This paper investigates set stabilization and robust set stabilization of periodically time-varying Boolean control networks (PTVBCNs) by combining state-flipping mechanism and state feedback control. Firstly, two algorithms are proposed to check whether systems with or without disturbance inputs can be stabilized to the set under the hybrid control. Next, the state feedback matrices are designed by a constructive method such that systems can be stabilized to the given set for two cases. In addition, some algorithms are proposed to find the corresponding flip sequence with minimum cardinality that drives any initial state to the given set in two cases. Finally, some examples are given to illustrate the good performance of the obtained results. Note to Practitioners—In this paper, we address the problems of set stabilization and robust set stabilization of periodically time-varying Boolean control networks using the semi-tensor product. This provides essential theoretical support for the interventional treatment of gene regulatory networks, aiming to transfer all states in the network to a healthy state, which is significant for gene therapy. In gene regulatory networks, we need to consider whether the system’s evolution can transfer all states to a healthy state and how to apply external effects to states that cannot achieve a healthy condition through the system’s evolution alone. Choosing when and how to exert external influence can achieve our goals, which is the significance of our research. This paper provides effective methods to solve the above problems.

Combining with the reinforcement learning (RL) strategy and adaptive backstepping method, an event-triggered-based adaptive optimized bipartite consensus control protocol is constructed for heterogeneous nonlinear strict-feedback multi-agent systems (MASs). The control objective is to synchronize the state variables of the MASs and obtain the optimized bipartite tracking performance. In order to finish the control objective, a fuzzy logic system (FLS) based RL method is employed in the critic-actor structure. Different with the exist RL methods, the RL updating laws in this article is stemmed from a simple positive function which is derived by Hamilton-Jacobi-Bellman (HJB) equation. The FLSs are used to release the persistence excitation condition and the switching threshold event-triggered strategy is designed to reduce the calculation and communication frequency. It is shown that the developed control protocol not only achieves the bipartite consensus tracking performance of the studied heterogeneous MASs but also maintains the stability of the whole closed-loop system. Finally, the simulation results are provided to demonstrate the effectiveness of proposed control protocol.Note to Practitioners—Nowadays, energy conservation and environmental protection have become the current trend. Therefor, it is imperative to consider efficiency improvement as the fundamental principle of modern control design. In this paper, an optimal control method is employed to find a control protocol for considered MASs to accomplish the control task with the minimum utilization of control resources. In some practical application scenarios such as sea voyage for deep-sea exploitation or ocean transportation, the designed optimal control protocol can not only reduce the massive energy consumption for surface vessels but also eliminate the persistence of excitation assumption in Zhang and Feng (2021), Tang and Lau (2022), and Ren et al. (2022). The developed switching threshold event-triggered strategy and bipartite control design can effectively reduce the call frequency of channel resources in practical and divide all agents into two groups in surface vessels collaboration. Thus, our control algorithm can be easily applied in practical engineering.