Stabilisation of hybrid stochastic differential equations by delay feedback control

This paper is concerned with the exponential mean-square stabilisation of hybrid stochastic differential equations (also known as stochastic dierential equations with Markovian switching) by delay feedback controls. Although the stabilisation by non-delay feedback controls for such equations has been discussed by several authors, there is so far little on the stabilisation by delay feedback controls and our aim here is mainly to close the gap. To make our theory more understandable as well as to avoid complicated notations, we will restrict our underlying hybrid stochastic dierential equations to a relatively simple form. However our theory can certainly be developed to cope with much more general equations without any diculty

Intermittent predictive control of an inverted pendulum

Intermittent predictive pole-placement control is successfully applied to the constrained-state control of a prestabilised experimental inverted pendulum

Control of posture with FES systems

One of the major obstacles in restoration of functional FES supported standing in paraplegia is the lack of knowledge of a suitable control strategy. The main issue is how to integrate the purposeful actions of the non-paralysed upper body when interacting with the environment while standing, and the actions of the artificial FES control system supporting the paralyzed lower extremities. In this paper we provide a review of our approach to solving this question, which focuses on three inter-related areas: investigations of the basic mechanisms of functional postural responses in neurologically intact subjects; re-training of the residual sensory-motor activities of the upper body in paralyzed individuals; and development of closed-loop FES control systems for support of the paralyzed joints

Maximum information gain in weak or continuous measurements of qudits: complementarity is not enough

To maximize average information gain for a classical measurement, all outcomes of an observation must be equally likely. The condition of equally likely outcomes may be enforced in quantum theory by ensuring that one's state $\rho$ is maximally different, or complementary, to the measured observable. This requires the ability to perform unitary operations on the state, conditioned on the results of prior measurements. We consider the case of measurement of a component of angular momentum for a qudit (a $D$-dimensional system, with $D=2J+1$). For weak or continuous-in-time (i.e. repeated weak) measurements, we show that the complementarity condition ensures an average improvement, in the rate of purification, of only 2. However, we show that by choosing the optimal control protocol of this type, one can attain the best possible scaling, $O(D^{2})$, for the average improvement. For this protocol the acquisition of information is nearly deterministic. Finally we contrast these results with those for complementarity-based protocols in a register of qbits.Comment: 21 pages, 21 figures. V2 published versio