Stabilization of Unknown Nonlinear Systems using a Cognition-based Framework

Abstract

AbstractThis contribution considers an adaptive control method based on a cognition-based framework to stabilize unknown nonlinear systems in real time. Although important improvements have been made to deal with the control problem of unknown nonlinear system, the processes of both modeling and designing control input for different nonlinear dynamical systems are still mostly accomplished by humans. In order to solve this task, a cognition-based framework has been developed for the controller to stabilize the dynamical behavior of unknown systems. Using this framework, the controller requires neither the information about the systems dynamical structure nor the knowledge about system physical behaviors. The task is solved using only the system outputs, which are assumed as measurable. The structure of the proposed framework consists of three parts. The first part is based on a dynamic recurrent neural network (DRNN) to be used not only for local identification of the unknown nonlinear system in real time, but also for multi-step prediction, which is further used to design the control inputs within a cost function in the third part. In the second part, a set of given input values, leading to the stabilization of the behavior of the closed-loop system, will be calculated numerically with a geometrical criterion based on a suitable definition of quadratic stability. In the third part, suitable control input values are chosen for the next predefined time interval according to a suitable chosen cost function from the set of input values generated in the second part. The controller using the proposed framework is able to gain useful local knowledge and define autonomously suitable local control inputs for the next predefined time interval with respect to the requirements of the cost function including online realized stability judgement. Numerical examples are shown to demonstrate the successful application and performance of the method.