• Robust control of uncertain systems
  The contribution given in [t.1, j.1, c.1] concerns a comparison between classical robust stability conditions for linear time-invariant systems under unstructured perturbations. Some properties of the families of systems whose stabilization through a given compensator is guaranteed by each of the considered robust stability conditions, are formally derived, and specific situations where the use of the one condition is preferable to the use of the others, because it guarantees the stabilization of a larger class of perturbed systems, are illustrated.
  The paper [c.2] proposes two sufficient conditions guaranteeing robust stability and performance in the face of unstructured perturbations expressed in linear fractional form. The proposed conditions generalize some known conditions related to particular cases of unstructured perturbations, namely multiplicative and additive perturbations. One of the two conditions can be applied in the context of a wide class of performance specifications.
  Recent contributions deal with the topic of robust anti-windup. In [c.6], a two-step algorithm for the synthesis of output feedback weakened anti-windup compensators is proposed for the case of additively perturbed systems. The first step determines a state feedback stabilizing law guaranteeing a finite L₂ gain on a suitable nonlinear "mismatch" system. In the second step, a loop-shaping approach is adopted to design a linear filter which ensures overall robust stability, meanwhile minimizing the amount of anti-windup performance sacrificed. Both steps can be efficiently implemented using standard LMI software. In [c.7], a quantitative measure of the performance/robustness trade-off involved in the weakened anti-windup definition is given. Then, a procedure for selecting suitable values for the parameters of the weakened anti-windup compensator is described.
• Piecewise affine system identification
  Piecewise affine system identification concerns the problem of identifying piecewise affine (PWA) models of discrete-time nonlinear systems from input-output data. PWA systems are collections of linear and/or affine subsystems. The switching between different dynamics is determined by the partition of the state and input space into a finite number of polyhedral regions. The interest in such a model class is motivated by the fact that it can approximate any nonlinear dynamics with arbitrary accuracy. In addition, given the equivalence between PWA systems and several classes of hybrid systems, PWA system identification techniques can be applied to obtain hybrid models.
  The identification of a PWA model is a difficult problem, because it involves the simultaneous estimation of the parameters of the affine submodels, and the hyperplanes defining the partition of the state and input space (or the regressor space, for models in regression form). This issue underlies a classification problem, namely each data point must be associated to the most suitable submodel. The problem becomes even more difficult when the number of submodels must be also estimated.
  The contribution developed in [t.2, j.2, b.1, c.3, c.4] is an algorithm for the identification of PWA models in regressive form inspired by ideas from set-membership identification. The proposed approach characterizes the model by imposing a bound for prediction errors on the estimation data set. This makes it possible to formulate the estimation of both the number and the parameters of the submodels, and the data classification, as a single combinatorial optimization problem, for whose solution a greedy randomized technique proposed in the literature has been adopted and enhanced. The polyhedral partition is finally estimated by means of classical linear separation techniques. The bound on the error can be used as a tuning knob in order to find the desired trade-off between the quality of fit and the model complexity. The algorithm has been successfully applied on real applications, for instance on the identification of an electronic component placement process in a pick-and-place machine.
  Another important issue that has been studied, is concerned with the definition of suitable criteria for validation and quality evaluation of the identified PWA models. Indeed, classical criteria such as residual analysis and whiteness tests, can be not satisfactory when applied to this non-smooth class of models. In the comparison papers [b.2, b.3], some quality indexes have been proposed, and used to compare several PWA system identification procedures recently appeared in the literature. Moreover, a tutorial paper covering different theoretical and methodological aspects of hybrid system identification, has been recently published [j.3].
  Current research is focusing on the problem of identifying a discrete-time nonlinear system composed by interconnected linear and nonlinear subsystems. A representation based on linear fractional transformations is adopted in [c.9] to model the considered class of systems. An iterative identification procedure is proposed, which alternates the estimation of the linear and the nonlinear subsystems. Standard identification techniques are applied to the linear subsystem, while the technique in [j.2] is employed to estimate a piecewise affine approximation of the nonlinear component. Numerical examples have shown that the proposed procedure is able to successfully profit from the knowledge of the interconnection structure.
• Equivalence of piecewise affine representations
  The conversion of discrete-time PieceWise Affine (PWA) models from state space to input-output form, has been addressed in [c.10], where necessary and sufficient conditions are given for a PWA state space model to admit equivalent input-output representations. When an equivalent input-output model exists, a constructive procedure has been presented to derive both its parameters and the partition of the regressor domain. It has been shown that the number of modes and the number of parameters may grow considerably when converting a PWA state space model into an equivalent input-output representation. The proposed equivalence results are expected to be helpful for transferring the prior knowledge possibly available in the state space to the identification of input-output models. Moreover, by clarifying the existing relations between equivalent state space and input-output representations, the proposed results can be also useful for tackling the minimal state space realization problem for PWARX models.
• Modeling and control of environmental systems
  A decision support system (DSS) for the management of coastal lagoons under strong anthropic exploitation, has been designed and developed in the context of the EU Project "DITTY". The papers [c.5] and [c.8] propose a multicriteria and interdisciplinary DSS, which integrates different mathematical and analytical models (such as biogeochemical, hydrodynamic, ecological, socio-economic models), and allows to analyze and evaluate the global impact of new management options on the ecosystem performance from the social, economic and environmental point of view. Since the socio-economic and environmental interests are typically contrasting objectives, between which a suitable trade-off has to be found, multicriteria analysis tools like the Analytic Hierarchy Process are used for evaluating, comparing and ranking the different management options.

Theses

Journal papers

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Submitted papers