Stabilization of unknown nonlinear systems using a cognition‐based framework

Abstract

This paper considers an adaptive control method based on a cognition-based framework to stabilize unknown nonlinear systems. In order to fulfill the task of stabilization, neither the information about the systems dynamical structure nor the knowledge about system physical behaviors, but the system states, which are assumed as measurable, are required. The structure of the proposed controller consists of three parts. The first part is based on a recurrent neural network (RNN) to be used for local identification of the unknown nonlinear system in real time. The network can be utilized as system characteristics, which is further used to design the controller within the third part. In the second part, the set of the given input values leading to stable 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, a suitable control input value is chosen accordingly to a time-relevant criteria from the set of input values generated in the second part of the controller. These three parts and their internal connections are arranged within a so-called cognition framework. The proposed cognitive controller is able to gain useful knowledge (with local validity) and define autonomously a suitable control input with respect to the requirements of the time-relevant criteria. Numerical examples are shown to demonstrate the successful application and performance of the method.