Modelling and control of nonlinear systems using Gaussian processes with partial model information

Gaussian processes are gaining increasing popularity among the control community, in particular for the modelling of discrete time state space systems. However, it has not been clear how to incorporate model information, in the form of known state relationships, when using a Gaussian process as a predictive model. An obvious example of known prior information is position and velocity related states. Incorporation of such information would be beneficial both computationally and for faster dynamics learning. This paper introduces a method of achieving this, yielding faster dynamics learning and a reduction in computational effort from O(Dn2) to O((D - F)n2) in the prediction stage for a system with D states, F known state relationships and n observations. The effectiveness of the method is demonstrated through its inclusion in the PILCO learning algorithm with application to the swing-up and balance of a torque-limited pendulum and the balancing of a robotic unicycle in simulation. © 2012 IEEE.

Single event molecular signalling for estimation and control

Cell biology is characterised by low molecule numbers and coupled stochastic chemical reactions with intrinsic noise permeating and dominating the interactions between molecules. Recent work [9] has shown that in such environments there are hard limits on the accuracy with which molecular populations can be controlled and estimated. These limits are predicated on a continuous diffusion approximation of the target molecule (although the remainder of the system is non-linear and discrete). The principal result of [9] assumes that the birth rate of the signalling species is linearly dependent on the target molecule population size. In this paper, we investigate the situation when the entire system is kept discrete, and arbitrary non-linear coupling is allowed between the target molecule and downstream signalling molecules. In this case it is possible, by relying solely on the event triggered nature of control and signalling reactions, to define non-linear reaction rate modulation schemes that achieve improved performance in certain parameter regimes. These schemes would not appear to be biologically relevant, raising the question of what are an appropriate set of assumptions for obtaining biologically meaningful results. © 2013 EUCA.