Controlled Lagrangians and the stabilization of mechanical systems. I. The first matching theorem

By Anthony M. Bloch, Naomi Ehrich Leonard, Jerrold E. Marsden. IEEE Transactions on Automatic Control, 2000

546 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/7d31d135a65ce2bb34d5acac98501f7109e6f456

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Citations in the corpus

Stable Synchronization of Mechanical System Networks (2008, background): “Further, it can be easily verified that each pendulum/cart system satisfies the simplified matching conditions [1] [2].”
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].”
Multidomain modeling of nonlinear networks and systems (2009, background): “Lastly, the role of energy and the interconnections between subsystems provide the basis for various control strategies [4], [6]–[8].”
Lyapunov-Based Controller for the Inverted Pendulum Cart System (2005, background): “This system has attracted the attention of many researchers, as seen by a growing list of articles (for example, see [12], [13], [3], [8],[4] and [9]).”
The matching conditions of controlled Lagrangians and IDA-passivity based control (2002, methodology): “Proposition 4: Assumption M-1 of Bloch et al. (2000) implies that the unchanged potential energy V matches.”
Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems (2002, background): “…possible to show that modifying the kinetic energy of a simple mechanical system without a:ecting the potential energy nor the damping (as done in Bloch et al. (2000)) is tantamount—in our formulation—to selecting the closed-loop interconnection matrix as J d ( q; p ) = (cid:2) 0 M − 1 ( q ) M d…”
Interconnection and Damping Assignment Passivity-Based Control: A Survey (2004, methodology): “Actually, the approach of [14] is more modest than IDA-PBC and [18,27] in that a physically inspired parameterization for the modified kinetic energy is assumed a priori.”
Putting energy back in control (2001, background): “In particular, it is possible to show that modifying the kinetic energy of a mechanical system without affecting the potential energy or the damping (as done in [29]) is tantamount—in our formulation—to selecting the closed-loop interconnection matrix as”
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”
Interconnection and damping assignment passivity-based control of mechanical systems with underactuation degree one (2004, methodology): “[6], [7], [4], [8], the need to solve the PDEs remains the main stumbling block for a wider applicability of these methods.”
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.”
Control by Interconnection and Standard Passivity-Based Control of Port-Hamiltonian Systems (2008, methodology): “Some simple calculations show that (43) becomes , which is known as the potential energy matching equation [3], [25].”
Controlled Lagrangians and the stabilization of mechanical systems. II. Potential shaping (2001, methodology): “As shown in [13], the controlled Lagrangian has the following useful structure.”