2015
DOI: 10.1007/s11045-015-0335-6
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Decentralized string-stability analysis for heterogeneous cascades subject to load-matching requirements

Abstract: A heterogeneous cascade of stable linear time-invariant subsystems is studied in terms of the spatial and temporal propagation of boundary conditions. The particular context requires constant spatial boundary conditions to be asymptotically matched by the interconnection signals along the string (e.g., to match supply to demand in steady state). Furthermore, the transient response associated with a step change in the spatial boundary condition must remain bounded across space in a string-length independent fas… Show more

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Cited by 11 publications
(12 citation statements)
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“…The leader is represented by a signal q 0 (t) ∈ R nq , which can be considered as a spatial boundary condition to the string. In some applications q 0 is interpreted as a reference signal to be asymptotically followed by the other components (e.g., reference position in longitudinal platooning problems (Ioannou and Chien, 1993), water flow-rate in automated irrigation channels (Soltanian and Cantoni, 2015)). The components of the string are denoted by Σ i , i ∈ N, and are described by the following LTI state-space equations…”
Section: Local Component Modelmentioning
confidence: 99%
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“…The leader is represented by a signal q 0 (t) ∈ R nq , which can be considered as a spatial boundary condition to the string. In some applications q 0 is interpreted as a reference signal to be asymptotically followed by the other components (e.g., reference position in longitudinal platooning problems (Ioannou and Chien, 1993), water flow-rate in automated irrigation channels (Soltanian and Cantoni, 2015)). The components of the string are denoted by Σ i , i ∈ N, and are described by the following LTI state-space equations…”
Section: Local Component Modelmentioning
confidence: 99%
“…The choice of space ∞ corresponds to spatially uniform boundedness of signals, a sensible assumption and requirement in most of the applications. The spatial boundary (reference) function is usually assumed to be q 0 ∈ L 2 or q 0 ∈ L ∞ or both (Soltanian and Cantoni, 2015). Variables of interest, z i , are often required to belong to L ∞ (e.g., spacing errors in platooning problems to avoid collisions).…”
Section: Definitions For Heterogeneous String Stability and Performancementioning
confidence: 99%
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“…This paper is about LQ optimal control problems with system dynamics arising from the cascade interconnection of N subsystems subject to constraints over a finite time horizon. Such systems can be found in the study of irrigation and drainage networks (Li, Cantoni, & Weyer, 2005;Puig et al, 2009;Soltanian & Cantoni, 2015), mutli-reservoir and hydro-power systems (Labadie, 2004;Şahin & Morari, 2010), vehicle platoons (Seiler, Pant, & Hedrick, 2004), and supply chain management (Disney & Towill, 2003). Attention is drawn to exploiting structure in the spatial dimension of the dynamics.…”
Section: Introductionmentioning
confidence: 99%