Gianfranco Parlangeli

On the Reachability and Observability of Path and Cycle Graphs

In this technical note 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 = 2i ; i ∈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.

Controllability and Observability of Grid Graphs via Reduction and Symmetries

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.

A fault tolerant sliding mode controller for accommodating actuator failures.

This paper addresses the actuator failure compensation problem, and considers an uncertain linear plant which is supposed to undergo unknown failures causing the plant input components to be stuck at some uncertain but bounded time functions. A control policy, based on sliding mode, is presented, which guarantees the detection of the fault and the identification of the failed component by means of a suitable test input. Once the failed component has been identified, the control law is reconfigured, redistributing the control activity among the controllers still working. The proposed controller has been tested by simulation on a benchmark problem.

Observability and reachability of grid graphs via reduction and symmetries

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.

Output zeroing of MIMO plants in the presence of actuator and sensor uncertain hysteresis nonlinearities

This note tackles the output zeroing problem of a square multiple-input-multiple-output plant containing uncertain nonsmooth hysteresis-like nonlinearities in actuator and sensor devices simultaneously. To this purpose, a robust sliding mode controller, based on the output of a reduced order observer, has been designed using it, such control law ensuring both the asymptotical zeroing of the sensing nonlinearities output and the boundedness of the unavailable states. Theoretical results have been validated by simulation.

Decentralized Air Traffic Management Systems: Performance and Fault Tolerance

Abstract In this paper, we investigate the advantages and disadvantages of a proposed decentralized Air Traffic Management (ATM) system, in which aircraft are allowed a larger degree of autonomy in deciding their route (“free flight”) instead of following prespecified “sky freeways”. A decentralized management scheme is described, which incorporates a hybrid control system switching among different optimal control solutions according to changes in the information structure between agents. The performance and robustness of this decentralization scheme is assessed by means of simulation trials, showing that, whereas optimality of plans is strictly nonincreasing, robustness to system failures is likely to improve.

Relative Pose Observability Analysis for 3D Nonholonomic Vehicles Based on Range Measurements Only

Abstract The paper addresses the nonlinear observability analysis of the 3D position and orientation (pose) of a nonhonomic floating vehicle based on range only measurements. The problem is of interest in several applications including underwater and aerospace scenarios where two or more vehicles need to estimate their relative pose for navigation purposes. The observability conditions depend on the systems velocities: observable and unobservable motions are identified for the considered kinematics model. The analysis is a necessary pre-requisite for the design of observer filters for the given nonlinear system.

On the observability of path and cycle graphs

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 = 2i; 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.

Robust control of nonlinear uncertain systems with sandwiched backlash.

This paper proposes a novel approach for the stabilization problem of a sandwich nonlinear system with a backlash nonlinearity between two dynamic blocks. To this purpose a robust sliding mode controller has been designed ensuring the convergence of the system trajectories in a neighborhood of the origin of arbitrary width (independently of the backlash size). Theoretical results have been validated by simulation.

Single range observability for cooperative underactuated underwater vehicles

The paper describes the single range observability issues related to a kinematics model of cooperating underwater vehicles. The paper extends previous results building on an augmented state technique allowing to reformulate the nonlinear observability problem in terms of a linear time varying one. As a result, all possible (globally) unobservable motions are characterized in terms of the systems initial conditions and velocity commands. These results are functional to the design of observers for the navigation of cooperating marine robots having an underactuated model as the one considered. The fundamental results reported are also illustrated by numerical simulations providing evidence of different motions generating the same output, i.e. lacking observability.