1 Deep Learning Optimization of Non-linear Chaotic System and Lyapunov Controller Parameters Amr Mahmoud, Youmna Ismaeil and Mohamed Zohdy Abstract—The introduction of unexpected system disturbances and dynamics doesn’t allow initially selected static system and controller parameters to guarantee continued system stability and high performance. In this research we present a novel approach for detecting early failure indicators of non-linear highly chaotic system and accordingly predict the best parameter calibrations to offset such instability using deep machine learning regression model. The approach proposed continuously monitors the system and controller signals. The Re-calibration of the system and controller parameters is triggered according to a set of conditions designed to maintain system stability without compromise to the system speed, intended outcome or required processing power. The deep neural model predicts the parameter values that would best counteract the expected system in-stability. To demonstrate the effectiveness of the proposed approach, it is applied to the non-linear complex combination of Duffing-Van der pol oscillators. The approach is also tested under different scenarios the system and controller parameters are initially chosen incorrectly or the system parameters are changed while running or new system dynamics are introduced while running to measure effectiveness and reaction time. Index Terms—System parametrization, Deep Machine Learn- ing, Complex system, non-linear controller, duffing-van der pol, Lyapunov control I. I NTRODUCTION Lyapunov control has been proven successful in controlling highly chaotic non-linear oscillators [1][2][3] . One of the fundamentals that contribute to the success or failure of any type of control strategy is the controller and system parameters. Therefore, researchers have explored different methods to find the precise parameters that would lead to achieving the best system results [4][5]. One of the methods that was utilized to achieve the previously mentioned goals is Genetic algorithm (GA). GAs have been successful in cases where all the system dynamics are clearly defined and known to some extent or with systems where limited system disturbances are introduced and minor parameter tuning is required [6][7]. In some cases, several system assumptions are needed in order to allow the GA to run successfully. Due to some of the limitations found in using GAs such as inability to quickly converge to the final solution or adapt A. Mahmoud is with the Department of Electrical and computer en- gineering, Oakland University Rochester, MI, 48307 USA e-mail: (amah- moud@oakland.edu). Y. Ismaeil is with the Department of computer science, Saarland University Saarbr¨ ucken,Germany e-mail: (s8yoisma@stud.uni-saarland.de). M. Zohdy is with the Department of Electrical and computer engi- neering, Oakland University Rochester, MI, 48307 USA e-mail: (mzo- hdy@oakland.edu). to unknown system dynamics or unknown disturbances. Researchers though after different approaches that wouldn’t reduce the system agility and at the same time would be able to handle unknown system characteristics. A hybrid approach of Fuzzy Control and GAs was researched [8] but system linearization is a requirement in order to use the previously mentioned method . Another approach that is recently being researched is the use of Machine Learning to enhance the controller performance. For example through the use of Episodic learning [9][10]. Most recently, there is the introduction neural lyapunov control which proposes the use of deep learning to find the control and Lyapunov functions. The approach mentioned in [9][10] is suitable for find the best system parameters that would initially lead the system to stability and reduced the system error. The problem with approach in [9][10] is that it assumes that the system is deterministic, time invariant, and affine in the control input. while in real life situation external perturbations might occur resulting in system failure at any moment while the system is running [11][12]. The approach proposed in [25] [26] and [27]attempts to predict the control and Lyapunov functions that would lead to system stability but under specific conditions where the system dynamics are deterministic in nature. The approach proposed in this research is novel to the best of our knowledge in that it discards the assumption of an ideal environment or fully known system dynamics and seeks continuous enhancement of the controller outcome through continuous monitoring of the system error, reference signal, system dynamics and control signal and accordingly adjust the system and controller parameters to improve the controller performance without the need to disrupt the system output. The focus of the research is to allow the Deep Learning Algorithm to learn the system from a continuously improving dataset and according to the slope of the output error the algorithm relearns the system and collects the needed information. The proposed method is applied to a non-linear chaotic combined system of Duffing and Van der pol oscillators[24]. The aforementioned system was chosen to test the Deep learning algorithm response to unpredicted system disturbances and unknown system dynamics[21][22][23]. An algorithm was developed to aid and trigger the Deep Neural Network when needed to adapt to new system dynamics and according to preset conditions. The algorithm records and feeds an updated data set to the DNN in order to relearn the system dynamics if certain conditions are detected to be true. arXiv:2010.14746v1 [eess.SY] 28 Oct 2020