Related papers: Ensuring Both Positivity and Stability Using Secto…
This paper investigates the robustness of the Lur'e problem under positivity constraints, drawing on results from the positive Aizerman conjecture and robustness properties of Metzler matrices. Specifically, we consider a control system of…
We study the local stability of nonlinear systems in the Lur'e form with static nonlinear feedback realized by feedforward neural networks (FFNNs). By leveraging positivity system constraints, we employ a localized variant of the Aizerman…
In recent years, Neural Networks (NNs) have been employed to control nonlinear systems due to their potential capability in dealing with situations that might be difficult for conventional nonlinear control schemes. However, to the best of…
This survey paper deals with the stabilization of nonlinear systems by analyzing the controlling method in terms of state feedback and output feedback. A brief overview of some literature on how the feedback controller of some dynamic…
Neural network controllers have shown potential in achieving superior performance in feedback control systems. Although a neural network can be trained efficiently using deep and reinforcement learning methods, providing formal guarantees…
Stability and control of a non-linear system represent an important system configuration that frequently arises in practical engineering. Stability covers a vast range of systems that do not obey the superposition principle and applies to…
This paper proposes a data-driven approach to design a feedforward Neural Network (NN) controller with a stability guarantee for plants with unknown dynamics. We first introduce data-driven representations of stability conditions for Neural…
This paper addresses the problem of stabilization for infinite-dimensional systems. In particular, we design nonlinear stabilizers for both linear and nonlinear abstract systems. We focus on two classes of systems: the first class comprises…
Recent research has shown that supervised learning can be an effective tool for designing optimal feedback controllers for high-dimensional nonlinear dynamic systems. But the behavior of these neural network (NN) controllers is still not…
The paper shows that positive linear systems can be stabilized using positive Luenberger-type observers. This is achieved by structuring the observer as monotonically converging upper and lower bounds on the state. Analysis of the…
Neural network controllers have the potential to improve the performance of feedback systems compared to traditional controllers, due to their ability to act as general function approximators. However, quantifying their safety and…
In this report we deal with the problem of global output feedback stabilization of a class of $n$-dimensional nonlinear positive systems possessing a one-dimensional unknown, though measured, part. We first propose our main result, an…
In this paper, we study the positivity and (uniform) exponential stability of a large class of perturbed semigroups. Our approach is essentially based on the feedback theory of infinite-dimensional linear systems. The obtained results are…
Typically, it is desirable to design a control system that is not only robustly stable in the presence of parametric uncertainties but also guarantees an adequate level of system performance. However, most of the existing methods need to…
This paper proposes a Recurrent Neural Network (RNN) controller for lane-keeping systems, effectively handling model uncertainties and disturbances. First, quadratic constraints cover the nonlinearities brought by the RNN controller, and…
Recent research shows that supervised learning can be an effective tool for designing near-optimal feedback controllers for high-dimensional nonlinear dynamic systems. But the behavior of neural network controllers is still not well…
Classical conditions for ensuring the robust stability of a linear system in feedback with a sector-bounded nonlinearity include small gain, circle, passivity, and conicity theorems. In this work, we present a similar stability condition,…
This note studies the robust output feedback stabilization problem of a class of multi-input multi-output invertible nonlinear systems, for which an "ideal" state feedback based on feedback linearization can be designed under certain mild…
Neural networks have become increasingly popular in controller design due to their versatility and efficiency. However, their integration into feedback systems can pose stability challenges, particularly in the presence of uncertainties.…
Stability certification and identifying a safe and stabilizing initial set are two important concerns in ensuring operational safety, stability, and robustness of dynamical systems. With the advent of machine-learning tools, these issues…