Optimal control in a noisy system.

We describe a simple method to control a known unstable periodic orbit (UPO) in the presence of noise. The strategy is based on regarding the control method as an optimization problem, which allows us to calculate a control matrix A. We illustrate the idea with the Rossler system, the Lorenz system, and a hyperchaotic system that has two exponents with positive real parts. Initially, a UPO and the corresponding control matrix are found in the absence of noise in these systems. It is shown that the strategy is useful even if noise is added as control is applied. For low noise, it is enough to find a control matrix such that the maximum Lyapunov exponent lambda(max)<0, and with a single non-null entry. If noise is increased, however, this is not the case, and the full control matrix A may be required to keep the UPO under control. Besides the Lyapunov spectrum, a characterization of the control strategies is given in terms of the average distance to the UPO and the control effort required to keep the orbit under control. Finally, particular attention is given to the problem of handling noise, which can affect considerably the estimation of the UPO itself and its exponents, and a cleaning strategy based on singular value decomposition was developed. This strategy gives a consistent manner to approach noisy systems, and may be easily adapted as a parametric control strategy, and to experimental situations, where noise is unavoidable.

Laryngeal mask for difficult intubation in children.

We present a new intubation technique using an oral preformed tracheal tube passed through a laryngeal mask. Six patients (neonate to six months old) with craniofacial malformations of head and neck and scheduled for reconstructive plastic surgery are the basis of this report. An inhalation induction with increasing doses of halothane in oxygen while maintaining spontaneous ventilation was performed. Once an adequate anaesthetic depth was achieved, a direct laryngoscopy was performed. The epiglottis could not be seen in any of the patients. Anaesthesia was deepened in order to insert the laryngeal mask, size 1 or 2, with an oral preformed 3.5 or 4.0 tracheal tube inside it. Correct position of the mask was confirmed by capnography. The preformed tracheal tube was then advanced 1-2 cm. and its position in the trachea verified. The 15 mm connector was then removed, and an adult intubating stylet was attached to the end of the tracheal tube. The laryngeal mask was removed, holding the stylet and tube in place. Once the mask was removed, the stylet was disconnected, and the 15 mm connector reattached. Our experience was that this takes about 20 to 30 s. We recommended this technique in paediatric patients in which a difficult intubation is foreseen.