Adaptive control and neural network control of nonlinear discrete-time systems

Abstract

Nowadays nearly all the control algorithms are implemented digitally and consequently discrete-time systems have been receiving ever increasing attention. However, for the development of nonlinear adaptive control and neural network (NN) control, which are generally regarded as smart ways to deal with system uncertainties, most researches are conducted in continuous-time, such that many well developed methods are not directly applied in discrete-time, due to fundament difference between differential and difference equations for modeling continuous-time and discrete-time systems, respectively. Therefore, nonlinear adaptive control and neural network control of discrete-time systems need to be further investigated.In the first part of the thesis, a framework of future states prediction based adaptive control is developed to avoid possible noncausal problems in high order systems control design. Based on the framework, a novel adaptive compensation approach for nonparametric model uncertainties in both matched and unmatched condition is constructed such that asymptotic tracking performance can be achieved. By proper incorporating discrete Nussbaum gain, the adaptive control becomes insensitive to system control directions and the bounds of control gain become not necessary for control design. The adaptive control is also studied with incorporation of discrete-time Prandtl-Ishlinskii (PI) model to deal with hysteresis type input constraint. Furthermore, adaptive control is designed for block-triangular nonlinear multi-input-multi-output (MIMO) systems with strict-feedback subsystems coupled together. By exploiting block triangular structure properties and construction of uncertainties compensations, the design difficulties caused by the couplings among various inputs and states, as well as the uncertainties in the couplings are solved.In the second part of the thesis, it is established that for single-input-single-output (SISO) case, under certain conditions both pure-feedback systems and nonlinear autoregressive-moving-average-with-exogenous-inputs (NARMAX) systems are transformable into a suitable input-output form and adaptive NN control design for both systems can be carried out in a unified approach without noncausal problem. To overcome the difficulty associated with nonaffine appearance of control variables, implicit function theorem is exploited to assert the existence of a desired implicit control. In the control design, discrete Nussbaum gain is further extended to deal with time varying control gains. The adaptive NN control constructed for nonaffine SISO systems is also extended to nonaffine MIMO systems in block triangular form and NARMAX form.The research work conducted in this thesis is meant to push the boundary of academic results further beyond. The systems considered in this thesis represent several general classes of discrete-time nonlinear systems. Numerical simulations are extensively carried out to illustrate the effectiveness of the proposed controls.