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In linear regulation theory, it is well-known that embedding in the control loop a suitable internal model of the exogenous disturbances and references permits to achieve perfect regulation of the desired variables robustly with respect to parametric uncertainties in the plant's equations. However, it was recently proved that this principle does not extend, in general, to nonlinear systems or non-parametric perturbations. Indeed, there exist systems for which no smooth finite-dimensional regulator can exist that regulates the desired variables to zero in spite of unstructured uncertainties affecting the plant's dynamics. This article complements such a negative result by proving that, in the canonical context of minimum-phase normal forms, a nonlinear regulator of the Luenberger type that guarantees robust asymptotic regulation with respect to unstructured uncertainties and possesses a star-shaped attractor necessarily behaves as a linear system on such an attractor. This result further strengthens the conjecture that robust regulation is essentially a linear property. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We consider a problem of robust estimation over a network in an errors-in-variables context. Each agent measures noisy samples of a local pair of signals related by a linear regression defined by a common unknown parameter, and the agents must cooperate to find the unknown parameter in presence of uncertainty affecting both the regressor and the regressand variables. We propose a recursive least squares estimation method providing global exponential convergence to the unknown parameter in absence of uncertainty, and robust stability of the estimate, formalized in terms of input-to-state stability, in presence of uncertainty affecting all the variables. The result relies on a cooperative excitation assumption that is proved to be strictly weaker than persistency of excitation of each local data set. The proposed estimator is validated on an adaptive road pricing application. [ABSTRACT FROM AUTHOR]

The problem of output regulation for general multivariable linear systems has been solved in the 70s, in the seminal works of Francis, Wonham and Davison, under the assumption that the reference signals and the disturbances acting on the system are generated by a known exogenous linear system (the exosystem). The regulator is designed to embed an internal model of the exosystem, which ensures that asymptotic regulation is maintained under arbitrary plant perturbations that do not destroy linearity and closed-loop stability. This robustness property, however, is inexorably lost whenever the internal model does not match exactly the exosystem. In this paper we endow the linear regulator with a discrete-time adaptive unit that adapts the regulator's internal model on the basis of the closed-loop evolution. Compared to existing approaches, adaptation here is cast as an identification problem, and the corresponding optimal predictor is designed independently from the underlying control system. This permits to separate stabilization and adaptation, thus naturally handling general non-square multivariable non minimum-phase plants. Closed-loop stability is guaranteed and, if the dimension of the internal model is large enough and a persistency of excitation condition is fulfilled, asymptotic regulation is achieved for references and disturbances generated by an unknown exosystem. Robustness to parametric uncertainties is inherited by the linear regulator and robustness to additional unmodeled disturbances is proved to hold. [ABSTRACT FROM AUTHOR]

The paper deals with the distributed minimum sharing problem: a set of decision-makers compute the minimum of some local quantities of interest in a distributed and decentralized way by exchanging information through a communication network. We propose an adjustable approximate solution which enjoys several properties of crucial importance in applications. In particular, the proposed solution has good decentralization properties and it is scalable in that the number of local variables does not grow with the size or topology of the communication network. Moreover, a global and uniform (both in the initial time and in the initial conditions) asymptotic stability result is provided towards a steady state which can be made arbitrarily close to the sought minimum. Exact asymptotic convergence can be recovered at the price of losing uniformity with respect to the initial time. [ABSTRACT FROM AUTHOR]

In Marconi et al. (2007), the theory of nonlinear Luenberger observers was exploited to prove that a solution to the asymptotic output regulation problem for minimum-phase normal forms always exists. The paper provided an existence result and a very general regulator structure, although unfortunately, no constructive method was given to design all the degrees of freedom of the regulator. In this paper, we complete this design by introducing an adaptive unit tuning the regulator online by employing system identification algorithms selecting the "best" parameters according to a certain optimization policy. Instead of focusing on a single identification scheme, we give general conditions under which an algorithm may be used in the framework, and we develop a particular least-squares identifier satisfying these requirements. Closed-loop stability results are given, and it is shown that the asymptotic regulation error is related to the prediction capabilities of the identifier evaluated along the ideal error-zeroing steady-state trajectories. [ABSTRACT FROM AUTHOR]

This work proposes a redesign method for nonlinear observers to reduce the effect of a particular class of output disturbances. Specifically, it is considered a disturbance composed of a term generated from a known system and an unstructured term. The proposed approach does not require modifying the original observer and is based on adding a simple filter that includes an internal model of the disturbance generator. Sufficient conditions for stability of the proposed filter-observer architecture are given. Moreover, the approach is validated through numerical simulations. [ABSTRACT FROM AUTHOR]

Traffic congestion in urban environment is one of the most critical issue for drivers and city planners for both environment and efficiency reasons. Traffic lights are one of the main tools used to regulate traffic by diverting the drivers between different paths. Rational drivers, in turn, react to the traffic light duration by evaluating their options and, if necessary, by changing direction in order to reach their destination quicker. In this paper, we introduce a macroscopic traffic model for urban intersections that incorporates this rational behavior of the drivers. Then, we exploit it to show that, by providing additional information about the expected red-time duration to the drivers, one can decrease the amount of congestion in the network and the overall length of the queues at the intersections. Additionally, we develop a control policy for the traffic lights that exploits the reaction of the drivers in order to divert them to a different route to further increase the performances. These claims are supported by extensive numerical simulations. • A traffic-flow macroscopic model of the drivers' rational decision-making. • It considers origin-destination pairs and the ability to show the red time duration. • Numerical simulations illustrate the effectiveness of showing the red time duration. • A novel control policy that exploit the drivers' reaction to the red time duration. • The increased efficiency of the controller is validated with extensive simulations. [ABSTRACT FROM AUTHOR]