Ph. D. Project
Title:
Control and state observer design of under-actuated and/or constrained nonlinear systems. Application to 2D-3D robots.
Dates:
2024/05/01 - 2027/04/30
Supervisor(s):
Description:
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.
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.
Keywords:
Nonlinear systems - control - state estimation - underactuated - constrained - AI
Department(s):
| Control Identification Diagnosis |