Abstract: The virtual reference feedback tuning is a direct method that aims at minimizing a cost function of the 2-norm type by using a set of dates. To a nonlinear optimization problem with ellipsoid constrained conditions, the objective criterion function and two constrained conditions were converted to its corresponding linear matrix inequity. Then the ellipsoid optimization iterative algorithm was adopted to generate a sequence of ellipsoids with decreasing volume. An upper bound on the maximum number of possible iterates steps was derived. When considering the initialization of the ellipsoid optimization iterative algorithm, an initial ellipsoid strategy based on the level set of convex optimization theory was proposed. Finally, the simulation example results confirm the theoretical results. Then the results show when the virtual reference feedback tuning is used to design the two controllers in the closedloop system, the controller parameter estimation values are more accurate and the convergence speed of the ellipsoid optimization algorithm is fast.  

Key words: virtual reference feedback tuning (VRFT) control, linear matrix inequity, ellipsoid algorithm, initial ellipoid