1. Control of systems subject to constraints.
• Anti-windup for exponentially unstable plants: for this class of systems, the null controllability region is bounded, and then the requirement of boundedness of trajectories (implicit in the anti-windup problem definition) is challenging. Constructive solutions based on nonlinear compensation have been proposed in [9,20,22].
• Anti-windup for plants without exponentially unstable modes: nontrivial extensions of the switching technique proposed by Zaccarian and Teel in a IEEE-TAC technical note in 2004 have been developed in [17]. The approach proposed in [17] yields semiglobal exponential stabilization if a finite number of switching regions is used, and global asymptotic stabilization if an infinite number of switching regions is used (e.g. computing in real time a new region when needed). In order to alleviate the computational burden associated with an infinite number of switching regions, a scheduled approach has been proposed in [16], where a strognly nonlinear control law is obtained via a suitable interpolation of predesigned region (obtained from the design procedure of the switching compensator). The result has been extended to deal with bounded control stabilization in [19], where the MIMO case is also considered.
• Anti-windup for plants with amplitude and rate limited inputs: in [18] a solution to this problem has been proposed, based on a suitable model of the rate and amplitude saturation nonlinearity.
• Anti-windup for discrete-time plants: previously available results for the continuous-time case have been extended to the discrete-time case in [21].
• Global asymptotic stabilization of marginally stable/unstable linear plants with bounded inputs: in order to limit the number of precomputed regions to be stored in memory, in [16] the switching scheme of [17] has been modified in a scheduled scheme, leading to a strongly nonlinear compensation law which interpolates among previously computed gains (designed as in the switching law in [17]). The result in [16], applying to single input systems, has been generalized to multi input system and adapted to anti-windup copensation in [19].
• Stabilization of systems with bounded inputs by linear controllers involving an internal deadzone loop: it has been shown in [8] that using such a compensator (including an internal deadzone loop) leads to higher performance than simply using a linear controller. The compensator design problem has been cast as a convex optimization problem (involving the solution of a set of Linear Matrix Inequalities [LMIs]).
• Stability and performance analysis for linear systems with bounded inputs: a new method has been proposed in [7], generalizing a method by Popov and using a Lyapunov function containing saturation terms.
• Stabilization of planar systems with bounded inputs: a family of global stabilizers for this class of plants has been proposed in [10], where it was also shown that the free parameters in the family can be chosen in order to guarantee an almost time-optimal (or almost fuel-optimal) regulation; moreover, any stabilizer in the proposed family is robust as a consequence of its Lipschitz continuity.
2. Control of systems subject to impacts.
The local asymptotic tracking problem for both precisely known [12,14] and uncertain [13] systems subject to impacts (in particular, elliptical billiard systems) has been solved by using a suitable generalization of the internal model principle involving jumps in its state in order to deal with discontinuities in the periodic reference and in the billiards trajectory. The proposed results have been generalized to solve the problem of periodic trajectory tracking for a wider class of linear hybrid systems in [11]. In [15] a high-gain extended observer has been proposed for the simultaneous estimation of both the velocity and the coefficient of restitution for mechanical systems subject to impacts.
3. Hybrid systems.
The collaboration with prof. Teel (Univ. of California, Santa Barbara, USA) and prof. Nesic (Univ. of Melbourne, Australia) has led to new results (published in [29]) in the field of reset systems, where the state of the controller is reset to zero when specific events occur (tipically, when the state of the controller reaches a given hypersurface). A new representation of systems containing First Order Reset Elements (FORE) has been proposed in [24]. The construction of Lyapunov functions valid as stability and performance certificates of reset systems has been described in [23]. A solution to the problem of periodic trajectory tracking for a class of linear hybrid systems with references generated by an exosystem in the same class has been given in [11].
4. Dynamic allocation for plants having redundant actuators.
A new approach has been proposed in [28], which is expected to lead to interesting results in many application fields (specific applications are now being considered in the fields of thermonuclear fusion, hybrid cars, attitude control of satellites, dual actuator hard disks).
5. Real world applications.
• Thermonuclear fusion: in collaboration with ENEA laboratories in Frascati (Roma) where the Frascati Tokamak Upgrade (FTU) experiment is located. Innovations in the real-time control software (enabling the fast deployment of innovative control algorithms) have been developed as reported in [3,27,4,2]. Extremum seeking techniques for the maximization of the Lower Hybrid power absorption during the radio frequency heating phase of plasma have been described in [6, 5, 1]. In the same context, the nonlinear effects in the power amplifiers of FTU, responsible for the instabilities detected during some experiments, have been studied in [26]. The invited session “Control of Tokamak Plasmas: past, present and future perspectives” at 2008 Conference on Decision and Control (Cancun, Mexico) has been co-organized by L. Zaccarian.
• Control of irrigation channels: in collaboration with University of Melbourne, Australia. Anti-windup techniques have been applied for the control of irrigation channels, in particular experimentation has been conducted on a channel in Queensland (Australia) [30].
• Unknown frequency sinusoidal disturbance suppression: the approach described in [25] has been studied in simulation for the suppression of a sinusoidal disturbance with unknown frequency in [12], and experiments are planned as soon as the experimental setup will be available.

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