ASYMPTOTIC STABILITY AND OPTIMAL CONTROL OF A NONLINEAR TIME-VARYING SYSTEM WITH JOINT CONSTRAINTS AND EPIDEMIC ILLUSTRATIVE EXAMPLE

We study the optimal value of a functional cost for a control problem whose control function is piecewise continuous in a bounded closed space. We then use the convexity of the Hamiltonian function to prove the necessary and sufficient conditions for optimality. The optimal values of the control problem are determined by the optimality principle. Finally, we propose the study of a control problem for a simple non-vaccination model of the corona virus epidemic as an illustrative example.