992 research outputs found
Putting energy back in control
A control system design technique using the principle of energy balancing was analyzed. Passivity-based control (PBC) techniques were used to analyze complex systems by decomposing them into simpler sub systems, which upon interconnection and total energy addition were helpful in determining the overall system behavior. An attempt to identify physical obstacles that hampered the use of PBC in applications other than mechanical systems was carried out. The technique was applicable to systems which were stabilized with passive controllers
Lyapunov constraints and global asymptotic stabilization
In this paper, we develop a method for stabilizing underactuated mechanical systems by imposing kinematic constraints (more precisely Lyapunov constraints). If these constraints can be implemented by actuators, i.e., if there exists a related constraint force exerted by the actuators, then the existence of a Lyapunov function for the system under consideration is guaranteed. We establish necessary and sufficient conditions for the existence and uniqueness of constraint forces. These conditions give rise to a system of PDEs whose solution is the required Lyapunov function. To illustrate our results, we solve these PDEs for certain underactuated mechanical systems of interest such as the inertia wheel-pendulum, the inverted pendulum on a cart system and the ball and beam system
Exponential Networks and Representations of Quivers
We study the geometric description of BPS states in supersymmetric theories
with eight supercharges in terms of geodesic networks on suitable spectral
curves. We lift and extend several constructions of Gaiotto-Moore-Neitzke from
gauge theory to local Calabi-Yau threefolds and related models. The
differential is multi-valued on the covering curve and features a new type of
logarithmic singularity in order to account for D0-branes and non-compact
D4-branes, respectively. We describe local rules for the three-way junctions of
BPS trajectories relative to a particular framing of the curve. We reproduce
BPS quivers of local geometries and illustrate the wall-crossing of finite-mass
bound states in several new examples. We describe first steps toward
understanding the spectrum of framed BPS states in terms of such "exponential
networks."Comment: 82 pages, 60 figures, typos fixe
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