Controlled Lagrangians and the stabilization of mechanical systems. II. Potential shaping

By Anthony M. Bloch, Dong Eui Chang, Naomi Ehrich Leonard, Jerrold E. Marsden. IEEE Transactions on Automatic Control, 2001

413 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/dfab5d6e93f4c191873ef7418a3794c830f8ece5

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In Control and Systems Engineering

In Statistical and Nonlinear Physics

Citations in the corpus

Adaptive group consensus in uncertain networked Euler–Lagrange systems under directed topology (2015, background): “In general, coordination problems encountered in engineering applications can often be rephrased as the controlled synchronization or consensus problems of multi-agent systems, which aim to enhance both the robustness and performance of networked control systems [1–7].”
Controlling the inverted pendulum by means of a nested saturation function (2008, methodology): “In [2], the authors present a control strategy based on the method of controlled Lagrangian, in conjunction with some symmetry properties that the system satisfies.”
The Dynamics of Legged Locomotion: Models, Analyses, and Challenges (2006, methodology): “It provides unified Lagrangian and Hamiltonian descriptions for stability and control [41, 37, 71] and has been used to derive equations of motion, identify conserved quantities, and analyze equilibria and periodic orbits and their stability for such problems as the “snakeboard” [224], segmented cra”
Coordinated patterns of unit speed particles on a closed curve (2007, methodology): “In this spirit, methods such as energy shaping [4,27] are applied with 47 promising results for formations in the plane cf.”
Optimal and Cooperative Control of Vehicle Formations (2002, methodology): “Within the universe of nonlinear controller design tools, the method of controlled Lagrangians developed by Bloch, Leonard, Marsden and their students [5, 8, 9, 10] stands out as a natural choice for implementation in this setting.”
Dirac structures in Lagrangian mechanics Part II: Variational structures (2006, background): “• An analog of controlled Lagrangians and related stability problems for implicit Lagrangian systems; Bloch, Leonard, and Marsden [2000]; Bloch, Chang, Leonard, and Marsden [2001] ; Zenkov, Bloch, and Marsden [1998].”
Geometric control of mechanical systems (2004, positive): “The literature, historically • Godbillon [1969], Abraham and Marsden [1978], Arnol’d [1978]: Geometrization of mechanics in the 1960’s.”
Global Stabilisation of Underactuated Mechanical Systems via PID Passivity-Based Control (2016, methodology): “The parameters and initial conditions used in the simulations have been chosen according to [4] and they are given as follows: m = 0.”
Stabilization of Underactuated Mechanical Systems Via Interconnection and Damping Assignment (2000, methodology): “Remark 6 A method to stabilize simple mechanical system by modifying the kinetic energy, but without a ecting the potential energy nor the damping, has recently been proposed in [1].”
Stable Synchronization of Mechanical System Networks (2008, methodology): “In [1], it is also shown how to select new, useful coordinates (x α , y a , ˙ x α , ˙ y a ).”