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中文摘要：
采用虚拟参考反馈校正控制方法，通过最小化由一簇输入／输出观测数据组成的L2范数的代价函数来设计控制器；对于含有椭球约束不等式条件的非线性优化问题，将目标准则函数和两约束条件转化为线性矩阵不等式形式，采用椭球优化迭代算法产生一系列体积逐渐减小的椭球序列，并最终收敛于一个最优解，同时，推导出椭球优化迭代算法所需迭代次数的一个上界；针对椭球优化迭代算法的初始化，提出一种基于凸优化理论水平集的初始椭球选取策略，采用仿真算例验证了所提出方法的有效性．结果表明：采用虚拟参考校正控制来设计闭环系统中的2个控制器时，可以得到较为准确的控制器参数估计值；采用椭球优化算法可以得到较快的收敛速度．
英文摘要：
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 corre sponding 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 optimiza tion algorithm is fast.
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