Optimal Energy-Saving Control for a Thermal Plant of a Linear Singularly Perturbed Discrete System with a Small Step

This scientific article is devoted to the construction of asymptotic solutions for the problem of controlling the dynamic regimes of thermal processes, the control objects in which, is described by a linear singularly perturbed discrete system with a small step. Based on the joint use of methods for separating motions and moments, an algorithm for a uniform zero asymptotic solution of the considered problem is proposed. The main result of the work is the obtained optimal trajectory, which consists of three components, the first of which describes the main optimal trajectory, which, for some time, is near the trajectory of the limiting problem (the duration of the stay in this position of the main optimal trajectory depends on the nature of the small parameter μ). The remaining two boundary functions carry out transitions from the initial state to the main optimal trajectory and from the main optimal trajectory to the final state. The correction to the next approximations is not difficult, since all the above procedures are similarly repeated for all higher approximations.