Model based control of Nonlinear Hybrid Dynamical Systems

Abstract

Most of the dynamical systems around us are inherently nonlinear. Systems which are newlinecharacterized by interacting of continuous nonlinear dynamics along with discrete dynamics known as Nonlinear Hybrid Dynamical Systems (NHDS). These systems are capable newlineof exhibiting simultaneously continuous dynamics, discrete dynamics, jump phenomena, newlineswitching characteristics. Classical way to control a nonlinear plant by selecting few operating points which cover the required span of the system and a linear model is obtained. newlineThe controller is designed for each model and activates one of these controllers when the newlineprocess is operating in the neighborhood of the corresponding operating point. newlineThe aim of our work is to design event wise multiple linearized model based controller newlinewith appropriate stability analysis of the NHDS. To this aim, the NHDS is approximated newlineas PieceWise Affine autoRegressive eXogeneous (PWARX) models. Firstly, an algorithm newlineto estimate the number of discrete events presents in the NHDS is proposed. Built upon newlinethis result, a weighted least squares based PWARX model identification technique is newlineproposed. The equivalence between PWARX model and event wise linearized model is newlineprovided. The event wise linearized models are used for the formulation of the optimal newlinecontrol laws, which are then patched together through switching to become a control newlinelaw for the NHDS. The Hamilton-Jacobi-Bellman (HJB) equation is formulated using newlinea suitable quadratic term in the objective function. By the use of the direct method newlineof Lyapunov stability, the control law is shown to be optimal with respect to objective newlinefunctional and stabilized the event wise linearized models. The proposed modeling and newlinecontrol algorithm have been applied on the different NHDS. Necessary simulation and newlineexperimental results are presented to demonstrate the performance and validation of the newlineproposed algorithm. newlineRobust control law is formulated for the NHDS under matched and unmatched model newlineuncertainties. The HJB equation based optimal control problem is for