Subject Ph. D.

The thesis topic, jointly supervised by the University of Lorraine and the University of Gabes, concerns both the control and state estimation of a class of underactuated and/or constrained nonlinear dynamical systems using hybrid approaches based on the mathematical Model and Artificial Intelligence (AI) [1]-[2]. The practical aspect focuses on both soft and rigid robots, specifically cable-driven robots and the double inverted pendulum. The obtained results will be tested and validated through numerical simulations, and subsequently by implementing these robots.

To date, classical control theory implicitly or explicitly uses the system model to construct a state estimator, a control law, or for diagnostics. For a class of systems, under certain assumptions such as observability and/or controllability, the stability of these approaches can be demonstrated. However, in many cases, even when the model is known, finding analytical solutions based solely on the model can be challenging. The use of hybrid approaches based on models and AI techniques for controlling and observing complex systems opens up a relatively unexplored field with significant potential.

In a recent study [3] using reinforcement learning techniques with specific activation functions, the authors show that solutions could exist for optimization problems with constraints for a class of dynamical systems, unlike the classical approach that does not provide a solution.

Another significant aspect, demonstrating the importance of AI techniques in control, involves the use of learning algorithms based on available data when the model is partially known, difficult to model, time-varying, or completely unknown.

The thesis topic consists of two main parts:

1. A methodological aspect aimed at developing generic approaches, based on machine learning, for the control and observation of a class of dynamical systems. This study focuses on the use of neural networks with particular attention to real-time implementation. The considered dynamical systems are nonlinear, underactuated, with or without constraints.

2. A part dedicated to validate the obtained results through numerical simulations and experimental validation on 2D/3D robots: - A robot with four motors and an effector that moves using four cables. - A vertically stabilized double inverted pendulum using an electric cart.

The key advantage of this platform is its representation of a wide range of nonlinear dynamical systems with additional challenges of being underactuated and constrained.

References [1] I. Goodfellow, Y. Bengio, and A. Courville. Deep learning. MIT-Press, 2016. [2] Y. LeCun, Y. Bengio, G. Hinton. Deep learning. Nature 521, pp. 436-444, 2015. [3] Farnaz Adib Yaghmaie and David J Braun. Reinforcement learning for a class of continuous-time input constrained optimal control problems. Automatica, 99 :221- 227, 2019.