributed Approximate Optimal State and Output Control of Affine Nonlinear Interconnected Systems


This paper presents an approximate optimal distributed control scheme for a known interconnected system composed of input affine nonlinear subsystems using event-triggered state and output feedback via a novel hybrid learning scheme. First, the cost function for the overall system is redefined as the sum of cost functions of individual subsystems. A distributed optimal control policy for the interconnected system is developed using the optimal value function of each subsystem. To generate the optimal control policy, forward-in-time, neural networks are employed to reconstruct the unknown optimal value function at each subsystem online. In order to retain the advantages of event-triggered feedback for an adaptive optimal controller, a novel hybrid learning scheme is proposed to reduce the convergence time for the learning algorithm. The development is based on the observation that, in the event-triggered feedback, the sampling instants are dynamic and results in variable interevent time. To relax the requirement of entire state measurements, an extended nonlinear observer is designed at each subsystem to recover the system internal states from the measurable feedback. Using a Lyapunov-based analysis, it is demonstrated that the system states and the observer errors remain locally uniformly ultimately bounded and the control policy converges to a neighborhood of the optimal policy. Simulation results are presented to demonstrate the performance of the developed controller.


Electrical and Computer Engineering

Research Center/Lab(s)

Intelligent Systems Center


This was supported by the Intelligent Systems Center, Rolla, under Grant NSF ECCS 1406533 and Grant NSF CMMI 1547042.

Keywords and Phrases

Controllers; Cost functions; Distributed parameter control systems; Large scale systems; Learning algorithms; Optimal control systems; Distributed control schemes; Distributed optimal control; Lyapunov-based analysis; Nonlinear interconnected systems; Nonlinear subsystems; Optimal control policy; Optimal value functions; Uniformly ultimately bounded; Feedback; Event-triggered control (ETC); Hamilton-Jacobi-Bellman (HJB) equation; Neural network control; Optimal control

International Standard Serial Number (ISSN)

2162-237X; 2162-2388

Document Type

Article - Journal

Document Version


File Type





© 2018 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 Jul 2018