Design And Implementation Of Robust Relatively Optimal Control Schemes For Nonlinear Affine Systems

Abstract

newline Many systems such as airplanes, launch vehicles, missiles and helicopters taking off newlinefrom a helipad are operated from a fixed initial condition. The optimal trajectory newlinefrom the nominal initial condition is essential for all these systems. However, stability newlineneeds to be ensured from all other initial conditions. The state and input constraints newlineon the system need to be satisfied during the operation. The parameter uncertainties newlinearising during system modeling as well as the external disturbances acting on these newlinesystems make the optimal control of such systems a sophisticated control problem. newlineThe constrained optimal control namely relatively optimal control (ROC) can newlinebe adopted for the control of such systems as it guarantees optimal response for newlinenominal initial conditions and stable response for non-nominal initial conditions. newlineThe advantages of methods such as state feedback control using the pole placement newlinemethod, linear quadratic regulator (LQR) and Model predictive control (MPC) are newlineexhibited by ROC. However, it is found from the literature that the applications of newlineconventional ROC are limited to the stabilization of the nominal linear model of a newlinesystem. Consequently, the nonlinear nature of the system, parameter uncertainties, newlineand disturbances stand as a threat to the practical implementation of conventional newlineROC. To bridge this gap there exists a need for converting the conventional ROC to newlinerobust ROC. newlineAs a first step towards the development of robust ROC, a modification is proposed newlinein the objective function considered for the design of conventional ROC for newlinecontinuous-time linear time-invariant (LTI) models. In the conventional ROC, the newlineobjective function is formed by considering states and inputs of the system only to newlineresult in a minimum expenditure of control energy in the regulation of states.The