Approximate Optimal Control in the Infinite Time Horizon Problem with Phase Constraints
Keywords:
Optimal control problem, phase constraints, reliability theory, piecewise constant controls, Hamiltonian system, growth models.Abstract
The paper investigates a control problem of optimal distribution of investments directed towards improvement of the resource productivity and/or purchasing the natural resources. The problem is based on the growth model of the effective resource consumption under the condition on resources’ exhaustion. The paper provides an interpretation of phase variables in terms of
the reliability theory. The optimal solution of the problem is approximated by piecewise constant controls that guarantee convergence of the trajectories to the unique equilibrium of the Hamiltonian system. The derived approximation satisfies the phase constraints and matches with the stabilized solutions constructed on the basis of the nonlinear regulator approach.
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