By Alessandro Astolfi, Lorenzo Marconi
This ebook is a tribute to Prof. Alberto Isidori at the get together of his sixty fifth birthday. Prof. Isidori’s proli?c, pioneering and high-impact study task has spanned over 35 years. all through his profession, Prof. Isidori has built ground-breaking effects, has initiated researchdirections and has contributed towardsthe foundationofnonlinear controltheory.In addition,his commitment to give an explanation for problematic concerns and di?cult suggestions in an easy and rigorous approach and to inspire younger researchers has been instrumental to the highbrow progress of the nonlinear keep watch over group around the globe. the quantity collects 27 contributions written by means of a complete of fifty two researchers. The crucial writer of every contribution has been chosen one of the - searchers who've labored with Prof. Isidori, have in?uenced his study job, or have had the privilege and honour of being his PhD scholars. The contributions handle a signi?cant variety of keep watch over themes, together with th- retical matters, complex purposes, rising keep watch over instructions and educational works. the range of the components lined, the variety of members and their foreign status supply proof of the impression of Prof. Isidori within the keep watch over and structures conception groups. The ebook has been divided into six elements: process research, Optimization equipment, suggestions layout, rules, Geometric equipment and Asymptotic research, re?ecting vital keep an eye on components that have been strongly in- enced and, often times, pioneered by way of Prof. Isidori.
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Additional info for Analysis and design of nonlinear control systems : in honor of Alberto Isidori
The behavioral framework treats a model for what it is: an exclusion law. Of course, in applications, the behavior B must be speciﬁed somehow, and it is here that diﬀerential equations (and diﬀerence equations for discrete-time systems) enter the scene. In the equations describing a behavior, very often other variables appear in addition to those the model aims at. The origin of these auxiliary variables varies from case to case. They may be state variables (as in ﬂows, automata, and input/state/output systems); they may be potentials (as in the wellknown expressions for the solutions of Maxwell’s equations); most frequently and most germane for the purposes of the present article, they are interconnection variables.
Whence a (dynamical) system is deﬁned as a triple Σ = (T, W, B) with B, the behavior , a subset of WT (WT is standard mathematical notation for the set of all maps from T to W). The behavior is the central object in this deﬁnition. It formalizes which signals w : T → W are possible, according to the model: those in B, and which are not: those not in B. The behavioral framework treats a model for what it is: an exclusion law. Of course, in applications, the behavior B must be speciﬁed somehow, and it is here that diﬀerential equations (and diﬀerence equations for discrete-time systems) enter the scene.
C. 4 The Module Embedding The module embedding (i) associates with each vertex of the interconnection architecture a module, and (ii) speciﬁes for every vertex a 1 ↔ 1 assignment between the edges and leaves adjacent to the vertex and the terminals of the module that has been associated with this vertex. This is illustrated in the ﬁgure below. Fig. 6. Terminal assignment Since each edge is adjacent to two vertices, each edge is associated by the module embedding with 2 terminals. ), or of opposite type (one input, one output) if the terminals are of logical type.
Analysis and design of nonlinear control systems : in honor of Alberto Isidori by Alessandro Astolfi, Lorenzo Marconi