In this study, the output tracking of delayed logical control networks (DLCNs) with state and control constraints is further investigated. Compared with other delays, state-dependent delay updates its value depending on the current state values and a pseudo-logical function. Multiple constraints mean that state values are constrained in a nonempty set and the design of the controller is conditioned. Using the semi-tensor product of matrices, dynamical equations of DLCNs are converted into an algebraic description, and an equivalent augmented system is constructed. Based on the augmented system, the output tracking problem is transformed into a set stabilization problem. A deformation of the state transition matrix is computed, and a necessary and sufficient condition is derived for the output tracking of a DLCN with multi-constraint. This condition is easily verified by mathematical software. In addition, the admissible state-feedback controller is designed to enable the outputs of the DLCN to track the reference signal. Finally, theoretical results are illustrated by an example.

在这项研究中，进一步研究了具有状态和控制约束的延迟逻辑控制网络（DLCN）的输出跟踪。与其他延迟相比，基于状态的延迟会根据当前状态值和伪逻辑函数更新其值。多重约束意味着状态值被约束在一个非空集中，并且控制器的设计受到限制。使用矩阵的半张量积，将DLCN的动力学方程转换为代数描述，并构建了等效的扩充系统。基于增强系统，将输出跟踪问题转换为集合稳定问题。计算状态转移矩阵的变形，并导出具有多约束的DLCN的输出跟踪的充要条件。此条件可以通过数学软件轻松验证。另外，可允许的状态反馈控制器设计为使DLCN的输出能够跟踪参考信号。最后，通过一个例子说明了理论结果。