Optimization of time-varying systems

A method of self-optimization using system models to compute error-criterion gradients in a parameter space is extended to time-varying systems. When the parameters are permitted to vary only slowly, the gradient computer is similar to that used for stationary systems of fixed configuration. When the parameters vary more rapidly, it is found that only the gradient with respect to the plant input function is meaningful. This influence function is obtained as the output from a model which can be defined whether or not a state-variable representation for the plant is known; a procedure for computing optimal control functions in a variety of linear and nonlinear systems is thus obtained.