Paper Info
Title
Neural network-based finite-horizon optimal control of uncertain affine nonlinear discrete-time systems.
Abstract
In this paper, the finite-horizon optimal control design for nonlinear discrete-time systems in affine form is presented. In contrast with the traditional approximate dynamic programming methodology, which requires at least partial knowledge of the system dynamics, in this paper, the complete system dynamics are relaxed utilizing a neural network (NN)-based identifier to learn the control coefficient matrix. The identifier is then used together with the actor-critic-based scheme to learn the time-varying solution, referred to as the value function, of the Hamilton-Jacobi-Bellman (HJB) equation in an online and forward-in-time manner. Since the solution of HJB is time-varying, NNs with constant weights and time-varying activation functions are considered. To properly satisfy the terminal constraint, an additional error term is incorporated in the novel update law such that the terminal constraint error is also minimized over time. Policy and/or value iterations are not needed and the NN weights are updated once a sampling instant. The uniform ultimate boundedness of the closed-loop system is verified by standard Lyapunov stability theory under nonautonomous analysis. Numerical examples are provided to illustrate the effectiveness of the proposed method.
Year
DOI
Venue
2015
10.1109/TNNLS.2014.2315646
IEEE Trans. Neural Netw. Learning Syst.
Keywords
Field
DocType
uncertain systems,optimal control,actor-critic-based scheme,neurocontrollers,sampling instant,control system synthesis,matrix algebra,hamilton???jacobi???bellman (hjb) equation,time-varying solution,neural network (nn),hamilton-jacobi-bellman (hjb) equation,closed-loop system,finite-horizon optimal control design,neural network-based identifier,nonlinear control systems,finite-horizon,value function,optimal control.,terminal constraint error,discrete time systems,uniform ultimate boundedness,uncertain affine nonlinear discrete-time systems,nn,sampling methods,hjb,dynamic programming,stability,neural network-based finite-horizon optimal control,approximate dynamic programming methodology,nonautonomous analysis,hamilton-jacobi-bellman equation,closed loop systems,standard lyapunov stability theory,time-varying activation functions,lyapunov methods,control coefficient matrix,artificial neural networks,hamilton jacobi bellman equation
Affine transformation,Hamilton–Jacobi–Bellman equation,Mathematical optimization,Optimal control,Nonlinear system,Computer science,Control theory,Lyapunov stability,Bellman equation,System dynamics,Discrete time and continuous time
Journal
Volume
Issue
ISSN
26
3
2162-2388
Citations 
PageRank 
References 
19
0.68
7
Authors
3
Name
Order
Citations
PageRank
Qiming Zhao1313.26
Hao Xu221414.63
Sarangapani Jagannathan3113694.89