Robust Model-Free Software Sensors for the HIV/AIDS Infection Process

Abstract

This paper considers the problem of the HIV/AIDS Infection Process filtering characterized by three compounds, namely, the number of healthy T-cells, the number of infected T-cells and free virus particles. Only the first and third of them can be measurable during the medical treatment process. Moreover, the exact parameter values are admitted to be also unknown. So, here we deal with an uncertain dynamic model that excludes the application of classical filtering theory and requires the application of robust filters successfully working in the absence of a complete mathematical model of the considered process. The problem is to estimate the number of infected T-cells based on the available information. Here we admit the presence of stochastic “white noise” in current observations. To do that we apply the Luenberger-like filter (software sensor) with a matrix gain, which should be adjusted at the beginning of the process in such a way that the filtering error would be as less as possible using the Attractive Ellipsoid Method (AEM). It is shown that the corresponding trajectories of the filtering error converge to an ellipsoidal set of a prespecified form in mean-square sense. To generate the experimental data sequences in the test-simulation example, we have used the well-known simplified HIV/ AIDS model. The obtained results confirm the effectiveness of the suggested approach.