A tracking performance analysis method for autonomous systems with neural networks⁎⁎The paper funded by the National Research, Development and Innovation Office (NKFIH) under OTKA Grant Agreement No. K 135512. The research was supported by the Ministry of Innovation and Technology NRDI Office within the framework of the Autonomous Systems National Laboratory Program. The work of Bálazs Németh was partially supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences and the UNKP-20-5 New National Excellence Program of the Ministry for Innovation and Technology from the source of the National Research, Development and Innovation Fund.

Intelligent manufacturing and automated systems several complex control tasks must be carried out. A possible way for improving the performance level of the systems is the application of machine-learning-based agents, e.g. neural networks in the control loop. A novel challenge of these complex systems is to provide analysis and synthesis methods, with which their performance levels can be assessed. The paper proposes analysis method for tracking control systems, whose control loop contains feed-forward neural networks. Through the method the asymptotic stability and the tracking performance through decay rate are assessed. The proposed method is based on the linear approximation of the closed-loop system, and thus, a polytopic set of linear systems is resulted. Using the resulted polytopic system an analysis method based on an optimization is formed, whose result approximates the decay rate of the system. The effectiveness of the method is illustrated through a benchmark example, i.e. the torque control of a one-degree-of-freedom robotic arm.