A general framework for boundary equilibrium bifurcations of Filippov systems

As parameters are varied a boundary equilibrium bifurcation (BEB) occurs when an equilibrium collides with a discontinuity surface in a piecewise-smooth system of ODEs. Under certain genericity conditions, at a BEB the equilibrium either transitions to a pseudo-equilibrium (on the discontinuity surface) or collides and annihilates with a coexisting pseudo-equilibrium. These two scenarios are distinguished by the sign of a certain inner product. Here it is shown that this sign can be determined from the number of unstable directions associated with the two equilibria by using techniques developed by Feigin. A new normal form is proposed for BEBs in systems of any number of dimensions. The normal form involves a companion matrix, as does the leading order sliding dynamics, and so the connection to the stability of the equilibria is explicit. In two dimensions the parameters of the normal form distinguish, in a simple way, the eight topologically distinct cases for the generic local dynamics at a BEB. A numerical exploration in three dimensions reveals that BEBs can create multiple attractors and chaotic attractors, and that the equilibrium at the BEB can be unstable even if both equilibria are stable. The developments presented here stem from seemingly unutilised similarities between BEBs in discontinuous systems (specifically Filippov systems as studied here) and BEBs in continuous systems for which analogous results are, to date, more advanced

The ASLOTS concept: An interactive, adaptive decision support concept for Final Approach Spacing of Aircraft (FASA). FAA-NASA Joint University Program

This presentation outlines a concept for an adaptive, interactive decision support system to assist controllers at a busy airport in achieving efficient use of multiple runways. The concept is being implemented as a computer code called FASA (Final Approach Spacing for Aircraft), and will be tested and demonstrated in ATCSIM, a high fidelity simulation of terminal area airspace and airport surface operations. Objectives are: (1) to provide automated cues to assist controllers in the sequencing and spacing of landing and takeoff aircraft; (2) to provide the controller with a limited ability to modify the sequence and spacings between aircraft, and to insert takeoffs and missed approach aircraft in the landing flows; (3) to increase spacing accuracy using more complex and precise separation criteria while reducing controller workload; and (4) achieve higher operational takeoff and landing rates on multiple runways in poor visibility

Scaling laws for large numbers of coexisting attracting periodic solutions in the border-collision normal form

A wide variety of intricate dynamics may be created at border-collision bifurcations of piecewise-smooth maps, where a fixed point collides with a surface at which the map is nonsmooth. For the border-collision normal form in two dimensions, a codimension-three scenario was described in previous work at which the map has a saddle-type periodic solution and an infinite sequence of stable periodic solutions that limit to a homoclinic orbit of the saddle-type solution. This paper introduces an alternate scenario of the same map at which there is an infinite sequence of stable periodic solutions due to the presence of a repeated unit eigenvalue in the linearization of some iterate of the map. It is shown that this scenario is codimension-four and that the sequence of periodic solutions is unbounded, aligning with eigenvectors corresponding to the unit eigenvalue. Arbitrarily many attracting periodic solutions coexist near either scenario. It is shown that if $K$ denotes the number of attracting periodic solutions, and $\varepsilon$ denotes the distance in parameter space from one of the two scenarios, then in the codimension-three case $\varepsilon$ scales with $\lambda^{-K}$, where $\lambda > 1$ denotes the unstable stability multiplier associated with the saddle-type periodic solution, and in the codimension-four case $\varepsilon$ scales with $K^{-2}$. Since $K^{-2}$ decays significantly slower than $\lambda^{-K}$, large numbers of attracting periodic solutions coexist in open regions of parameter space extending substantially further from the codimension-four scenarios than the codimension-three scenarios.Comment: 37 pages, 5 figures, submitted to: Int. J. Bifurcation Chao

An investigation of air transportation technology at the Massachusetts Institute of Technology, 1990-1991

Brief summaries are given of research activities at the Massachusetts Institute of Technology (MIT) under the sponsorship of the FAA/NASA Joint University Program. Topics covered include hazard assessment and cockpit presentation issues for microburst alerting systems; the situational awareness effect of automated air traffic control (ATC) datalink clearance amendments; a graphical simulation system for adaptive, automated approach spacing; an expert system for temporal planning with application to runway configuration management; deterministic multi-zone ice accretion modeling; alert generation and cockpit presentation for an integrated microburst alerting system; and passive infrared ice detection for helicopter applications

MARYLAND'S REGULATORY APPROACH TO NUTRIENT MANAGEMENT

Environmental Economics and Policy,