Sensor and actuator selection problems (SASPs) are some of the core problems in dynamic systems design and control. These problems correspond to determining the optimal selection of sensors (measurements) or actuators (control nodes) such that certain estimation/control objectives can be achieved. While the literature on SASPs are indeed inveterate, the vast majority of the work focuses on linear(ized) representation of the network dynamics, resulting in the placements of sensors or actuators (SAs) that are valid for confined operating regions. As an alternative, herein we propose a new general framework for addressing SASPs in nonlinear dynamic systems (NDSs), assuming that the inputs and outputs are linearly coupled with the nonlinear dynamics. This is investigated through (i) classifying and parameterizing the NDSs into various nonlinear function sets, (ii) utilizing rich Lyapunov theoretic formulations, and (iii) designing a new customized branch-and-bound (BnB) algorithm that exploits problem structure of the SASPs. The newly designed BnB routines are computationally more attractive than the standard one and also directly applicable to solve SASPs for linear systems. In contrast with contemporary approaches from the literature, our approach is suitable for finding the optimal SAs combination for stable/unstable NDSs that ensures stabilization of estimation error and closed-loop dynamics through a simple linear feedback control policy.

传感器和执行器选择问题 (SASP) 是动态系统设计和控制中的一些核心问题。这些问题对应于确定传感器（测量）或执行器（控制节点）的最佳选择，以便可以实现某些估计/控制目标。虽然关于 SASP 的文献确实是根深蒂固的，但绝大多数工作都集中在网络动态的线性（化）表示上，从而导致对受限操作区域有效的传感器或执行器 (SA) 的放置。作为替代方案，我们在这里提出了一个新的通用框架，用于解决非线性动态系统 (NDS) 中的 SASP，假设输入和输出与非线性动态线性耦合。这通过（i）进行调查将 NDS 分类和参数化为各种非线性函数集，(ii)利用丰富的李雅普诺夫理论公式，以及(iii)设计一种新的定制分支定界 (BnB) 算法，该算法利用 SASP 的问题结构。新设计的 BnB 例程在计算上比标准例程更具吸引力，并且还直接适用于求解线性系统的 SASP。与文献中的当代方法相比，我们的方法适用于寻找稳定/不稳定 NDS 的最佳 SA 组合，通过简单的线性反馈控制策略确保估计误差和闭环动态的稳定性。