arXiv subjects

Dave Auckly

Publications and source records attributed to Dave Auckly.

21 records · Page 2Linked to original sources

arXiv2001

On the lambda-equations for matching control laws

We discuss matching control laws for underactuated systems. We previously showed that this class of matching control laws is completely charactarized by a linear system of first order partial differential equations for one set of variables followed by a linear system of first order PDEs for a second set of variables. Here we derive a new first order system of partial differential equations that encodes all compatibility conditions for the lambda-equations. We give four examples illustrating different features of matching control laws. The last example is a system with two unactuated degrees of freedom that admits only basic solutions to the matching equations. There are systems with many matching control laws where only basic solutions are potentially useful. We introduce a rank condition indicating when this is likely to be the case.

math.OC↗

arXiv1999

Control of nonlinear underactuated systems

In this paper we introduce a new method to design control laws for non-linear underactuated systems. Our method produces an infinite dimensional family of control laws, whereas most control techniques only produce a finite dimensional family. These control laws each come with a natural Lyapunov function. The inverted pendulum cart is used as an example. In addition, we construct an abstract system which is open loop unstable and cannot be stabilized using any linear control law, and demonstrate that our method produces a stabilizing control law.

math.OC↗

arXiv1997

A topological method to compute spectral flow

This paper describes a topological method to compute the spectral flow of a family of twisted Dirac operators, it includes two detailed examples. Briefly, a formula of Atiyah, Patodi and Singer expresses the spectral flow in terms of Chern-Simons invariants and rho invariants. The first step is to construct a flat cobordism to a new bigger 3-manifold. The advantage of the new connection is that it is in the path component of a reducible connection. The second step is to calculate the effect of these operations on the invariants. The final step is an application of the G-signature theorem to compute the invariants.

math.GT↗