Franco Garofalo

Controllability of complex networks via pinning.

We study the problem of controlling a general complex network towards an assigned synchronous evolution, by means of a pinning control strategy. We define the pinning-controllability of the network in terms of the spectral properties of an extended network topology. The roles of the control and coupling gains as well as of the number of pinned nodes are also discussed.

Variable structure model reference adaptive control systems

Model reference adaptive controllers, when only input and output measurements are available, are designed using the theory of variable structure systems. State variable filters are used in order to obtain differentiator-free controllers. The proposed design allows the error transient to be prescribed in advance. The drawbacks deriving from the typical high-frequency chattering of the control signal during the sliding motion can be partially eliminated by means of a little modification of the adaptation law that does not cause the error signal to deteriorate considerably.

Synchronization of complex networks through local adaptive coupling

Two local adaptive strategies for the synchronization of complex networks are discussed in this paper. One, termed as vertex-based, uses local adaptive coupling gains at each node in the network. The other, named edge-based, associates to each edge in the network an adaptive coupling gain, determined solely on the basis of local information. The global asymptotic stability of the synchronous evolution is proven for both strategies using appropriate Lyapunov-based techniques. The effectiveness of the adaptive methodologies presented in the paper is shown via two representative examples: adaptive consensus and the adaptive synchronization of a network on N coupled Chuas circuits.

Robust model tracking control for a class of nonlinear plants

We propose a new model-following control scheme for a class of nonlinear plants. The feedback control signal is a continuous function of all its arguments. It is shown that this scheme guarantees that tracking error remains bounded and tends to a neighborhood of the origin with a rate not inferior to an exponential one; furthermore, it allows the designer to arbitrarily prescribe the rate of convergence and the size of the set of ultimate boundedness.

Stability robustness of interval matrices via Lyapunov quadratic forms

A sufficient condition for the robust stability of a class of interval matrices is derived using the Lyapunov approach. The matrices considered have elements which are nonlinear functions of a vector of independent and bounded parameters. The robust stability condition requires that a quadratic form be positive definite in a finite number of conspicuous points of an enlarged parameter space. >

Optimal tracking for automotive dry clutch engagement

Abstract Based on a state space dynamic model of a typical automotive driveline, a new control technique for the dry clutch engagement process is proposed. The feedback controller is designed following an optimal control approach by using the crankshaft speed and the clutch disk speed as state variables: a tracking problem is formulated and solved by using the engine torque and the clutch torque as control variables. The controller guarantees fast engagement, minimum slipping losses and comfortable lock-up. The critical standing start operating conditions are considered. Numerical results show the good performance obtained with the proposed controller.

New sufficient conditions for the stability of slowly varying linear systems

The frozen-time approach is used to state some new sufficient conditions for the stability of linear time-varying systems. An upper bound on the norm of the time derivative of system matrix which, under different assumptions on frozen-time system eigenvalues, guarantees asymptotic stability or exponential stability of the system is established. >

New results on composite control of singularly perturbed uncertain linear systems

Abstract We consider the problem of “stabilizing” uncertain, singularly perturbed, linear, time-varying, systems whose fast dynamics can be unstable. We propose a class of nonlinear composite controllers which assure global uniform ultimate boundedness of the trajectories of the closed loop system, provided the singular perturbation parameter is sufficiently small. These controllers consist of a fast controller which stabilizes the fast dynamics and a slow controller which yields the desired stability properties for the slow dynamics. We consider the structure of the fast controller to be simpler than structures previously proposed in the literature. To obtain these controllers, we first develop some new results for singularly perturbed systems under output feedback. In particular, it is shown that the matching assumption , which deals with the manner in which the uncertainties enter the system, and is made on the reduced-order system, is invariant under linear feedback of the fast variable.

Smooth engagement for automotive dry clutch

Two piecewise linear time-invariant models of the automotive driveline are presented and their hybrid structure due to the presence of the dry clutch is highlighted. Based on a second order model, a slip control technique for the dry clutch engagement process is proposed. The feedback controller is designed by using the crankshaft speed and the clutch disk speed as measured variables. The controller guarantees comfortable lock-up and avoids the engine stall by decoupling the control of engine speed and slip speed. The regulation of the slip acceleration at the lock-up is shown to reduce the undesired driveline oscillations. The critical standing start operating conditions are considered and numerical results show the good performance of the proposed controller.

Bifurcations in piecewise-smooth feedback systems

This paper is concerned with the analysis and classification of non-standard bifurcations in piecewise smooth feedback systems. Bifurcations involving fixed points in maps, equilibria and limit cycles in flows are considered with particular attention to: border collisions of fixed points in maps; non-smooth bifurcations of equilibria, grazing bifurcations and sliding bifurcations of limit cycles in flows. The aim is to describe existing and novel results to form the basis of a consistent theory of bifurcations in such systems. In so doing, a novel approach to classify non-smooth bifurcations of equilibria in flows is presented. Experimental results on pulse-width modulated voltage-mode controlled DC/DC power converters motivates the relevance to applications of the analysis proposed.