Control and optimization in a collision avoidance problem in oscillating systems

Abstract

The development of control algorithms, including optimal control ones, in the collision avoidance problem for a system of two pendulums with a controllable common base is considered. Two problems are solved. The first one searches for the law of variation of the bounded control force that makes the system move from its initial state of rest to the given final state of rest during a finite time and ensures the pendulums do not collide in the process of oscillatory motions. The second problem searches for the performance-optimal law of variation of acceleration of the base and the bounded force that generates the acceleration. The algorithms for constructing the sought controls that use Kalman controllability conditions and Pontryagin’s maximum principle method are presented. The dynamics of the system involved is simulated for the constructed control laws. The numerical results of both problems are compared to find that implementation of the developed performance-optimal control algorithm can help significantly decrease the releasing time of the pendulums while preventing a possible collision.