Distributed Adaptive Optimal Regulation of Uncertain Large-Scale Interconnected Systems using Hybrid Q-Learning Approach


A novel hybrid Q-learning algorithm is introduced for the design of a linear adaptive optimal regulator for a large-scale interconnected system with event-sampled inputs and state vector. Here, the time-driven Q-learning along with proposed iterative parameter learning updates are utilised within the event-sampled instants to both improve efficiency of the optimal regulator and obtain a more generalised online Q-learning framework. The network-induced losses due to the presence of a communication network among the subsystems are considered along with the uncertain system dynamics. Stochastic model-free Q-learning and dynamic programming are utilised in the hybrid learning mode for the optimal regulator design. The asymptotic convergence of the system state vector and boundedness of the parameter vector is demonstrated using Lyapunov analysis. Further, when the regression vector of the Q-function estimator satisfies the persistency of excitation condition, the Q-function parameters converge to the expected target values. The analytical design is evaluated using numerical examples via simulation. The net result is the design of a data-driven event-sampled adaptive optimal regulator for an uncertain large-scale interconnected system.


Electrical and Computer Engineering

Research Center/Lab(s)

Intelligent Systems Center


This research supported in part by NSF ECCS #1128281 and #1406533 and Intelligent Systems Center, at the Missouri University of Science and Technology, Rolla.

Keywords and Phrases

Algorithms; Design; Dynamic programming; Iterative methods; Large scale systems; Stochastic control systems; Stochastic models; Stochastic systems; Telecommunication networks; Uncertainty analysis; Vectors; Asymptotic convergence; Large-scale interconnected systems; Lyapunov analysis; Optimal regulators; Parameter learning; Parameter vectors; Persistency of excitation; Regression vectors; Learning algorithms

International Standard Serial Number (ISSN)

1751-8644; 1751-8652

Document Type

Article - Journal

Document Version


File Type





© 2016 Institution of Engineering and Technology (IEE), All rights reserved.

Publication Date

01 Aug 2016