Abstract
This paper is dealing with designing a state feedback controller without colliding so that the multivariable plant output is regulated not only to follow an output of the reference model but also to keep from an output of dynamical avoidance obstacle under following assumptions.
(A.1) The plant control input is implemented on a basis of knowledge concerning parameters as well as a degree difference and concerning available measurements of states and inputs of plant, reference model and avoidance obstacle.
(A.2) Each signal of reference model and avoidance obstacle inputs is produced without any knowledge on three systems and is not influenced by states and inputs of any other systems.
(A.3) The obstacle output does not exist on a line between the plant and the reference outputs. Several features of the proposed controller are shown.
(1) The controller is composed of safety following and avoiding controllers.
(2) The gains of a safety following controller are designed from conditions not only to make the plant closed loop stable but also not to collide with the reference model output.
(3) The gains of a safety avoidance controller are determined so that the plant closed loop is made unstable as well as the plant output does not collide with the avoidance obstacle output.
(4) A switching function is introduced to adjust to switch the gains of safety following controllers to the ones of safety avoidance controller dependent on whether plant output meets across the prohibited region.
