Constraints on the feedback structure arise in many control systems due to implementing cost, hardware limitations and operational reliability. The parameter space method aims to solve the robust structured controller design problems based on a convex reformulation technique. Despite its attractiveness, the structural constraints are limited to be either decentralized or linear dependence among entries within the same row or column in the current literature. And the global optimal solution is yet to be guaranteed, since a non-convex constraint is introduced in the parameter space after reformulating it as the output feedback synthesis problem. In this paper, we extend the parameter space method to a more generalized structured optimal control problem, such that the linear dependence can occur among its arbitrary entries. A bilinear factorization to the feedback gain matrix is proposed by a special Kronecker product decomposition. Subsequently, an equivalent transformation is proposed to convert this structured control design problem to a controller synthesis problem under decentralized full-state feedback. Thereby, the prior non-convex constraint in the parameter space is removed and the globally optimal structured controller is synthesized by convex programming. Examples such as integrated design and formation control demonstrate its practical appeals.

由于实施成本、硬件限制和操作可靠性，许多控制系统中出现了对反馈结构的限制。参数空间方法旨在解决基于凸重构技术的鲁棒结构化控制器设计问题。尽管它很有吸引力，但在当前文献中，结构约束仅限于同一行或同一列中条目之间的分散或线性依赖。并且全局最优解尚未得到保证，因为在将其重新表述为输出反馈综合问题后，在参数空间中引入了非凸约束。在本文中，我们将参数空间方法扩展到更广义的结构化最优控制问题，使其任意项之间可以发生线性相关。通过特殊的 Kronecker 乘积分解提出了反馈增益矩阵的双线性分解。随后，提出了一个等效变换，将这个结构化控制设计问题转化为分散全状态反馈下的控制器综合问题。从而去除参数空间中的先验非凸约束，通过凸规划合成全局最优结构化控制器。集成设计和编队控制等示例证明了其实际吸引力。去除参数空间中的先验非凸约束，通过凸规划合成全局最优结构化控制器。集成设计和编队控制等示例证明了其实际吸引力。去除参数空间中的先验非凸约束，通过凸规划合成全局最优结构化控制器。集成设计和编队控制等示例证明了其实际吸引力。