A Model‐Free Stability‐Based Adaptive Control Method for Unknown Nonlinear Systems

Abstract

This contribution considers an adaptive control method based on a cognition-based framework to stabilize unknown nonlinear systems online. This method requires only the system outputs, which are assumed as measurable. The structure of the framework consists of three parts. The first part is based on a dynamic recurrent neural network (DRNN) to be used for local identification, analysis and multi-step-ahead prediction of the system. In the second part, a set of given input values will be calculated numerically with a geometrical criterion based on a suitable definition of quadratic stability. In the third part, the most suitable control input value is chosen for the next predefined time interval according to a suitable cost function. The proposed controller is able to gain useful local knowledge and define autonomously suitable local control input according to the stability criterion. Numerical examples using inverted pendulum system and Lorenz system are shown to demonstrate the successful application and performance of the method.

Data-driven stabilization of unknown nonlinear dynamical systems using a cognition-based framework

“…The method of exhaustive grid search can be used to determine optimization target (26) as firstly detailed in [22] and therefore briefly repeated in the sequel. The endpoint of each subinterval will be considered as a possible value of the corresponding input signal.…”

“…A similar proof regarding the controlled system is given in [29]. The vector w is obtained by the transformation of all system states x, x = 0 with (22) using ϕ as an orthogonal matrix.…”

“…The details of each module and their interconnections are illustrated in the sequel. Cognition-based framework for stabilization [22] As shown in the figure, in the external environment, the system to be controlled is an unknown system, which means that the related mathematical model is not known neither to the stabilizer nor to the designer, and therefore the system model is not used. The inputs and outputs including the disturbances as well as the given goal of the stabilization task are the only information about the unknown system which are used for design and are transmitted during operation to the cognitive stabilizer.…”

“…In order to solve the stabilization problem above, the cognition-based framework for stabilization is developed in [22] and shown repeatedly in Fig. 1.…”

“…Previous publications of the authors Nowak (née Shen) and Söfkker are related to similar topics. In [22], the cognitive stabilizer is developed firstly using a simple but not optimal algorithm applied to a SIMO simulation example. In [18], the cognitive stabilizer is improved with another algorithm and applied to a SIMO chaotic nonlinear system numerically.…”