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Linear And Nonlinear Programming

In this paper, the stability and stabilization problems for a class of switched linear systems with mode-dependent average dwell time (MDADT) are investigated in both continuous-time and discrete-time contexts. The proposed switching law is more applicable in practice than the average dwell time (ADT) switching in which each mode in the underlying system has its own ADT. The stability criteria for switched systems with MDADT in nonlinear setting are firstly derived, by which the conditions for stability and stabilization for linear systems are also presented. A numerical example is given to show the validity and potential of the developed techniques.

Stability and Stabilization of Switched Linear Systems With Mode-Dependent Average Dwell Time

Cyclostationarity: half a century of research

This paper first investigates the stability and l 2-gain problems for a class of discrete-time switched systems with average dwell time (ADT) switching by allowing the Lyapunov-like functions to increase during the running time of subsystems. The obtained results then facilitate the studies on the issue of asynchronous control, where "asynchronous" means the switching of the controllers has a lag to the switching of system modes. In light of the proposed Lyapunov-like functions, the desired mode-dependent controllers can be designed since the unmatched controllers are allowed to perform in the interval of asynchronous switching before the matched ones are applied. The problem of asynchronous H infin control for the underlying systems in linear cases is then formulated. The conditions of the existence of admissible asynchronous H infin controllers are derived, and a numerical example is provided to show the potential of the developed results.

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Stability, ${l}_{2}$ -Gain and Asynchronous ${H}_{{\infty}}$ Control of Discrete-Time Switched Systems With Average Dwell Time

Good estimates of vehicle mass and road grade are important in automation of heavy duty vehicles, vehicle following manoeuvres or traditional powertrain control schemes. Recursive least square (RLS) with multiple forgetting factors accounts for different rates of change for different parameters and thus, enables simultaneous estimation of the time-varying grade and the piece-wise constant mass. An ad hoc modification of the update law for the gain in the RLS scheme is proposed and used in simulation and experiments. We demonstrate that the proposed scheme estimates mass within 5% of its actual value and tracks grade with good accuracy provided that inputs are persistently exciting. The experimental setups, signals, their source and their accuracy are discussed. Issues like lack of persistent excitations in certain parts of the run or difficulties of parameter tracking during gear shift are explained and suggestions to bypass these problems are made.

/pdf/recursive-least-squares-with-forgetting-for-online-469zzljz1x.pdf

Recursive least squares with forgetting for online estimation of vehicle mass and road grade: theory and experiments

This paper is devoted to stability analysis and control design of switched linear systems in both continuous and discrete-time domains. A particular class of matrix inequalities, the so-called Lyapunov--Metzler inequalities, provides conditions for open-loop stability analysis and closed-loop switching control using state and output feedback. Switched linear systems are analyzed in a general framework by introducing a quadratic in the state cost determined from a series of impulse perturbations. Lower bounds on the cost associated with the optimal switching control strategy are derived from the determination of a feasible solution to the Hamilton--Jacobi--Bellman inequality. An upper bound on the optimal cost associated with a closed-loop stabilizing switching strategy is provided as well. The solution of the output feedback problem is based on the construction of a full-order linear switched filter whose state variable is used by the mechanism for the determination of the switching rule. Throughout, the theoretical results are illustrated by means of academic examples. A realistic practical application related to the optimal control of semiactive suspensions in road vehicles is reported.

Dynamic Output Feedback Control of Switched Linear Systems

Stochastic stability of Positive Markov Jump Linear Systems

Brief paper: Markov Jump Linear Systems with switching transition rates: Mean square stability with dwell-time

Despite progress in clinical care for patients with coronavirus disease 2019 (COVID-19)1, population-wide interventions are still crucial to manage the pandemic, which has been aggravated by the emergence of new, highly transmissible variants. In this study, we combined the SIDARTHE model2, which predicts the spread of SARS-CoV-2 infections, with a new data-based model that projects new cases onto casualties and healthcare system costs. Based on the Italian case study, we outline several scenarios: mass vaccination campaigns with different paces, different transmission rates due to new variants and different enforced countermeasures, including the alternation of opening and closure phases. Our results demonstrate that non-pharmaceutical interventions (NPIs) have a higher effect on the epidemic evolution than vaccination alone, advocating for the need to keep NPIs in place during the first phase of the vaccination campaign. Our model predicts that, from April 2021 to January 2022, in a scenario with no vaccine rollout and weak NPIs ([Formula: see text] = 1.27), as many as 298,000 deaths associated with COVID-19 could occur. However, fast vaccination rollouts could reduce mortality to as few as 51,000 deaths. Implementation of restrictive NPIs ([Formula: see text] = 0.9) could reduce COVID-19 deaths to 30,000 without vaccinating the population and to 18,000 with a fast rollout of vaccines. We also show that, if intermittent open-close strategies are adopted, implementing a closing phase first could reduce deaths (from 47,000 to 27,000 with slow vaccine rollout) and healthcare system costs, without substantive aggravation of socioeconomic losses.

/pdf/modeling-vaccination-rollouts-sars-cov-2-variants-and-the-430qo2unil.pdf

Modeling vaccination rollouts, SARS-CoV-2 variants and the requirement for non-pharmaceutical interventions in Italy.

This work deals with the problem of quadratic stabilization of switched affine systems, where the state of the switched system has to be driven to a point ("switched equilibrium") which is not in the set of subsystems equilibria. Quadratic stability of the switched equilibrium is assessed using a continuous Lyapunov function, having piecewise continuous derivative. A necessary and sufficient condition is given for the case of two subsystems and a sufficient condition is given in the general case. Two switching rules are presented: a state feedback, in which sliding modes may occur, and an hybrid feedback, in which sliding modes can be avoided. Two examples illustrate our results.

/pdf/quadratic-stabilization-of-a-switched-affine-system-about-a-3k7vdqwxev.pdf

Paolo Bolzern

Papers

Dynamic Output Feedback Control of Switched Linear Systems

Stochastic stability of Positive Markov Jump Linear Systems

Brief paper: Markov Jump Linear Systems with switching transition rates: Mean square stability with dwell-time

Modeling vaccination rollouts, SARS-CoV-2 variants and the requirement for non-pharmaceutical interventions in Italy.

Quadratic stabilization of a switched affine system about a nonequilibrium point