Approximate Reduction of Dynamical Systems

The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction of nonlinear systems is typically performed in an exact manner - as is the case with mechanical systems with symmetry--which, unfortunately, limits the type of systems to which it can be applied. The goal of this paper is to consider a more general form of reduction, termed approximate reduction, in order to extend the class of systems that can be reduced. Using notions related to incremental stability, we give conditions on when a dynamical system can be projected to a lower dimensional space while providing hard bounds on the induced errors, i.e., when it is behaviorally similar to a dynamical system on a lower dimensional space. These concepts are illustrated on a series of examples

On Exact/Approximate Reduction of Dynamical Systems Living on Piecewise linear Partition

Abstract. Order reduction problem for dynamical systems living on piecewise linear partitions is addressed in this paper. This problem is motivated by analysis and control of hybrid systems. The technique presented is based on the transformation of affine dynamical systems inside the cells into a new structure and it can be applied for both exact reduction and also approximate model re-duction. In this method both controllability and observability of the affine system inside the poly-topes are considered for the reduction purpose. The framework is illustrated with a numerical ex-ample.

A Control-Oriented Notion of Finite State Approximation

We consider the problem of approximating discrete-time plants with finite-valued sensors and actu- ators by deterministic finite memory systems for the purpose of certified-by-design controller synthesis. Building on ideas from robust control, we propose a control-oriented notion of finite state approximation for these systems, demonstrate its relevance to the control synthesis problem, and discuss its key features.Comment: IEEE Transactions on Automatic Control, to appea