Live briefing
Everything about Control-Lyapunov function
Function in control theory
In control theory, a control-Lyapunov function (CLF) is an extension of the idea of Lyapunov function to systems with control inputs. The ordinary Lyapunov function is used to test whether a dynamical system is (Lyapunov) stable or asymptotically stable. Lyapunov stability means that if the system starts in a state in some domain, then the state will remain in for all time. For asymptotic stability, the state is also required to converge to. A control-Lyapunov function is used to test whether a system is asymptotically stabilizable, that is whether for any state there exists a control such that the system can be brought to the zero state asymptotically by applying the control. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Control-Lyapunov functionA 5-minute orientation
- Skim a recent paper: Exponential Control Lyapunov-Barrier Function Using a Filtering-Based Concurrent Learning Adaptive ApproachInfluential work since 2022
- Pick up a classic book: Nonlinear control of engineering systemsThe most-reprinted book on the subject
- Read the landmark paper: A Lyapunov Function for Economic Optimizing Model Predictive ControlCited 458 times
- Go sideways: Small control propertyA closely related topic
- Go sideways: Artstein's theoremA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
A Lyapunov Function for Economic Optimizing Model Predictive Control
Stabilization with guaranteed safety using Control Lyapunov–Barrier Function
A control Lyapunov function approach to multiagent coordination
NONLINEAR OPTIMAL CONTROL: A CONTROL LYAPUNOV FUNCTION AND RECEDING HORIZON PERSPECTIVE
A Survey on the Control Lyapunov Function and Control Barrier Function for Nonlinear-Affine Control Systems
Barrier Lyapunov function-based adaptive control for hypersonic flight vehicles
A Control Lyapunov Function Approach to Feedback Stabilization of Logical Control Networks
Control Lyapunov-Barrier function-based model predictive control of nonlinear systems
🆕 Influential since 2022
Exponential Control Lyapunov-Barrier Function Using a Filtering-Based Concurrent Learning Adaptive Approach
Vector Control Lyapunov Function Based Stabilization of Nonlinear Systems in Predefined Time
Integral Barrier Lyapunov Function-Based Adaptive Event-Triggered Control of Flexible Riser Systems
Barrier Lyapunov function and adaptive backstepping-based control of a quadrotor UAV
Control Lyapunov‐barrier function‐based safe reinforcement learning for nonlinear optimal control
📚 Books worth reading
Nonlinear control of engineering systemsWarren E. Dixon, S. Nagarkatti · 2003
Hybrid dynamical systemsRafal Goebel · 2012
Robust Filtering for Uncertain SystemsHuijun Gao, Xianwei Li · 2014
Lyapunov-based control of mechanical systemsMarcio S. de Queiroz, Darren Dawson · 2000
Networked and Distributed Predictive ControlPanagiotis D. Christofides · 2011- 📕Pokazateli Li︠a︡punova v teorii lineĭnykh sistem upravlenii︠a︡Efim Natanovich Rozenvasser · 1977
Liapunov functions and stability in control theoryAndrea Bacciotti, Lionel Rosier · 2001- 📕Variable structure and Lyapunov controlA. S. I. Zinober · 1993
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Small control property For applied mathematics, in nonlinear control theory, a non-linear system of the form x ˙ = f ( x , u ) {\displaystyle {\dot {x}}=f(x,u)} is said to satisfy…
- Artstein's theorem Artstein's theorem states that a nonlinear dynamical system in the control-affine form x ˙ = f ( x ) + ∑ i = 1 m g i ( x ) u i {\displaystyle {\dot {\mathbf…
- Input-to-state stability Input-to-state stability (ISS) is a stability notion widely used to study stability of nonlinear control systems with external inputs. Roughly speaking…
- Lyapunov stability Various types of stability may be discussed for the solutions of differential equations or difference equations describing dynamical systems. The most…
- Backstepping In control theory, backstepping is a technique developed circa 1990 by Petar V. Kokotovic, and others for designing stabilizing controls for a special…
- RISE controllers The robust integral of the sign of the error controllers or RISE controllers constitute a class of continuous robust control algorithms developed for nonlinear…
- Sliding mode control In control systems, sliding mode control (SMC) is a nonlinear control method that alters the dynamics of a nonlinear system by applying a discontinuous…
- Comparison function In applied mathematics, comparison functions are several classes of continuous functions, which are used in stability theory to characterize the stability…