Ricerc@Sapienza

The paper addresses the problem of an observer design for a nonlinear system for which a linear approach is followed for the control synthesis. The linear context driven by the control design allows to focus the observers design in the class of local, i.e. linear, observers. It is shown that when the control contains an external reference, the solution obtained working with the linear approximation to get local solutions produces non consistent results in terms of local regions of convergence for the system and for the observer.

We highlight the equivalence between the motion of an elastic joint and the two-body problem in classical mechanics. Based on this observation, a change of coordinates is introduced that reduces the two-body problem to a pair of decoupled one-body problems. This allows to treat the rest-to-rest motion problem with bounded actuator torque in an elegant geometric fashion. Instead of dealing directly with the fourth-order dynamics, we consider two equivalent masses whose motions have to be synchronized in separate phase spaces.

In this paper we extend the notions of sample and Euler stabilizability to a set of a control system to a wide class of systems with unbounded controls, which includes nonlinear control-polynomial systems. In particular, we allow discontinuous stabilizing feedbacks, which are unbounded approaching the target. As a consequence, sampling trajectories may present a chattering behaviour and Euler solutions have in general an impulsive character.

We consider a weakly coupled system of discounted Hamilton-Jacobi equations set on a closed Riemannian manifold. We prove that the corresponding solutions converge to a specific solution of the limit system as the discount factor goes to 0. The analysis is based on a generalization of the theory of Mather minimizing measures for Hamilton-Jacobi systems and on suitable random representation formulae for the discounted solutions.

A linear-quadratic optimal control problem is considered for the infinite-dimensional model of a one-link flexible arm. Two boundary inputs are assumed to be available, namely the joint torque at the link base and a transverse force at the tip of the link. The problem is formulated and solved using semigroup theory and duality arguments. Simulation results are provided to support the theoretical findings, comparing the proposed optimal LQ law with a more conventional PD/state feedback controller in terms of cost and transient performance.

When dealing with epidemic spread, a very common And dangerous situation is the presence of an epidemic disease and a complication, especially in an elderly population or a weakened one. In this case the complication, that alone is not, in general, a fatal disease, may become risky. The ad hoc resource allocation becomes a mandatory task, aiming at the most rationale control strategy.

In this paper the problem of the HIV/AIDS spread reduction is addressed in the framework of optimal control theory. A model recently proposed has been adopted; it considers two classes of susceptible subjects, the wise people and the people with incautious behaviors, and three classes of infected, the ones still not aware of their status, the pre-AIDS patients and the AIDS ones.

The paper studies the problem of determining the optimal control when singular arcs are present in the solution.
In the general classical approach the expressions obtained depend on the state and the costate variables at the
same time, so requiring a forward-backward integration for the computation of the control. In this paper,
sufficient conditions on the dynamics structure are provided and discussed in order to have both the control
and the switching function depending on the state only, so simplifying the computation avoiding the necessity

An optimal control design approach is applied to a novel HIV/AIDS model to reduce the infection diffusion. Two classes of susceptible subjects, the wise one and the incautious ones, and three classes of infectious subjects, the ones not aware of their condition and the subjects in the pre-aids or in the aids status, are considered. The control input, represented by information campaigns and the medication action, is designed by means of a linear quadratic approach on the linearized model.

The control of an epidemic disease consists in introducing the strategies able to reduce the number of infected subjects by means of medication/quarantine actions, and the number of the subjects that could catch the disease through an informative campaign and, when available, a vaccination strategy. Some diseases, like the influenza, do not guarantee immunity; therefore, the subjects could get ill again by different strain of the same viral subtype.