Giancarlo Ferrari-Trecate

A clustering technique for the identification of piecewise affine systems

We propose a new technique for the identification of discrete-time hybrid systems in the piecewise affine (PWA) form. This problem can be formulated as the reconstruction of a possibly discontinuous PWA map with a multi-dimensional domain. In order to achieve our goal, we provide an algorithm that exploits the combined use of clustering, linear identification, and pattern recognition techniques. This allows to identify both the affine submodels and the polyhedral partition of the domain on which each submodel is valid avoiding gridding procedures. Moreover, the clustering step (used for classifying the datapoints) is performed in a suitably defined feature space which allows also to reconstruct different submodels that share the same coefficients but are defined on different regions. Measures of confidence on the samples are introduced and exploited in order to improve the performance of both the clustering and the final linear regression procedure.

Containment Control in Mobile Networks

In this paper, the problem of driving a collection of mobile robots to a given target destination is studied. In particular, we are interested in achieving this transfer in an orderly manner so as to ensure that the agents remain in the convex polytope spanned by the leader-agents, while the remaining agents, only employ local interaction rules. To this aim we exploit the theory of partial difference equations and propose hybrid control schemes based on stop-go rules for the leader-agents. Non-Zenoness, liveness and convergence of the resulting system are also analyzed.

Average consensus problems in networks of agents with delayed communications

The present paper is devoted to the study of average consensus problems for undirected networks of dynamic agents having communication delays. The accent is put here on the study of the time-delays influence: both constant and time-varying delays are considered, as well as uniform and non uniform repartitions of the delays in the network. The main results provide sufficient conditions (also necessary in most cases) for existence of average consensus under bounded, but otherwise unknown, communication delays. Simulations are provided that show adequation with these results.

Identification of Hybrid Systems A Tutorial

This tutorial paper is concerned with the identification of hybrid models, i.e. dynamical models whose behavior is determined by interacting continuous and discrete dynamics. Methods specifically aimed at the identification of models with a hybrid structure are of very recent date. After discussing the main issues and difficulties connected with hybrid system identification, and giving an overview of the related literature, this paper focuses on four different approaches for the identification of switched affine and piecewise affine models, namely an algebraic procedure, a Bayesian procedure, a clustering-based procedure, and a bounded-error procedure. The main features of the selected procedures are presented, and possible interactions to still enhance their effectiveness are suggested.

Stability and stabilization of piecewise affine and hybrid systems: an LMI approach

In this paper we present various algorithms both for stability analysis and state-feedback design for discrete-time piecewise affine systems. Our approach hinges on the use of piecewise quadratic Lyapunov functions that can be computed as the solution of a set of linear matrix inequalities. We show that the continuity of the Lyapunov function is not required in the discrete-time case. Moreover, the basic algorithms are made less conservative by exploiting the switching structure of piecewise affine systems and by using relaxation procedures.

Moving horizon estimation for hybrid systems

We propose a state-smoothing algorithm for hybrid systems based on moving-horizon estimation (MHE) by exploiting the equivalence between hybrid systems modeled in the mixed logic dynamical form and piecewise affine systems. We provide sufficient conditions on the time horizon and the penalties on the state at the beginning of the estimation horizon to guarantee asymptotic convergence of the MHE scheme. Moreover, we propose two practical algorithms for the computation of penalties that allow us to implement MHE by solving a mixed-integer quadratic program.

Distributed Moving Horizon Estimation for Linear Constrained Systems

This paper presents a novel distributed estimation algorithm based on the concept of moving horizon estimation. Under weak observability conditions we prove convergence of the state estimates computed by any sensors to the correct state even when constraints on noise and state variables are taken into account in the estimation process. Simulation examples are provided in order to show the main features of the proposed method.

Comparison of four procedures for the identification of hybrid systems

In this paper we compare four recently proposed procedures for the identification of PieceWise AutoRegressive eXogenous (PWARX) and switched ARX models. We consider the clustering-based procedure, the bounded-error procedure, and the Bayesian procedure which all identify PWARX models. We also study the algebraic procedure, which identifies switched linear models. We introduce quantitative measures for assessing the quality of the obtained models. Specific behaviors of the procedures are pointed out, using suitably constructed one dimensional examples. The methods are also applied to the experimental identification of the electronic component placement process in pick-and-place machines.

A Clustering Technique for the Identification of Piecewise Affine Systems

We propose a new technique for the identification of discrete-time hybrid systems in the Piece-Wise Affine (PWA) form. The identification algorithm proposed in [10] is first considered and then improved under various aspects. Measures of confidence on the samples are introduced and exploited in order to improve the performance of both the clustering algorithm used for classifying the data and the final linear regression procedure. Moreover, clustering is performed in a suitably defined space that allows also to reconstruct different submodels that share the same coefficients but are defined on different regions.

Observability and controllability of piecewise affine and hybrid systems

We prove, in a constructive way, the equivalence between hybrid and piecewise affine systems. By focusing our investigation on the latter class, we show through counter-examples that observability and controllability properties cannot be easily deduced from those of the component linear subsystems. Instead, we propose practical numerical tests based on mixed-integer linear programming.