We address the output regulation problem for a general class of linear stochastic systems. Specifically, we formulate and solve the ideal full-information and output-feedback problems, obtaining perfect, but noncausal, asymptotic regulation. A characterisation of the problem solvability is deduced. We point out that the ideal problems cannot be solved in practice because they unrealistically require that the Brownian motion affecting the system is available for feedback. Drawing from the ideal solution, we formulate and solve approximate versions of the full-information and output-feedback problems, which do not yield perfect asymptotic tracking but can be solved in a realistic scenario. These solutions rely on two key ideas: first we introduce a discrete-time a-posteriori estimator of the variations of the Brownian motion obtained causally by sampling the system state or output; second we introduce a hybrid state observer and a hybrid regulator scheme which employ the estimated Brownian variations. The approximate solution tends to the ideal as the sampling period tends to zero. The proposed theory is validated by the regulation of a circuit subject to electromagnetic noise.

The problem of output regulation for linear stochastic systems is addressed. The controlled system belongs to a general class of linear systems, namely the state, the control input and the exogenous input appear in both the drift and diffusion terms of the differential equations. Building upon the solution of the ideal, non-causal, stochastic regulator problem, we define an approximate full-information problem. By means of measurements of the state vector, we provide a way to compute a sequence of scalars approximating a posteriori the variations of the Brownian motion. Then, we propose a hybrid control architecture which solves the approximate problem. The continuous-time part of the controller is deterministic, whereas the discrete-time part has the function of "correcting" the control action by means of the approximate discretetime Brownian motion. The solution of the ideal stochastic regulator problem is recovered as the sampling time tends to zero. We illustrate the results by means of a numerical example and conclude the paper with some final remarks: the proposed control architecture is the first causal solution of the full-information output regulation problem and is an essential intermediate step for the solution of the error-feedback problem.

The implementation of lockdowns has been a key policy to curb the spread of COVID-19 and to keep under control the number of infections. However, quantitatively predicting in advance the effects of lockdowns based on their stringency and duration is a complex task, in turn making it difficult for governments to design effective strategies to stop the disease. Leveraging a novel mathematical “hybrid” approach, we propose a new epidemic model that is able to predict the future number of active cases and deaths when lockdowns with different stringency levels or durations are enforced. The key observation is that lockdown-induced modifications of social habits may not be captured by traditional mean-field compartmental models because these models assume uniformity of social interactions among the population, which fails during lockdown. Our model is able to capture the abrupt social habit changes caused by lockdowns. The results are validated on the data of Israel and Germany by predicting past lockdowns and providing predictions in alternative lockdown scenarios (different stringency and duration). The findings show that our model can effectively support the design of lockdown strategies by stringency and duration, and quantitatively forecast the course of the epidemic during lockdown.

A distributed cooperative control law for persistent coverage tasks is proposed, capable of coordinating a team of heterogeneous agents in a structured environment. Team heterogeneity is considered both at vehicles' dynamics and at coverage capabilities levels. More specifically, the general dynamics of nonholonomic vehicles are considered. Agent heterogeneous sensing capabilities are addressed by means of the descriptor function framework, a set of analytical tools for controlling agents involved in generic coverage tasks. By means of formal arguments, we prove that the team performs the task and no collision occurs between agents nor with obstacles. A numerical simulation validates the proposed strategy.

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