A generalized methodology for the inverse optimal control of a class of input affine nonlinear systems

Abstract

The optimal control of nonlinear systems has a preeminent place all throughout the newlineprogression of control theory. This is on account of the desired ability to trade off state newlineerrors and control expenditure. Moreover, optimal control laws guarantee adequate newlinestability margins, which are key to basic robustness properties that a system should newlinepossess. However, the solution to this classical problem is hindered by the need to solve newlinethe Hamilton-Jacobi-Bellman (HJB) partial differential equation, which is an infeasible newlinetask in most cases. Therefore several approximate solution strategies based on geometric newlinetools, power series expansion and numerical techniques which lead to suboptimal newlinesolutions have been proposed. Such methodologies may not ensure a closed-form newlinesolution and are often associated with complex algorithms which require the aid of high newlinespeed computational features for real-time implementation. This work focuses on the newlineconcept of inverse optimal control (IOC) which presents an attractive alternative to newlinedetermine a closed-form solution to the nonlinear optimal control problem. Another newlineprominent advantage of IOC approach is that it circumvents the tedious task of solving newlinethe HJB equation. newlineThe fundamental concept of IOC lies in determining a stabilizing state feedback newlinecontrol based on a control Lyapunov function (CLF). Further, this CLF based IOC newlineanalytically solves the HJB equation corresponding to a meaningful performance newlinemeasure, which is deduced posteriori. This work addresses the following fundamental newlineissues in the context of IOC: Firstly, the resultant meaningful performance measures that newlineare optimized may be complex mathematical functions of the state and control vectors newlinewhich may not be worth minimizing in the practical context. Secondly, the construction newlineof CLF itself is a prevalent concern, as even the existence of one cannot be assessed for newlinea given control affine system.