Ricerc@Sapienza

Boundary observer design of a system of n chi-ODEs coupled to nx-hyperbolic PDEs with positive convective speeds is studied. An infinite dimensional observer is used to solve the considered state estimation problem. The interconnection of the observer and the system is written in estimation error coordinates and analyzed as an abstract dynamical system on a specific Hilbert space. The design of the observer is performed to achieve global exponential stability of the estimation error with respect to a suitable norm.

This paper is concerned with stability and control of the parabolic p-Laplace equation. The autonomous equation is shown to be asymptotically stable, while the stronger property of exponential stability is guaranteed by the presence of lower-order terms satisfying a suitable growth condition. On the basis of these results, the problem of reference tracking using a distributed control input is investigated and, in particular, two approaches are discussed: finite-time stabilization and quadratic optimal control.

The problem of unknown input observer design is considered for coupled PDE/ODE linear systems subject to unknown boundary inputs. Assuming available measurements at the boundary of the distributed domain, the synthesis of the observer is based on geometric conditions and Lyapunov methods. Numerical simulations support and validate the theoretical findings, illustrating the robust estimation performances of the proposed unknown input observer.