Zonotope parameter identification for virtual reference feedback tuning control

The problem of designing two feedback controllers for an unknown plant based on input–output measurements is discussed within a linear setting. Virtual reference feedback tuning is a direct method that aims at minimising a cost function of the 2-norm type by using a set of data, then no model identification is needed. When constructing the cost function, two model-matching problems are considered between closed loop transfer function and sensitivity function simultaneously. In model-matching procedures, we design the virtual reference input signal and virtual disturb signal respectively. When applied virtual reference feedback tuning to a closed loop system with two degrees of freedom controllers, two filters used to reprocess the input–output measurements are derived. To relax the strict probabilistic description on disturbance, zonotope parameter identification algorithm is proposed to calculates a set that contains the unknown parameters consistent with the measured output and the given bound of the disturbance. To guarantee our derived zonotope not growing unbounded with iterations, a sufficient condition for this requirement to hold may be formulated as one linear matrix inequality. An application of zonotope parameter identification to a flight simulation with two unknown PID controllers is studied to demonstrate the effectiveness of our algorithms.