With the development of Industry 4.0, mobile agents are deployed to coordinate with multi-loop control systems to perform manufacturing tasks, leading to heterogeneous Internet of Things (IoT). Due to shadow fading induced by the movement of mobile agents, the wireless channel closing the control loops is inherently unreliable, which can compromise the control system performance. This paper addresses the co-design problem of transmission scheduling and agents’ movement to ensure both control performance and energy efficiency. A generalized cyber-physical-agent framework is proposed to capture the coupling between IoT systems and a mobile agent through a state-dependent fading channel. Moreover, the movement of the mobile agent among areas exhibiting different levels of shadow effects is modeled by Markov decision process. To address such heterogeneous dynamics, the co-design problem is formulated into the optimization of a logic-based stochastic switched system by utilizing the semi-tensor product technique. Based on state mergence andH-representation methods, a tractable and effective algorithm is then proposed to design co-design policies, minimizing the average joint cost of communication and control. A parallel scheme is further developed to alleviate the computation burden of the algorithm. Theoretical guarantees are provided to ensure control system performance. Finally, simulation results are given to demonstrate effectiveness of the proposed method.

The optimal strategy estimation of random evolutionary Boolean games (REBGs) is discussed in this article. First, using the minimum mean square error criterion, the optimal strategy estimator is proposed for REBGs. Then, a matrix approach is developed to calculate the optimal strategy estimator by the aid of a semitensor product of matrices, which includes the prediction matrix, updating distribution, and strategy iterative formula. Finally, an elucidative example is included to show the obtained results are valid.

This article analyzes the function perturbation impact on the finite-time stability and stabilization of the probabilistic Boolean networks (PBNs). First, the concept of stability in the distribution of PBNs is divided into two disjoint concepts, that is, finite-time stability with probability one (FTSPO) and asymptotical stability with probability one (ASPO), and a new criterion is proposed for the verification of ASPO. Second, by constructing a parameterized set, it is shown that PBNs subject to function perturbation keep FTSPO if and only if the perturbed point does not belong to the parameterized set, while PBNs become ASPO if and only if the perturbed point belongs to the parameterized set. Third, as an application of perturbed stability analysis, the robust state-feedback stabilization is discussed for probabilistic Boolean control networks (PBCNs) with function perturbation. Finally, the obtained results are applied to a WNT5A network and lac operon in the Escherichia coli, respectively.

Observability is a fundamental concept for the synthesis of both linear systems and nonlinear systems. This article devotes to discussing the robustness of observability for multivalued logical networks (MVLNs) subject to function perturbation and establishing a graph-based framework. First, based on the transition graph of undistinguishable pairs of states, a new graph-based criterion is presented for the observability of MVLNs. Second, a candidate set consisting of all suspicious undistinguishable pairs of states is defined, based on the cardinality of which and the graph-based condition, a series of effective criteria are proposed for the robustness of observability subject to function perturbations. Finally, the obtained results are applied to the robust observability analysis of the p53-MDM2 negative feedback regulatory loop.

The control design problem plays a fundamental role in the study of logical control networks (LCNs). This paper presents a detailed survey on new developments in control design techniques of LCNs. First, some preliminary results on the semi-tensor product method and LCNs are reviewed. Then, we move on to some new developments for control design techniques of LCNs, including the reachable set approach, the pinning control technique, the control Lyapunov function approach, the event-triggered control technique, and the sampled-data control technique. Finally, an illustrative example is given to demonstrate the effectiveness of these techniques.