A Modified Gradient Procedure for Adaptation in Nonlinear Control Systems

Abstract

A modified gradient procedure is proposed for making discrete-time changes in the adjustable parameters of a continuous-time nonlinear control system during normal operating conditions. The algorithm employs the best available estimate of the unknown plant parameters as well as the estimates of disturbance, state, and output variables. The importance of the metric properties of a performance index is discussed, and the necessary and sufficient conditions for the integral squared error index to possess metric properties are derived. Theoretical conditions for the error correctiveness of the algorithm are formulated in terms of the constrained extrema of quadratic functionals.