In this paper, we investigate the controllability and observability properties of a family of linear dynamical systems, whose structure is induced by the Laplacian of a grid graph. This analysis is motivated by several applications in network control and estimation, quantum computation and discretization of partial differential equations. Specifically, we characterize the structure of the grid eigenvectors by means of suitable decompositions of the graph. For each eigenvalue, based on its multiplicity and on suitable symmetries of the corresponding eigenvectors, we provide necessary and sufficient conditions to characterize all and only the nodes from which the induced dynamical system is controllable (observable). We discuss the proposed criteria and show, through suitable examples, how such criteria reduce the complexity of the controllability (respectively, observability) analysis of the grid.

This paper addresses the issue of planning smooth (C^infty) 2D paths with bounded curvature and curvature derivative connecting two assigned poses (positions and orientations). The solution builds on an approximation of Dubins shortest paths and it can be used also to link an ordered sequence of via-points. The effectiveness of the proposed planning method is validated by simulations.

Most cooperative motion tasks of multi vehicle systems require the agents to share relative localization information. Assuming the relative velocity of the vehicles to be known, under suitable observability conditions, relative localization among a pair of agents can be performed based on single range measurements. The problem addressed consists in designing a relative localization solution for a networked group of vehicles measuring mutual ranges: in particular, the objective is to exploit the presence of intra-vehicle communications to enhance the range-based relative position estimation. Geometrical constraints associated to the agents' (unknown) positions are explicitly accounted for in the estimation schema. The approach brings together a recent single range localization solution with a projection based Kalman filter estimation technique in the presence of state space constraints. Simulation examples are provided showing the effectiveness of the proposed solution.

In this paper we investigate the observability and reachability properties of a network system, running a Laplacian based average consensus algorithm, when the communication graph is a grid or a torus. More in detail, under suitable conditions on the eigenvalue multiplicity, we provide necessary and sufficient conditions, based on simple algebraic rules from number theory, to characterize all and only the nodes from which the network system is observable (reachable). For any set of observation (leader) nodes, we provide a closed form expression for the unobservable (unreachable) eigenvalues and for the eigenvectors of the unobservable (unreachable) subsystem.

In this paper we investigate the observability and reachability properties of a network system, running a Laplacian based average consensus algorithm, when the communication graph is a grid. More in detail, we characterize the structure of the grid eigenvectors by means of suitable decompositions of the graph. For each eigenvalue, based on its multiplicity and on suitable symmetries of the corresponding eigenvectors, we provide necessary and sufficient conditions to characterize all and only the nodes from which the network system is observable (reachable). We discuss the proposed criteria and show, through suitable examples, how such criteria reduce the complexity of the observability (respectively reachability) analysis of the grid.

In this paper we investigate the observability properties of a network system, running a Laplacian based average consensus algorithm, when the communication graph is a path or a cycle. More in detail, we provide necessary and sufficient conditions, based on simple algebraic rules from number theory, to characterize all and only the nodes from which the network system is observable. Interesting immediate corollaries of our results are: (i) a path graph is observable from any single node if and only if the number of nodes of the graph is a power of two, n = 2^i, i ∈ N, and (ii) a cycle is observable from any pair of observation nodes if and only if n is a prime number. For any set of observation nodes, we provide a closed form expression for the unobservable eigenvalues and for the eigenvectors of the unobservable subspace.

In this paper we investigate the reachability and observability properties of a network system, running a Laplacian based average consensus algorithm, when the communication graph is a path or a cycle. Specifically, we provide necessary and sufficient conditions, based on simple rules from number theory, to characterize all and only the nodes from which the network system is reachable (respectively observable). Interesting immediate corollaries of our results are: (i) a path graph is reachable (observable) from any single node if and only if the number of nodes of the graph is a power of two, n = 2^i; i in N, and (ii) a cycle is reachable (observable) from any pair of nodes if and only if n is a prime number. For any set of control (observation) nodes, we provide a closed form expression for the (unreachable) unobservable eigenvalues and for the eigenvectors of the (unreachable) unobservable subsystem.

Recent studies relative to range-only localization in underwater robotics applications have focused primarily on (nonlinear) observability analysis. In particular, local weak observ- ability is guaranteed as long as the motion of the system to be localized is sufficiently rich, i.e. persistency of excitation conditions need to be satisfied. These conditions typically depend on the initial state of the system and on its inputs. Once that the challenging problem of identifying the necessary initial state and input constraints for guaranteeing local weak observability has been solved, state estimation can be performed resorting to linear (Kalman-like) filters. Yet the convergence of such state estimation approaches is local. Building on recent results in this area, this paper addresses the problem of designing input signals for a class of underactuated underwater vehicles allowing global range-only pose estimation.

A Real Time implementation of an Optimal Control Strategy for a Plug-in Hybrid Electric Vehicle is presented. The optimization aimed at minimizing the overall CO2 emission of the vehicle by considering a Well-To-Wheel approach: the control objective has been achieved by applying the Pontryagin’s Minimum Principle to a mathematical model of an experimental Plug-In Series Hybrid Electric Vehicle, the ITAN500. Realistic urban driving cycles have been used in the present investigation, in order to obtain more accurate and truthful results in terms of CO2 emissions and fuel consumption, rather than those achievable by using standard speed profiles. Some important issues in terms of how to determine a suitable realtime behavior using a Hardware In the Loop (HIL) framework have been deeply discussed. Results in terms of Partial and Full Knowledge of the driving cycle have been presented.