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Optimal control problem with partial derivative equation (PDE) constraint is a numerical-wise difficult problem because the optimality conditions lead to PDEs with mixed types of boundary values. The authors provide a new approach to solve this type of problem by space discretization and transform it into a standard optimal control for a multi-agent system. This resulting problem is formulated from a microscopic perspective while the solution only needs limited the macroscopic measurement due to the approach of Hamilton-Jacobi-Bellman (HJB) equation approximation. For solving the problem, only an HJB equation (a PDE with only terminal boundary condition) needs to be solved, although the dimension of that PDE is increased as a drawback. A pollutant elimination problem is considered as an example and solved by this approach. A numerical method for solving the HJB equation is proposed and a simulation is carried out.

China implemented strict non-pharmaceutical interventions to contain COVID-19 at the early stage. We aimed to evaluate the impact of COVID-19 on HIV care continuum in China.

A number of strategies for state and parameter estimation for a centrifugal compressor system are investigated using a nonlinear dynamical model. It is found that high frequency measurements can be combined with lower frequency measurements to achieve high fidelity state estimation for stable equilibria, limit cycles, as well as transients using either a multirate discrete extended Kalman filter or a data fusion based algorithm with one independent estimator per measurement. When there is a change in one of the parameters of the system only a filter designed to adapt to such changes produces estimates with acceptable errors for a locally stable equilibrium.