Model reduction for hybrid systems with state-dependent jumps

Abstract

In this paper we present a model reduction technique based on moment matching for a class of hybrid systems with state-dependent jumps. The problem of characterizing the steady-state for this class of systems is studied and a result which allows to described the steadystate response of hybrid systems through the use of a hybrid mapping is given. Then a family of hybrid reduced order models which achieve moment matching and are easily parameterizable is provided. The special case of periodic input signals is analyzed and conditions for applying the technique are given for this class. A numerical simulation illustrates the results.

Model reduction for linear differential inclusions: moment-set and time-variance

“…Model reduction for differential equations is a mature field. Several approaches have been proposed for linear differential equations [8]- [17], nonlinear differential equations [18]- [23], and more general classes of differential equations [24]- [29], just to cite a few. For differential inclusions the problem of model reduction is almost completely unexplored, with few possible exceptions.…”

Multiple conformance to hybrid-automata-modelled requirements for detecting indoor temperature anomalies

“…Conformance testing checks observable behaviours of implementation with that described by its specification, i.e., whether the implementation satisfies the properties provided by the specification. 12,42 It can be applied to various areas, e.g., protocol engineering, [43][44][45] process mining, 46 model reduction, [47][48][49] build a model from a simple one, and verification of implementation against the specification. 12,13,50 A test sequence is needed to apply conformance testing to a protocol implementation.…”

“…48 Conformance testing checks the conformity of the low dimensional system with its original one. Scarciotti and Astolfi 49 proposed a hybrid characterization of the mapping describing the steady-state response of hybrid systems with state-dependent jumps. Mazzi et al 47 presented a methodology for the construction of a reduced-order hybrid model that is approximatively equivalent to a given hybrid system.…”

“…Conformance relations include refinement, 50 inputoutput conformance, 42,[53][54][55] and closeness of output trajectories. 12,13,47,49,56,57 The conformance relation is between a system under test and the formal model that represents its specification. Useful relations are that relying on some ordering from abstract to more concrete models.…”

Model reduction for linear switched systems with autonomous switching

“…In contrast to [25], the current paper provides an error bound, and the proposed model reduction procedure is based on balanced truncation using the common grammians. In [26], [27], a model reduction procedure which guarantees that the reduced model has the same steady-state output response to certain inputs as the original model. In contrast, the current paper proposes error bounds for all finite energy inputs.…”