No abstract

Abstract-Handling delays in control systems is difficult and is of long-standing interest. It is well known that, given a finite-dimensional linear time-invariant (FDLTI) plant and controller forming a strictly proper stable feedback connection, closed-loop stability will be maintained under a small delay in the feedback loop, although most closed loop systems become unstable for large delays. One previously unsolved fundamental problem in this context is whether, for a given FDLTI plant, an arbitrarily large delay margin can be achieved using LTI control. Here, we adopt a frequency domain approach and demonstrate that, for a strictly proper real rational plant, there is a uniform upper bound on the delay that can be tolerated when using an LTI controller, if and only if the plant has at least one closed right half plane pole not at the origin. We also give several explicit upper bounds on the achievable delay margin, and, in some special cases, demonstrate that these bounds are tight.

No abstract

While the original classical parameter adaptive controllers did not handle noise or unmodelled dynamics well, redesigned versions were proven to have some tolerance; however, exponential stabilization and a bounded gain on the noise was rarely proven. Here we consider a classical pole placement adaptive controller using the original projection algorithm rather than the commonly modified version; we impose the assumption that the plant parameters lie in a convex, compact set. We demonstrate that the closed-loop system exhibits very desireable closed-loop behaviour: there are linear-like convolution bounds on the closed loop behaviour, which confers exponential stability and a bounded noise gain, and can be leveraged to prove tolerance to unmodelled dynamics and plant parameter variation. We emphasize that there is no persistent excitation requirement of any sort; the improved performance arises from the vigilant nature of the parameter estimator.

The phase transition from a superfluid to a Mott insulator has been observed in a 23 Na BoseEinstein condensate. A dye laser detuned ≈ 5 nm red of the Na 3 2 S→ 3 2 P 1/2 transition was used to form the three dimensional optical lattice. The heating effects of the small detuning as well as the three-body decay processes constrained the timescale of the experiment. Certain lattice detunings were found to induce a large loss of atoms. These loss features were shown to be due to photoassociation of atoms to vibrational levels in the Na2 (1) 3 Σ + g state.