We propose an extension of the input-output feedback linearization for a class of multivariate systems that are not input-output linearizable in a classical manner. The key observation is that the usual input-output linearization problem can be interpreted as the problem of solving simultaneous linear equations associated with the input gain matrix: thus, even at points where the input gain matrix becomes singular, it is still possible to solve a part of linear equations, by which a subset of input-output relations is made linear or close to be linear. Based on this observation, we adopt the task priority-based approach in the input-output linearization problem. First, we generalize the classical Byrnes-Isidori normal form to a prioritized normal form having a triangular structure, so that the singularity of a subblock of the input gain matrix related to lower-priority tasks does not directly propagate to higher-priority tasks. Next, we present a prioritized input-output linearization via the multi-objective optimization with the lexicographical ordering, resulting in a prioritized semilinear form that establishes input output relations whose subset with higher priority is linear or close to be linear. Finally, Lyapunov analysis on ultimate boundedness and task achievement is provided, particularly when the proposed prioritized input-output linearization is applied to the output tracking problem. This work introduces a new control framework for complex systems having critical and noncritical control issues, by assigning higher priority to the critical ones.

翻译：本文针对一类无法通过经典方式实现输入-输出线性化的多变量系统，提出了一种扩展的输入-输出反馈线性化方法。关键发现是：常规输入-输出线性化问题可被解释为与输入增益矩阵相关的联立线性方程组求解问题；因此，即使在输入增益矩阵出现奇异的点上，仍可通过求解部分线性方程，使部分输入-输出关系呈现线性或近似线性特性。基于这一发现，我们在输入-输出线性化问题中引入了任务优先级方法。首先，将经典的Byrnes-Isidori标准型推广为具有三角结构的优先级标准型，使得与低优先级任务相关的输入增益子矩阵的奇异性不会直接传播至高优先级任务。其次，通过字典序多目标优化实现优先级输入-输出线性化，得到具有任务优先级的半线性形式——该形式建立的输入-输出关系中，高优先级子集呈现线性或近似线性特性。最后，针对所提出的优先级输入-输出线性化方法在输出跟踪问题中的应用，进行了关于最终有界性和任务完成度的李雅普诺夫分析。本文通过为关键控制问题分配更高优先级，为同时包含关键与非关键控制问题的复杂系统提供了新的控制框架。