Point-actuated feedback control of multidimensional interfaces

We consider the application of feedback control strategies with point actuators to stabilise desired interface shapes. We take a multidimensional Kuramoto--Sivashinsky equation as a test case; this equation arises in the study of thin liquid films, exhibiting a wide range of dynamics in different parameter regimes, including unbounded growth and full spatiotemporal chaos. In the case of limited observability, we utilise a proportional control strategy where forcing at a point depends only on the local observation. We find that point-actuated controls may inhibit unbounded growth of a solution, if they are sufficient in number and in strength, and can exponentially stabilise the desired state. We investigate actuator arrangements, and find that the equidistant case is optimal, with heavy penalties for poorly arranged actuators. We additionally consider the problem of synchronising two chaotic solutions using proportional controls. In the case when the full interface is observable, we construct feedback gain matrices using the linearised dynamics. Such controls improve on the proportional case, and are applied to stabilise non-trivial steady and travelling wave solutions

Point-actuated feedback control of multidimensional interfaces

We consider the application of feedback control strategies with point actuators to stabilise desired interface shapes. We take a multidimensional Kuramoto--Sivashinsky equation as a test case; this equation arises in the study of thin liquid films, exhibiting a wide range of dynamics in different parameter regimes, including unbounded growth and full spatiotemporal chaos. In the case of limited observability, we utilise a proportional control strategy where forcing at a point depends only on the local observation. We find that point-actuated controls may inhibit unbounded growth of a solution, if they are sufficient in number and in strength, and can exponentially stabilise the desired state. We investigate actuator arrangements, and find that the equidistant case is optimal, with heavy penalties for poorly arranged actuators. We additionally consider the problem of synchronising two chaotic solutions using proportional controls. In the case when the full interface is observable, we construct feedback gain matrices using the linearised dynamics. Such controls improve on the proportional case, and are applied to stabilise non-trivial steady and travelling wave solutions.Comment: 28 page

Sparse tree search optimality guarantees in POMDPs with continuous observation spaces

Partially observable Markov decision processes (POMDPs) with continuous state and observation spaces have powerful flexibility for representing real-world decision and control problems but are notoriously difficult to solve. Recent online sampling-based algorithms that use observation likelihood weighting have shown unprecedented effectiveness in domains with continuous observation spaces. However there has been no formal theoretical justification for this technique. This work offers such a justification, proving that a simplified algorithm, partially observable weighted sparse sampling (POWSS), will estimate Q-values accurately with high probability and can be made to perform arbitrarily near the optimal solution by increasing computational power

Ground state magnetic dipole moment of 35K

The ground state magnetic moment of 35K has been measured using the technique of nuclear magnetic resonance on beta-emitting nuclei. The short-lived 35K nuclei were produced following the reaction of a 36Ar primary beam of energy 150 MeV/nucleon incident on a Be target. The spin polarization of the 35K nuclei produced at 2 degrees relative to the normal primary beam axis was confirmed. Together with the mirror nucleus 35S, the measurement represents the heaviest T = 3/2 mirror pair for which the spin expectation value has been obtained. A linear behavior of gp vs. gn has been demonstrated for the T = 3/2 known mirror moments and the slope and intercept are consistent with the previous analysis of T = 1/2 mirror pairs.Comment: 14 pages, 5 figure