Hysteresis-based supervisory control with application to non-pharmaceutical containment of COVID-19.

The recent COVID-19 outbreak has motivated an extensive development of non-pharmaceutical intervention policies for epidemics containment. While a total lockdown is a viable solution, interesting policies are those allowing some degree of normal functioning of the society, as this allows a continued, albeit reduced, economic activity and lessens the many societal problems associated with a prolonged lockdown. Recent studies have provided evidence that fast periodic alternation of lockdown and normal-functioning days may effectively lead to a good trade-off between outbreak abatement and economic activity. Nevertheless, the correct number of normal days to allocate within each period in such a way to guarantee the desired trade-off is a highly uncertain quantity that cannot be fixed a priori and that must rather be adapted online from measured data. This adaptation task, in turn, is still a largely open problem, and it is the subject of this work. In particular, we study a class of solutions based on hysteresis logic. First, in a rather general setting, we provide general convergence and performance guarantees on the evolution of the decision variable. Then, in a more specific context relevant for epidemic control, we derive a set of results characterizing robustness with respect to uncertainty and giving insight about how a priori knowledge about the controlled process may be used for fine-tuning the control parameters. Finally, we validate the results through numerical simulations tailored on the COVID-19 outbreak.

Post-lockdown abatement of COVID-19 by fast periodic switching.

COVID-19 abatement strategies have risks and uncertainties which could lead to repeating waves of infection. We show-as proof of concept grounded on rigorous mathematical evidence-that periodic, high-frequency alternation of into, and out-of, lockdown effectively mitigates second-wave effects, while allowing continued, albeit reduced, economic activity. Periodicity confers (i) predictability, which is essential for economic sustainability, and (ii) robustness, since lockdown periods are not activated by uncertain measurements over short time scales. In turn-while not eliminating the virus-this fast switching policy is sustainable over time, and it mitigates the infection until a vaccine or treatment becomes available, while alleviating the social costs associated with long lockdowns. Typically, the policy might be in the form of 1-day of work followed by 6-days of lockdown every week (or perhaps 2 days working, 5 days off) and it can be modified at a slow-rate based on measurements filtered over longer time scales. Our results highlight the potential efficacy of high frequency switching interventions in post lockdown mitigation. All code is available on Github at https://github.com/V4p1d/FPSP_Covid19. A software tool has also been developed so that interested parties can explore the proof-of-concept system.

Kemeny-based testing for COVID-19.

Testing, tracking and tracing abilities have been identified as pivotal in helping countries to safely reopen activities after the first wave of the COVID-19 virus. Contact tracing apps give the unprecedented possibility to reconstruct graphs of daily contacts, so the question is: who should be tested? As human contact networks are known to exhibit community structure, in this paper we show that the Kemeny constant of a graph can be used to identify and analyze bridges between communities in a graph. Our 'Kemeny indicator' is the value of the Kemeny constant in the new graph that is obtained when a node is removed from the original graph. We show that testing individuals who are associated with large values of the Kemeny indicator can help in efficiently intercepting new virus outbreaks, when they are still in their early stage. Extensive simulations provide promising results in early identification and in blocking the possible 'super-spreaders' links that transmit disease between different communities.

Distributed Fault-Tolerant Control of Multiagent Systems: An Adaptive Learning Approach.

This paper focuses on developing a distributed leader-following fault-tolerant tracking control scheme for a class of high-order nonlinear uncertain multiagent systems. Neural network-based adaptive learning algorithms are developed to learn unknown fault functions, guaranteeing the system stability and cooperative tracking even in the presence of multiple simultaneous process and actuator faults in the distributed agents. The time-varying leader's command is only communicated to a small portion of follower agents through directed links, and each follower agent exchanges local measurement information only with its neighbors through a bidirectional but asymmetric topology. Adaptive fault-tolerant algorithms are developed for two cases, i.e., with full-state measurement and with only limited output measurement, respectively. Under certain assumptions, the closed-loop stability and asymptotic leader-follower tracking properties are rigorously established.

An Integrated Learning and Filtering Approach for Fault Diagnosis of a Class of Nonlinear Dynamical Systems.

This paper develops an integrated filtering and adaptive approximation-based approach for fault diagnosis of process and sensor faults in a class of continuous-time nonlinear systems with modeling uncertainties and measurement noise. The proposed approach integrates learning with filtering techniques to derive tight detection thresholds, which is accomplished in two ways: 1) by learning the modeling uncertainty through adaptive approximation methods and 2) by using filtering for dampening measurement noise. Upon the detection of a fault, two estimation models, one for process and the other for sensor faults, are initiated in order to identify the type of fault. Each estimation model utilizes learning to estimate the potential fault that has occurred, and adaptive isolation thresholds for each estimation model are designed. The fault type is deduced based on an exclusion-based logic, and fault detectability and identification conditions are rigorously derived, characterizing quantitatively the class of faults that can be detected and identified by the proposed scheme. Finally, simulation results are used to demonstrate the effectiveness of the proposed approach.

Fault detection in mechanical systems with friction phenomena: an online neural approximation approach.

In this paper, the problem of fault detection in mechanical systems performing linear motion, under the action of friction phenomena is addressed. The friction effects are modeled through the dynamic LuGre model. The proposed architecture is built upon an online neural network (NN) approximator, which requires only system's position and velocity. The friction internal state is not assumed to be available for measurement. The neural fault detection methodology is analyzed with respect to its robustness and sensitivity properties. Rigorous fault detectability conditions and upper bounds for the detection time are also derived. Extensive simulation results showing the effectiveness of the proposed methodology are provided, including a real case study on an industrial actuator.

Active state estimation for nonlinear systems: a neural approximation approach.

In this paper, we consider the problem of actively providing an estimate of the state of a stochastic dynamic system over a (possibly long) finite time horizon. The active estimation problem (AEP) is formulated as a stochastic optimal control one, in which the minimization of a suitable uncertainty measure is carried out. Toward this end, the use of the Renyi entropy as an information measure is proposed and motivated. A neural control scheme, based on the application of the extended Ritz method (ERIM) and on the use of a Gaussian sum filter (GSF), is then presented. Simulation results show the effectiveness of the proposed approach.