Narrow Results

A new algorithm is developed to solve the collision avoidance problem for a host ship subject to kinematic, dynamic, and moment equations and steered via rudder under the assumptions that the rudder angle and rudder angle time rate are subject to upper and lower bounds. The objective of the collision avoidance maneuver is to maximize with respect to the state and control history the timewise minimum distance between a host ship and an intruder ship. Two limiting cases are considered: (i) the intruder ship is uncooperative and keeps its course unchanged during the encounter; (ii) the intruder ship is cooperative. In both cases, a differential game formulation is avoided and the collision avoidance problem is formulated as a maximin problem of optimal control.

Four problems are investigated and their solutions compared: Problems P1 and P2 deal with uncooperative collision avoidance, while Problems P3 and P4 deal with cooperative collision avoidance.

Numerical results show that the optimal control histories always involve multiple subarcs along which either the rudder angle is kept at one of the extreme positions or the rudder angle time rate is held at one of the extreme values.

Dragon-King^a is introduced in this paper as the manifestation of a disaster incident for a Smart Grid’s blackout for a day-ahead. The quintessential incident is being generated by an artificial black hole, it then spreads quickly into transmission lines. Consequently, it bursts into space-time transition regions. This paper reveals all the essential characteristics of the Dragon-King, it has non-isotropic stochastic kinematics. Regardless of its huge manifestation of unwanted phenomena, the Dragon-King is controllable. We also describe the mechanism of an updated complexity, spinning cosmic string and a messenger system in this paper. Furthermore, the control strategy of the feedback controller which ultimately leads to a stable normal operation is also reported in this paper.