Learning‐based robust neuro‐control: A method to compute control Lyapunov functions

Abstract

Nonlinear dynamical systems play a crucial role in control systems because, in practice, all the plants are nonlinear, and they are also a hopeful description of complex robot movements. To perform a control and stability analysis of a nonlinear system, usually, a Lyapunov function is used. In this article, we proposed a method to compute a control Lyapunov function (CLF) for nonlinear dynamics based on a learning robust neuro-control strategy. The procedure uses a deep neural network architecture to generate control functions supported by the Lyapunov stability theory. An estimation of the region of attraction is produced for advanced stability analysis. We implemented two numerical examples to compare the performance of the proposed technique with some existing methods.The proposed method computes a CLF that provides the stabilizability of the systems and produced better solutions to nonlinear systems in the design of stable controls without linear approximations and in the presence of disturbances.

Learning‐based robust control methodologies under information constraints

“…The authors in Reference 11, the authors proposed a method to compute a control Lyapunov function for nonlinear dynamics based on a deep learning robust neuro‐control strategy. An estimation of the region of attraction is produced for advanced stability analysis as well.…”

A Physics-Informed Neural Network Method to Approximate Homogeneous Lyapunov Functions

“…The authors in [10] provide the LyaNet technique for training ODEs that can give adequate prediction performance, quicker inference dynamics convergence, and more significant adversarial robustness. In [15], a deep neural network architecture is used to determine a numerical control Lyapunov function for nonlinear dynamics and an estimate of the region of the attraction, guaranteeing its stability.…”

Dynamic Lyapunov Machine Learning Control of Nonlinear Magnetic Levitation System

“…The National Academies journal has stated in 2016 that: "today's practice of CPS system design and implementation is often ad hoc and unable to support the level of complexity, scalability, security, safety, interoperability, and flexible design and operation that will be required to meet future needs". While previous literature in [17,18] focused on toggling the control law between two or more options through machine learning. In addition, several assumptions or utilizing machine learning are used to utilize the control law over multiple iterations.…”