System for continuous-time optimization with pre-defined finite-time convergence

Abstract

A controller for controlling a system is provided. The controller performs measuring variables via an interface to generate a vector of variables, providing a cost function, with respect to the system, based on the vector variables using weighting factors, wherein the vector variables are represented by a time-step, computing first-derivative of the cost function at an initial time-step, obtaining a convergence time from the first-derivative of the cost function, computing second derivative of the cost function and generating an optimization differential equation based on the first and second derivatives of the cost function, proceeding, starting with the initial time-step, to obtain a value of the optimization differential equation by solving the optimization differential equation, in an iteration manner, with a predetermined time step being multiplied with the value of the solved differential equation to obtain next vector variables corresponding to a next iteration time-step, until the time-step reaches the convergence time, and outputting optimal values of the vector of variables and the cost function.