Chaos in the square billiard with a modified reflection law.

The purpose of this paper is to study the dynamics of a square billiard with a non-standard reflection law such that the angle of reflection of the particle is a linear contraction of the angle of incidence. We present numerical and analytical arguments that the nonwandering set of this billiard decomposes into three invariant sets, a parabolic attractor, a chaotic attractor, and a set consisting of several horseshoes. This scenario implies the positivity of the topological entropy of the billiard, a property that is in sharp contrast with the integrability of the square billiard with the standard reflection law.

Observer design in switching control of neuromuscular blockade: clinical cases.

This paper concerns the application of multiple model switched methods to the control of neuromuscular blockade of patients undergoing anaesthesia. Since the model representing the neuromuscular blockade process is subject to a high level of uncertainty due both to inter-patient variability and time variations, switched methods provide the adaptation capability needed to achieve the desired performance. The paper contributions are twofold: first, it is shown that, for the type of process control problem considered, the design of the associated observer must be carefully performed. Guidelines are provided for adequate selection of the characteristic polynomial defining the observer error dynamics. Second, clinical results using atracurium as blocking agent are reported in order to illustrate the use of the proposed control structure in actual clinical practice.