A shooting algorithm for problems with singular arcs

In this article we propose a shooting algorithm for a class of optimal control problems for which all control variables appear linearly. The shooting system has, in the general case, more equations than unknowns and the Gauss-Newton method is used to compute a zero of the shooting function. This shooting algorithm is locally quadratically convergent if the derivative of the shooting function is one-to-one at the solution. The main result of this paper is to show that the latter holds whenever a sufficient condition for weak optimality is satisfied. We note that this condition is very close to a second order necessary condition. For the case when the shooting system can be reduced to one having the same number of unknowns and equations (square system) we prove that the mentioned sufficient condition guarantees the stability of the optimal solution under small perturbations and the invertibility of the Jacobian matrix of the shooting function associated to the perturbed problem. We present numerical tests that validate our method.Comment: No. RR-7763 (2011); Journal of Optimization, Theory and Applications, published as 'Online first', January 201

Estimate of the rate of unreported COVID-19 cases during the first outbreak in Rio de Janeiro

In this work we fit an epidemiological model SEIAQR (Susceptible - Exposed - Infectious - Asymptomatic - Quarantined - Removed) to the data of the first COVID-19 outbreak in Rio de Janeiro, Brazil. Particular emphasis is given to the unreported rate, that is, the proportion of infected individuals that is not detected by the health system. The evaluation of the parameters of the model is based on a combination of error-weighted least squares method and appropriate B-splines. The structural and practical identifiability is analyzed to support the feasibility and robustness of the parameters’ estimation. We use the Bootstrap method to quantify the uncertainty of the estimates. For the outbreak of March–July 2020 in Rio de Janeiro, we estimate about 90% of unreported cases, with a 95% confidence interval (85%, 93%)

Geometric and numerical methods in the contrast imaging problem in nuclear magnetic resonance

International audienceIn this article, the contrast imaging problem in nuclear magnetic resonance is modeled as a Mayer problem in optimal control. The optimal solution can be found as an extremal, solution of the Maximum Principle and analyzed with the techniques of geometric control. This leads to a numerical investigation based on so-called indirect methods using the HamPath software. The results are then compared with a direct method implemented within the Bocop toolbox. Finally lmi techniques are used to estimate a global optimum

Optimality conditions (In Pontryagin form)

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