While many epidemiological models were proposed to understand and handle COVID-19 pandemic, too little has been invested to understand human viral replication and the potential use of novel antivirals to tackle the infection. In this work, using a control theoretical approach, validated mathematical models of SARS-CoV-2 in humans are characterized. A complete analysis of the main dynamic characteristic is developed based on the reproduction number. The equilibrium regions of the system are fully characterized, and the stability of such regions is formally established. Mathematical analysis highlights critical conditions to decrease monotonically SARS-CoV-2 in the host, as such conditions are relevant to tailor future antiviral treatments. Simulation results show the aforementioned system characterization.
Robust asymptotic stability (asymptotic attractivity and -stability) of equilibrium regions under robust model predictive control (MPC) strategies was extensively studied in the last decades making use of Lyapunov theory in most cases. However, in spite of its potential application benefits, the problem of finite-time convergence under fixed prediction horizon has not received, with some few exceptions, much attention in the literature. Considering the importance in several applications of having finite-time convergence results in the context of fixed horizon MPC controllers and the lack of studies on this matter, this work presents a new set-based robust MPC (RMPC) for which, in addition to traditional stability guarantees, finite-time convergence to a target set is proved, and moreover, an upper bound on the time necessary to reach that set is provided. It is remarkable that the results apply to general nonlinear systems and only require some weak assumptions on the model, cost function, and target set.
Summary
This note presents a stochastic formulation of the model predictive control for tracking (MPCT), based on the results of the work of Lorenzen et al. The proposed controller ensures constraints satisfaction in probability, and maintains the main features of the MPCT, that are feasibility for any changing setpoints and enlarged domain of attraction, even larger than the one delivered by Lorenzen et al, thanks to the use of artificial references and relaxed terminal constraints. The asymptotic stability (in probability) of the minimal robust positively invariant set centered on the desired setpoint is guaranteed. Simulations on a DC‐DC converter show the benefits and the properties of the proposal.
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