Abstract
In this paper, a model reduction technique is introduced for piecewisesmooth (PWS) vector fields, whose trajectories fall into a Banach space, but the domain of definition of the vector fields is a nondense subset of the Banach space. The vector fields depend on a parameter that can assume different discrete values in two parts of the phase space and a continuous family of values on the boundary that separates the two parts of the phase space. In essence, the parameter parametrizes the possible vector fields on the boundary. The problem is to find one or more values of the parameter so that the solution of the PWS system on the boundary satisfies certain requirements. In this paper, we require continuous solutions. Motivated by the properties of applications, we assume that when the parameter is forced to switch between the two discrete values, trajectories become discontinuous. Discontinuous trajectories exist in systems whose domain of definition is nondense. It is shown that under our assumptions the trajectories of such PWS systems have unique forwardtime continuation when the parameter of the system switches. A finitedimensional reducedorder model is constructed, which accounts for the discontinuous trajectories. It is shown that this model retains uniqueness of solutions and other properties of the original PWS system. The model reduction technique is illustrated on a nonlinear bowed string model.
Original language  English 

Pages (fromto)  897960 
Number of pages  64 
Journal  Journal of Nonlinear Science 
Volume  29 
Issue number  3 
Early online date  30 Oct 2018 
DOIs  
Publication status  Published  15 Jun 2019 
Keywords
 Piecewisesmooth
 Model reduction
 Invariant manifolds
 Nondense domain
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Dr Robert Szalai
 Department of Engineering Mathematics  Senior Lecturer in Engineering Mathematics
 Dynamics and Control
 Applied Nonlinear Mathematics
Person: Academic , Member