On simple adaptive control of plants not satisfying almost strict passivity and positivity conditions: an introduction to parallel feedforward configuration

Simple adaptive control systems were known to be robust against a class of disturbances and globally stable if the controlled plant is almost strictly positive real, that is, if there exists a positive definite static output feedback (unknown and not needed for implementation) such that the resulting closed-loop transfer function is strictly positive real. The present paper discusses the simple adaptive control scheme for a non-almost strictly positive real plants and gives a brief review of the parallel feedforward which makes the augmented plant satisfy the almost passivity or positivity conditions based on the stabilisability property of the system. The validity of the simplified adaptive algorithm under the positivity condition is examined through numerical simulation for both single-inputs single-outputs and multi-inputs multi-outputs systems.