Control Refinement Using Particles Methods

Abstract

The purpose of this research is to propose a novel approach of control refinement to achieve control objective for non-linear systems in the presence of hard non-linear disturbances. The conventional methods to achieve this goal are either unable to handle or show limited improvement in the given scenario in case of disturbances. The disturbance is estimated conventionally as part of the observer and estimation error is employed. The neurodynamic approaches handle the problem but these are computationally intensive and limit the practical implementation of such techniques. To address the tracking problem of nonlinear systems in greater generality concerning practical nonlinear phenomena, along with computational convenience for real-time implementation, the novel idea through particle methods is presented. The traditional particle filters theory is used to propose the Particles-based refinement. The core theme of the proposed algorithm is that the tracking error is evaluated for a nominal control law which is designed for the nominal plant model that describes a nominal trajectory. The nominal trajectory is the desired convergent curve which describes the ideal system behavior specifying the ideal transient and steady-state response. It is the nominal trajectory that provides the basis for nominal controller design as well. The deviation from this trajectory is caused by uncertainties/ disturbances, which were obscure for the nominal control law. Based on this error, a necessary adjustment in the control input is estimated which would have resulted in perfect tracking. The required adjustment in the control input is modeled as a random signal and is estimated using particle methods. The probability density function (pdf) of this signal is represented as a function of weights, which are updated based on sequentially available tracking error data. The subsequent control input includes the estimated adjustment resulting in improved tracking performance. This phenomenon ii is termed control refinement. The advantage of particle methods is their ability to handle non-Gaussian distributions, which generalize the applicability of the proposed algorithm to a wide variety of physical nonlinear phenomena. The compensation of harder non-linearities like dead-zone is also considered for compensation. Instead of taking the nominal model in this case, an artificial neural network (ANN) based approximation of the actual plant has been modeled. Shallow networks with a minimum number of layers are proposed for this purpose to simplify the training and also the practical implementation simpler. The control refinement approach is combined with this ANN-based model to propose an improved tracking performance and to compensate for the effect of dead-zone in addition to multiple disturbances/ uncertainties. Comparison with existing techniques exhibits superior tracking performance. Contrary to the existing disturbance rejection techniques based on estimation error, the tracking error has been employed to estimate the disturbance at the controller. The philosophy has led to remarkable tracking performance. The computational complexity has been further reduced through numerical-based refinement, making it suitable for physical implementation.