Journal ArticleDOI
Controlled Lagrangians, Symmetries and Conditions for Strong Matching
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In this paper, the general matching problem is solved and the matching conditions are given a geometrical formulation, which is used for simplifying and extending the method of Auckly, Kapitanski and White.About:
This article is published in IFAC Proceedings Volumes.The article was published on 2000-03-01. It has received 52 citations till now.read more
Citations
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Journal ArticleDOI
Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment
TL;DR: This work describes a class of systems for which IDA-PBC yields a smooth asymptotically stabilizing controller with a guaranteed domain of attraction, given in terms of solvability of certain partial differential equations.
Journal ArticleDOI
Interconnection and damping assignment passivity-based control: a survey
TL;DR: The fundamental theory, main new results and practical applications of this control system design approach are reviewed as well as to discuss the current open problems and future directions.
Journal ArticleDOI
Controlled Lagrangians and the stabilization of mechanical systems. II. Potential shaping
TL;DR: The method of controlled Lagrangians is extended to include potential shaping, which achieves complete state-space asymptotic stabilization of mechanical systems and extends the method to include a class of mechanical system without symmetry such as the inverted pendulum on a cart that travels along an incline.
Journal ArticleDOI
Trajectory tracking control of port-controlled Hamiltonian systems via generalized canonical transformations
TL;DR: The main strategy adopted in this paper is to construct an error system, which describes the dynamics of the tracking error, by a passive port-controlled Hamiltonian system, via generalized canonical transformations and passivity-based control.
Journal ArticleDOI
The matching conditions of controlled Lagrangians and IDA-passivity based control
TL;DR: In this paper, the matching conditions resulting from the controlled Lagrangians method and the interconnection and damping assignment passivity based control (IDA-PBC) method are discussed.
References
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Proceedings ArticleDOI
Stabilization of mechanical systems using controlled Lagrangians
TL;DR: An algorithmic approach to stabilization of Lagrangian systems where energy methods can be used to find control gains that yield closed-loop stability.
Proceedings ArticleDOI
General matching conditions in the theory of controlled Lagrangians
TL;DR: In this article, the authors give necessary and sufficient conditions for matching and generalized matching and sufficient criteria for stabilizability by the generalized matching method, including an inverted pendulum on a cart.
Proceedings ArticleDOI
Matching and stabilization by the method of controlled Lagrangians
TL;DR: In this article, the authors describe a class of mechanical systems for which the "method of controlled Lagrangians" provides a family of control laws that stabilize an unstable (relative) equilibrium.
Proceedings ArticleDOI
Stabilization of the pendulum on a rotor arm by the method of controlled Lagrangians
TL;DR: Modifies the Lagrangian for the uncontrolled system so that the Euler-Lagrange equations derived from the modified or "controlled" Lagrangians describe the closed-loop system.