This article proposes a dimensionality reduction approach to study the output regulation problem (ORP) of Boolean control networks (BCNs), which has much lower computational complexity than previous results. First, an auxiliary system which is much smaller in scale than the augmented system in previous approach is constructed. By analyzing the set stabilization of the auxiliary system as well as the original BCN, a necessary and sufficient condition to detect the solvability of the ORP is presented. Second, a method to design the state feedback controls for the ORP is proposed. Finally, two biological examples are given to demonstrate the effectiveness and advantage of the obtained new results.

With an increase in tracking time, the operating cost of the controller will increase accordingly. Considering the biological applications of Boolean control networks (BCNs), it is necessary to study the control problem of BCNs over finite time. In this paper, we study the output tracking problem of a BCN with disturbance inputs in a given finite time. First, the logical form of BCNs is transformed into an algebraic form using the semi-tensor product (STP) method. Then, the robust output tracking problems of a reference output trajectory and the outputs of a reference system over finite time are transformed into the robust reachability problem of the BCNs. Based on the truth matrix technique, two necessary and sufficient conditions are provided for the trackability of the reference outputs over finite time. Moreover, two algorithms are proposed to design the controllers in the case of the traceable outputs. It should be pointed out that the truth matrix method we used here has some unique features, including its simple computation and concise expression. Finally, two illustrative examples are presented to demonstrate the results in this paper.

This article investigates the pursuit–evasion (PE) game under the pure pursuit (or evasion) strategy for multi-uncrewed surface vehicles (USVs), along with the decision-oriented fixed-time velocity regulation controller (FTVRC) design. A novel exponential-type function approximation (ETFA) method is utilized to construct a differentiable performance index (PI), which reflects the decision-making basis for the player. Based on the differentiable PI, the player autonomously decides to generate the expected pursuit and evasion velocity, which includes size and direction information. To enable the player to execute its decision result, the FTVRC with a simple structure and low computational burden is designed to track the generated expected velocity. To cope with the unknown exogenous disturbances, a fixed-time disturbance observer (FTDO) is proposed to estimate the exogenous disturbances in real-time. According to the Lyapunov theory, all errors can achieve fixed-time convergence and the settling time is upper bounded. Finally, the simulation results show that the control scheme proposed in this article can achieve the PE target, and the superiorities of the ETFA method and the fixed-time control (FTC) method are demonstrated in the comparative simulations.