Tochilin P.A.

The paper considers the problem of feedback control for a group of several quadrocopters. The main goal is to transfer this group from a given initial position to a given target position for a fixed period of time, provided that at each intermediate time instant the quadrocopters must be in a small neighborhood of a fixed smooth curve in space. A centralized group control scheme is used. The main difficulty here is the complex, nonlinear mathematical model, describing the movement of each individual aircraft. It is necessary to develop computationally efficient algorithms for approximate search for feedback control, which allow to cope simultaneously with nonlinear dynamics, point-to-point constraints on control parameters, as well as state constraints arising in connection with group motion (in particular, due to the requirements of pairwise collision avoidance). Modifications of ellipsoidal calculus methods are used here to construct such algorithms.

The paper is devoted to the development of a new method for the approximate construction of the reachability set for a nonlinear control system with discrete time. Pointwise restrictions are imposed on the control parameters. To solve this problem, a technique previously developed and applied for the case of continuous time and differential equations is used. The estimate of the reachability set can be obtained as the level set of a special piecewise affine value function constructed on a grid of simplices in the state space. The paper presents formulas for calculating the coefficients of such a function, which make it possible to analyze the difference between the case with discrete time and the case with continuous time. An example of calculation of piecewise affine value functions and corresponding internal and external estimates of the reachability set is considered.