34,241 research outputs found
Control refinement for discrete-time descriptor systems: a behavioural approach via simulation relations
The analysis of industrial processes, modelled as descriptor systems, is
often computationally hard due to the presence of both algebraic couplings and
difference equations of high order. In this paper, we introduce a control
refinement notion for these descriptor systems that enables analysis and
control design over related reduced-order systems. Utilising the behavioural
framework, we extend upon the standard hierarchical control refinement for
ordinary systems and allow for algebraic couplings inherent to descriptor
systems.Comment: 8 pages, 3 figure
Synthesizing Switching Controllers for Hybrid Systems by Continuous Invariant Generation
We extend a template-based approach for synthesizing switching controllers
for semi-algebraic hybrid systems, in which all expressions are polynomials.
This is achieved by combining a QE (quantifier elimination)-based method for
generating continuous invariants with a qualitative approach for predefining
templates. Our synthesis method is relatively complete with regard to a given
family of predefined templates. Using qualitative analysis, we discuss
heuristics to reduce the numbers of parameters appearing in the templates. To
avoid too much human interaction in choosing templates as well as the high
computational complexity caused by QE, we further investigate applications of
the SOS (sum-of-squares) relaxation approach and the template polyhedra
approach in continuous invariant generation, which are both well supported by
efficient numerical solvers
Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems
The present article presents a summarizing view at differential-algebraic
equations (DAEs) and analyzes how new application fields and corresponding
mathematical models lead to innovations both in theory and in numerical
analysis for this problem class. Recent numerical methods for nonsmooth
dynamical systems subject to unilateral contact and friction illustrate the
topicality of this development.Comment: Preprint of Book Chapte
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