Mehdi Gati

Analysis of coordination in multi-agent systems through partial difference equations

In this note, we introduce the framework of partial difference equations (PdEs) over graphs for analyzing the behavior of multi-agent systems equipped with decentralized control schemes. Both leaderless and leader-follower models are considered. PdEs mimic partial differential equations (PDEs) on graphs and can be studied by introducing concepts of functional analysis strongly inspired to the corresponding ones arising in PDEs theory. We generalize different models proposed in the literature by introducing errors in the agent dynamics and analyze agent coordination through the joint use of PdEs and automatic control tools. Moreover, for the simplest control schemes, we show that the resulting PdEs enjoy properties that are similar to those of well-known PDEs like the heat equation, thus allowing to exploit physical-based reasoning for conjecturing formation properties.

ANALYSIS OF COORDINATION IN MULTI-AGENT SYSTEMS THROUGH PARTIAL DIFFERENCE EQUATIONS. PART I: THE LAPLACIAN CONTROL

In this second part of the paper we exploit the framework of Partial difference Equations (PdEs) over graphs for analyzing the behavior of multi-agent systems equipped with potential field based control schemes. We consider agent dynamics affected by errors and model the collective dynamics through nonlinear PdEs. Hinging on the properties of the Laplacian operator on graph, discussed in Part I, we prove alignment and collision avoidance both in leaderless and leader-follower models.

Computation observability regions for discrete-time hybrid systems

In this paper we focus on observability for hybrid systems in the mixed-logic dynamical form. We show that the maximal set of observable states, that is usually nonconvex and disconnected, can be represented as the union of finitely many polytopic regions. The argument, which is based on multi-parametric programming theory, is constructive and provides an algorithm for the computation of the regions.

Observability analysis and state observers for automotive powertrains with backlash: a hybrid system approach

In this paper, the observability properties of automotive powertrains with backlash are analysed. We model the powertrain as a hybrid system in the piecewise affine form and use measurements of the torque and the angular speed of the engine for computing the maximal set of observable states. This set, that is usually non-convex and disconnected, captures in a precise way how the main variables and parameters of the driveline influence the possibility of estimating the shaft twist. Then, we show how to exploit the knowledge of observable states in order to build computationally efficient deadbeat observers for the reconstruction of the powertrain states.

Computation of Observability Regions for Piecewise Affine Systems: A Projection-Based Algorithm

In this paper we consider the problem of computing sets of observable states for discrete-time, piecewise affine systems. When the maximal set of observable states is full-dimensional, we provide an algorithm for reconstructing it up to a zero measure set. The core of the method is a quantifier elimination procedure that, in view of basic results on piecewise linear algebra, can be performed via the projection of polytopes on subspaces. We also provide a necessary condition on the minimal length of the observability horizon in order to expect a full-dimensional set of observable states. Numerical experiments highlight that the new procedure is considerably faster than the one proposed in [1].