2D systems feedback compensation: an approach based on commutative linear transformations

AbstractAlgebraic properties of a pair of commutative matrices associated with an ideal in R[z1, z2] are exploited for characterizing the closed loop polynomial variety of a 2D system. Also algorithms are given to find under what constraints the closed loop variety can be assigned and to compute the MFD of a compensator

Detectability subspaces and observer synthesis for two-dimensional systems

The notions of input-containing and detectability subspaces are developed within the context of observer synthesis for two-dimensional (2-D) Fornasini-Marchesini models. Specifically, the paper considers observers which asymptotically estimate the local state, in the sense that the error tends to zero as the reconstructed local state evolves away from possibly mismatched boundary values, modulo a detectability subspace. Ultimately, the synthesis of such observers in the absence of explicit input information is addressed

A note on the relationships between high gain state feedback and relay systems

In this note we study some relationships existing between two widely applied control techniques, namely relay feedback control and high-gain saturated feedback control

COVID-19 epidemic control using short-term lockdowns for collective gain

While many efforts are currently devoted to vaccines development and administration, social distancing measures, including severe restrictions such as lockdowns, remain fundamental tools to contain the spread of COVID-19. A crucial point for any government is to understand, on the basis of the epidemic curve, the right temporal instant to set up a lockdown and then to remove it. Different strategies are being adopted with distinct shades of intensity. USA and Europe tend to introduce restrictions of considerable temporal length. They vary in time: a severe lockdown may be reached and then gradually relaxed. An interesting alternative is the Australian model where short and sharp responses have repeatedly tackled the virus and allowed people a return to near normalcy. After a few positive cases are detected, a lockdown is immediately set. In this paper we show that the Australian model can be generalized and given a rigorous mathematical analysis, casting strategies of the type short-term pain for collective gain in the context of sliding-mode control, an important branch of nonlinear control theory. This allows us to gain important insights regarding how to implement short-term lockdowns, obtaining a better understanding of their merits and possible limitations. Effects of vaccines administration in improving the control law's effectiveness are also illustrated. Our model predicts the duration of the severe lockdown to be set to maintain e.g. the number of people in intensive care under a certain threshold. After tuning our strategy exploiting data collected in Italy, it turns out that COVID-19 epidemic could be e.g. controlled by alternating one or two weeks of complete lockdown with one or two months of freedom, respectively. Control strategies of this kind, where the lockdown's duration is well circumscribed, could be important also to alleviate coronavirus impact on economy

Kernel-based linear system identification: When does the representer theorem hold?

It holds for any physical (bounded) input if and only if the kernel is stable

Kernel-based learning of orthogonal functions

Estimating a set of orthogonal functions from a finite set of noisy data plays a crucial role in several areas such as imaging, dictionary learning and compressed sensing. The problem turns out especially hard due to its intrinsic non-convexity. In this paper, we solve it by recasting it in the framework of multi-task learning in Hilbert spaces, where orthogonality plays a role as inductive bias. Two perspectives are analyzed. The first one is mainly theoretic. It considers a formulation of the problem where non-orthogonal function estimates are seen as noisy data belonging to an infinite-dimensional space from which orthogonal functions have to be reconstructed. We then provide results concerning the existence and the convergence of the optimizers. The second one is more oriented towards applications. It consists in a learning scheme where orthogonal functions are directly inferred from a finite amount of noisy data. It relies on regularization in reproducing kernel Hilbert spaces and on the introduction of special penalty terms promoting orthogonality among tasks. The problem is then cast in a Bayesian framework, overcoming non-convexity through an efficient Markov chain Monte Carlo scheme. If orthogonality is not certain, our scheme can also understand from data if such form of task interaction really holds

Pasteurising system control methodology

The present invention relates to a control method for tunnel pasteurising systems in which, at the end of the treatment, each product must have remained above a predetermined temperature for at least a predetermined time, and accumulated at least a predetermined quantity of pasteurisation units. In tunnel systems, the products, like bottles or other containers, to be pasteurised are fed by a conveyor along a path which is usually divided into three main zones: a heating zone in which the product temperature is gradually raised; a heat treatment zone in which the product temperature is brought to and kept at the pasteurising temperature; and a cooling zone in which the product temperature is gradually lowered. The heat treatment zone is, in turn, divided into a plurality of sub-zones which operate independently. The product is heat treated by applying a flow of hot fluid at the required temperature on the product. Usually the fluid is a liquid, such as hot water, which is injected or sprayed or applied in an equivalent or similar manner on the product; other fluids are contemplatable, like gases, such hot air, which are injected on the product. In the following, the terms "injection", "inject", "injected" will be used to refer to any known manner for applying a flow of hot fluid on products in tunnel pasteurising systems