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.

Synchronization with partial state feedback on SO(n)

In this paper we consider the problem of constructing a distributed feedback law to achieve synchronization for a group of k agents whose states evolve on SO(n) and which exchange only partial state information along communication links. The partial state information is given by the action of the state on reference vectors in ℝn. We propose a gradient based control law which achieves exponential local convergence to a synchronization configuration under a rank condition on a generalized Laplacian matrix. Furthermore, we discuss the case of time-varying reference vectors and provide a convergence result for this case. The latter helps reach synchronization, requiring less communication links and weaker conditions on the instantaneous reference vectors. Our methods are illustrated on an attitude synchronization problem where agents exchange only their relative positions observed in the respective body frames. ©2009 IEEE.

A perturbation approach to the stabilization of nonlinear cascade systems with time-delay

The effect of bounded input perturbations on the stability of nonlinear globally asymptotically stable delay differential equations is analyzed. We investigate under which conditions global stability is preserved and if not, whether semi-global stabilization is possible by controlling the size or shape of the perturbation. These results are used to study the stabilization of partially linear cascade systems with partial state feedback.