Piecewise constant control approximations in the problem on effective resource consumption

The paper proposes the piecewise constant control approximations in the control problem in the infinite time interval that is based on the growth model of effective resource consumption under the condition on resources’ exhaustibility. The problem is analyzed within the Pontryagin maximum principle for the problems in the infinite time interval. We investigate the behavior of the dynamic system under different control regimes and search for the stationary levels of the Hamiltonian system. The paper constructs a piecewise constant control as an approximation of an optimal control that takes into account the condition on limited resources. The obtained approximate solutions are compared with the solutions derived using the non-linear stabilizer technique that is widely applied for the considered class of optimal control problems.