Anthony M. Bloch

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logical organization of the text and the proofs of its theorems, the text should be counted as a success. It is also clearly written, and there are some effective pedagogical devices. In the discussion of Cochran’s theorem about partitioning variance, the authors wisely limit the discussion to a partition into three parts, and point out that the reasoning(More)
We develop a method for the stabilization of mechanical systems with symmetry based on the technique of controlled Lagrangians. The procedure involves making structured modifications to the Lagrangian for the uncontrolled system, thereby constructing the controlled Lagrangian. The Euler–Lagrange equations derived from the controlled Lagrangian describe the(More)
We extend the method of controlled Lagrangians (CL) to include potential shaping, which achieves complete state-space asymptotic stabilization of mechanical systems. The CL method deals with mechanical systems with symmetry and provides symmetry-preserving kinetic shaping and feedback-controlled dissipation for state-space stabilization in all but the(More)
This paper studies the perturbation of a Lie-Poisson (or, equivalently an Euler-Poincaré) system by a special dissipation term that has Brockett’s double bracket form. We show that a formally unstable equilibrium of the unperturbed system becomes a spectrally and hence nonlinearly unstable equilibrium after the perturbation is added. We also investigate the(More)
We developed a new approach to investigate how the nervous system activates multiple redundant muscles by studying the endpoint force fluctuations during isometric force generation at a multi-degree-of-freedom joint. We hypothesized that, due to signal-dependent muscle force noise, endpoint force fluctuations would depend on the target direction of index(More)
The main goal of this paper is to prove that if the energymomentum (or energy-Casimir) method predicts formal instability of a relative equilibrium in a Hamiltonian system with symmetry, then with the addition of dissipation, the relative equilibrium becomes spectrally and hence linearly and nonlinearly unstable. The energy-momentum method assumes that one(More)
In this paper we develop a constructive approach to the determination of stabilizing control laws for a class of Lagrangian mechanical systems with symmetry* systems whose underlying dynamics are governed by the Euler}PoincareH equations. This work extends our previous work on the stabilization of mechanical control systems using the method of controlled(More)
This paper obtains feedback stabilization of an inverted pendulum on a rotor arm by the “method of controlled Lagrangians”. This approach involves modifying the Lagrangian for the uncontrolled system so that the Euler-Lagrange equations derived from the modified or “controlled” Lagrangian describe the closed-loop system. For the closed-loop equations to be(More)