Finite-Horizon Near-Optimal Output Feedback Neural Network Control of Quantized Nonlinear Discrete-Time Systems with Input Constraint


The output feedback-based near-optimal regulation of uncertain and quantized nonlinear discrete-time systems in affine form with control constraint over finite horizon is addressed in this paper. First, the effect of input constraint is handled using a nonquadratic cost functional. Next, a neural network (NN)-based Luenberger observer is proposed to reconstruct both the system states and the control coefficient matrix so that a separate identifier is not needed. Then, approximate dynamic programming-based actor-critic framework is utilized to approximate the time-varying solution of the Hamilton-Jacobi-Bellman using NNs with constant weights and time-dependent activation functions. A new error term is defined and incorporated in the NN update law so that the terminal constraint error is also minimized over time. Finally, a novel dynamic quantizer for the control inputs with adaptive step size is designed to eliminate the quantization error overtime, thus overcoming the drawback of the traditional uniform quantizer. The proposed scheme functions in a forward-in-time manner without offline training phase. Lyapunov analysis is used to investigate the stability. Simulation results are given to show the effectiveness and feasibility of the proposed method.


Electrical and Computer Engineering


This work was supported in part by the National Science Foundation under Grant ECCS-1128281 and in part by the Intelligent Systems Center.

Keywords and Phrases

Digital control systems; Dynamic programming; Errors; Nonlinear feedback; Approximate dynamic programming; Finite horizons; Hamilton-Jacobi-Bellman (HJB) equations; Neural network (NN); optimal regulation; Quantization; Discrete time control systems; Artificial neural network; Computer simulation; Feedback system; Nonlinear system; Time factor; Computer Simulation; Feedback; Neural Networks (Computer); Nonlinear Dynamics; Time Factors

International Standard Serial Number (ISSN)

2162-237X; 2162-2388

Document Type

Article - Journal

Document Version


File Type





© 2015 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 Aug 2015