Abstract
Nonlinear time-varying systems without mechanism models are common in application. They cannot be controlled directly by the traditional control methods based on precise mathematical models. Intelligent control is unsuitable for real-time control due to its computation complexity. For that sake, a multidimensional Taylor network (MTN) based output tracking control scheme, which consists of two MTNs, one as an identifier and the other as a controller, is proposed for SISO nonlinear time-varying discrete-time systems with no mechanism models. A MTN identifier is constructed to build the offline model of the system, and a set of initial parameters for online learning of the identifier is obtained. Then, an ideal output signal is selected relative to the given reference signal. Based on the system identification model, Pontryagin minimum principle is introduced to obtain the numerical solution of the optimal control law for the system relative to the given ideal output signal, with the corresponding optimal output taken as the desired output signal. A MTN controller is generated automatically to fit the numerical solution of the optimal control law using the conjugate gradient (CG) method, and a set of initial parameters for online learning of the controller is obtained. An adaptive back propagation (BP) algorithm is developed to adjust the parameters of the identifier and controller in real time, and the convergence for the proposed learning algorithm is verified. Simulation results show that the proposed scheme is valid.
Highlights
Nonlinear time-varying systems without mechanism models exist in practical engineering applications widely
Nonlinear autoregressive moving average with exogenous inputs (NARMAX) model describes an input-output relationship for a nonlinear dynamic system, by which the system output can be represented as a nonlinear functional expansion of its lagged inputs and outputs [7,8,9]
Neural network (NN) has the ability to approximate any continuous function with an arbitrary degree of accuracy over a compact set [15], and various kinds of NN have been used in system identification and control [7, 8, 16,17,18,19,20,21,22,23,24]
Summary
Nonlinear time-varying systems without mechanism models exist in practical engineering applications widely. As the polynomial function tends to be of infinity, the multidimensional Taylor network (MTN, whose idea was proposed by Hong-Sen Yan in 2010 and realization was done by Bo Zhou) is good at approximating or representing the general nonlinear dynamic system. MTN, first presented in [26], can reflect the dynamic characteristics of the system without knowing the order or other prior knowledge of the system It approximates any nonlinear function with an arbitrary high accuracy, widely being applied in the study of time series prediction problems successfully [27,28,29,30,31,32]. A MTN-based output tracking real-time control scheme, which consists of two MTNs, one as the identifier and the other as the controller, is proposed for SISO nonlinear time-varying discrete-time systems without mechanism models.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
