Optimal control of systems with intermediate phase constraints

1994 ◽  
Vol 30 (4) ◽  
pp. 561-567 ◽  
Author(s):  
S. B. Kirichenko
Keyword(s):  
Optimal Control ◽  
Intermediate Phase ◽  
Phase Constraints

Quadrocopter Control by Network Operator Method Based on Multi-Point Stabilization

2020 ◽  
Vol 21 (7) ◽  
pp. 428-438
Author(s):  
A. I. Diveev ◽  
E. Yu. Shmalko ◽  
O. Hussein
Keyword(s):  
Optimal Control ◽  
Control System ◽  
State Space ◽  
Operator Method ◽  
The State ◽  
Angular Motion ◽  
Stabilization System ◽  
Network Operator ◽  
System Synthesis ◽  
Phase Constraints

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.

Symmetric Control Systems

2021 ◽  
pp. 37-51
Author(s):  
A.I. Diveev ◽  
E.A. Sofronova
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Control Systems ◽  
Control Object ◽  
Terminal State ◽  
Initial State ◽  
Phase Constraints ◽  
The Mathematical Model

The paper focuses on the properties of symmetric control systems, whose distinctive feature is that the solution of the optimal control problem for an object, the mathematical model of which belongs to the class of symmetric control systems, leads to the solution of two problems. The first optimal control problem is the initial one; the result of its solution is a function that ensures the optimal movement of the object from the initial state to the terminal one. In the second problem, the terminal state is the initial state, and the initial state is the terminal state. The complexity of the problem being solved is due to the increase in dimension when the models of all objects of the group are included in the mathematical model of the object, as well as the emerging dynamic phase constraints. The presence of phase constraints in some cases leads to the target functional having several local extrema. A theorem is proved that under certain conditions the functional is not unimodal when controlling a group of objects belonging to the class of symmetric systems. A numerical example of solving the optimal control problem with phase constraints by the Adam gradient method and the evolutionary particle swarm method is given. In the example, a group of two symmetrical objects is used as a control object

Synthesized Optimal Control of Group Interaction of Quadrocopters Based on Multi-Point Stabilization

2020 ◽  
pp. 114-133
Author(s):  
A.I. Diveev ◽  
E.Yu. Shmalko ◽  
O. Hussein
Keyword(s):  
Optimal Control ◽  
Group Interaction ◽  
Operator Method ◽  
Quality Criterion ◽  
Initial Position ◽  
Time Interval ◽  
Flexible Rods ◽  
Optimal Value ◽  
Phase Constraints ◽  
Point Stabilization

The study examines the problem of optimal control of group interaction of three quadrocopters. A group of three quadrocopters must move the load on flexible rods from one point in space to another one without hitting obstacles, one quadrocopter being not able to complete the task due to the weight of the load. To solve the problem, the method of synthesized optimal control based on multi-point stabilization was used. The method is called synthesized, since the problem of synthesizing the stabilization system for each robot is first solved. At the next stage, the problem of the optimal location of stabilization points in the state space is solved in such a way that when these points are switched from one to another, at a given time interval, the quadrocopters move the load from the initial position to the final one with the optimal value of the quality criterion. The network operator method is used to solve the synthesis problem. All phase constraints describing group interaction and obstacles are included in the quality criterion by the method of penalty functions. An evolutionary particle swarm optimization algorithm was used to find the positions of points

Sign in / Sign up

Export Citation Format

Share Document