The paper presents a solution to the problem of optimal control of a quadrocopter under phase constraints by the numerical method of a network operator based on multi-point stabilization. According to this approach, the task of control system synthesis is initially solved. As a result, the quadrocopter is stabilized with respect to a certain point in the state space. At the second stage, a sequence of stabilization points is searched in the state space such that switching the stabilization points at fixed times ensures the movement of the quadrocopter from the initial state to the terminal state with an optimal value of the quality criterion taking into account phase constraints. To solve the problem of stabilization system synthesis, the network operator method is used. The method is numerical and, unlike the well-known analytical methods, allows to synthesize a control system automatically without a specific analysis of the right parts of the model. The method allows to find the structure and parameters of a mathematical expression in the encoded form using the genetic algorithm. The network operator code is an integer upper-triangular matrix. At the stage of solving the synthesis problem, the mathematical model of quadrocopter motion is decomposed into angular and spatial motions in order to separate control components for angular and spatial motions, respectively. The synthesized stabilization system consists of two subsystems connected in series for spatial and angular motion. As controls for spatial motion, moments around the axes and the total thrust of all quadcopter propellers were used. And the inputs for the angular motion stabilization system are the desired angles of inclination of the quadrocopter. The stabilization problem is considered as a general synthesis task for a control system. Using the network operator method, one control function is searched that provides stabilization of the object at a given point in the considered state space from the set of initial conditions. At the stage of the search for equilibrium points, the evolutionary particle swarm algorithm is used. A numerical example of solving the problem of optimal control of a quadrocopter with four phase constraints is given.
Optimal control of a dynamical system with intermediate phase constraints and applications in cash management
