Related papers: Learning Lyapunov Functions for Piecewise Affine S…
In this paper, we investigate the model reference adaptive control approach for uncertain piecewise affine systems with performance guarantees. The proposed approach ensures the error metric, defined as the weighted Euclidean norm of the…
This note presents an extension to the adaptive control strategy presented in [1] able to counter eventual instability due to disturbances at the input of an otherwise $\mathcal{L}_2$ stable closed-loop system. These disturbances are due to…
Establishing stability certificates for closed-loop systems under reinforcement learning (RL) policies is essential to move beyond empirical performance and offer guarantees of system behavior. Classical Lyapunov methods require a strict…
Traditional reinforcement learning lacks the ability to provide stability guarantees. More recent algorithms learn Lyapunov functions alongside the control policies to ensure stable learning. However, the current self-learned Lyapunov…
Constraint admissible positively invariant (CAPI) sets play a pivotal role in ensuring safety in control and planning applications, such as the recursive feasibility guarantee of explicit reference governor and model predictive control.…
Despite advances in learning-based methods, finding valid Lyapunov functions for nonlinear dynamical systems remains challenging. Current neural network approaches face two main issues: challenges in scalable verification and limited…
In this paper, we propose a new convex approach to stability analysis of nonlinear systems with polynomial vector fields. First, we consider an arbitrary convex polytope that contains the equilibrium in its interior. Then, we decompose the…
In this paper, we focus on the problem about direct way to design a stable controller for nonlinear system. A framework of learning controller with Lyapunov-based constraint is proposed, which is intended to transform designing and analyis…
While there has been increasing interest in using neural networks to compute Lyapunov functions, verifying that these functions satisfy the Lyapunov conditions and certifying stability regions remain challenging due to the curse of…
A controller synthesis method for state- and input-constrained nonlinear systems is presented that seeks continuous piecewise affine (CPA) Lyapunov-like functions and controllers simultaneously. Non-convex optimization problems are…
In this work we addressed the problem of stability analysis for an uncertain piecewise affine model of a genetic regulatory network. In particular we considered polytopic parameter uncertainties on the proteins production rate functions,…
While ensuring stability for linear systems is well understood, it remains a major challenge for nonlinear systems. A general approach in such cases is to compute a combination of a Lyapunov function and an associated control policy.…
The paper proposes a control-theoretic framework for verification of numerical software systems, and puts forward software verification as an important application of control and systems theory. The idea is to transfer Lyapunov functions…
The paper proposes a control-theoretic framework for verification of numerical software systems, and puts forward software verification as an important application of control and systems theory. The idea is to transfer Lyapunov functions…
In this paper, by using a characterization of functions having fractional derivative, we propose a rigorous fractional Lyapunov function candidate method to analyze stability of fractional-order nonlinear systems. First, we prove an…
This article establishes the existence of Lyapunov functions for analyzing the stability of a class of state-constrained systems, and it describes algorithms for their numerical computation. The system model consists of a differential…
We propose an automatic and formally sound method for synthesising Lyapunov functions for the asymptotic stability of autonomous non-linear systems. Traditional methods are either analytical and require manual effort or are numerical but…
Many modern nonlinear control methods aim to endow systems with guaranteed properties, such as stability or safety, and have been successfully applied to the domain of robotics. However, model uncertainty remains a persistent challenge,…
Barrier Lyapunov functions are suitable for learning control designs, due to their feature of finite duration tracking. This paper presents fractional barrier Lyapunov functions, provided and compared with the conventional ones in the…
Imitation learning is a paradigm to address complex motion planning problems by learning a policy to imitate an expert's behavior. However, relying solely on the expert's data might lead to unsafe actions when the robot deviates from the…