Data structures and software tools for the computer aided design of control systems: a survey.

CAD software can be structured as a set of modular 'software tools' only if there is some agreement on the data structures which are to be passed between tools. Beyond this basic requirement, it is desirable to give the agreed structures the status of 'data types' in the language used for interactive design. The ultimate refinement is to have a data management capability which 'understands' how to manipulate such data types. In this paper the requirements of CACSD are formulated from the point of view of Database Management Systems. Progress towards meeting these requirements in both the DBMS and the CACSD community is reviewed. The conclusion reached is that there has been considerable movement towards the realisation of software tools for CACSD, but that this owes more to modern ideas about programming languages, than to DBMS developments. The DBMS field has identified some useful concepts, but further significant progress is expected to come from the exploitation of concepts such as object-oriented programming, logic programming, or functional programming.

Representations and algorithms for finite-state bisimulations of linear discrete-time control systems

While a large amount of research over the past two decades has focused on discrete abstractions of infinite-state dynamical systems, many structural and algorithmic details of these abstractions remain unknown. To clarify the computational resources needed to perform discrete abstractions, this paper examines the algorithmic properties of an existing method for deriving finite-state systems that are bisimilar to linear discrete-time control systems. We explicitly find the structure of the finite-state system, show that it can be enormous compared to the original linear system, and give conditions to guarantee that the finite-state system is reasonably sized and efficiently computable. Though constructing the finite-state system is generally impractical, we see that special cases could be amenable to satisfiability based verification techniques. ©2009 IEEE.

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.