Lyapunov function
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About
A Lyapunov function is a scalar, energy-like mathematical function used to analyze the stability of dynamical systems without requiring explicit solutions to their governing equations. Named after Russian mathematician Aleksandr Lyapunov, it works by demonstrating that a system's "energy" decreases over time, guaranteeing convergence to a desired equilibrium or trajectory. In robotics and AI, Lyapunov functions are foundational tools for designing and verifying controllers — from robotic manipulators and mobile robots to aerial and underwater vehicles. Engineers construct these functions to formally prove that a control law will drive a robot to its goal state and remain stable despite uncertainties, disturbances, or nonlinear dynamics. They underpin techniques such as backstepping, sliding mode control, adaptive control, and neural network-based control, where stability guarantees are critical. The importance of Lyapunov functions lies in their ability to provide rigorous mathematical proof of safety and stability, which is essential when deploying autonomous systems in unpredictable real-world environments where failure carries significant consequences.
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A calculus for computing Filippov's differential inclusion with application to the variable structure control of robot manipulators
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Extended State Observer-Based Integral Sliding Mode Control for an Underwater Robot With Unknown Disturbances and Uncertain Nonlinearities
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Adaptive Parameter Estimation and Control Design for Robot Manipulators With Finite-Time Convergence
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<i>Non-linear Control for Underactuated Mechanical Systems</i>
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