Anticipative LQG Control

The continuous-time LQG problem with complete state observationis solved in the ‘clairvoyant’ case when controlis based on knowledge of the complete past and future of thenoise. This allows us to compute explicitly the expected valueof perfect information, i.e. the reduction in average cost thatis possible if the usual nonanticipativity constraint on thecontrols is waived.     

A Moving Boundary Problem for the Sphere

A new technique is employed to solve a moving boundary problemin a sphere. A transformation is given which considerably simplifiesthe non-linearities associated with the moving boundary andenables an iterative analytic series solution to be found. Threeterms of the series expansion are obtained analytically andnumerically evaluated for comparison with results of previousauthors. Graphs of the motion of the reaction (freezing) frontand concentration (temperature) profiles behind the front aregiven. Also tabulated are the times to complete reaction (freezing)of the particle (that is the time for the moving boundary toreach the centre of the sphere).