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Background: As an important mathematical model, the finite state machine (FSM) has been used in many fields, such as manufacturing system, health care, and so on. This paper analyzes the current development status of FSMs. It is pointed out that the traditional methods are often inconvenient for analysis and design, or encounter high computational complexity problems when studying FSMs. Method: The deep Q-network (DQN) technique, which is a model-free optimization method, is introduced to solve the stabilization problem of probabilistic finite state machines (PFSMs). In order to better understand the technique, some preliminaries, including Markov decision process, ϵ-greedy strategy, DQN, and so on, are recalled. Results: First, a necessary and sufficient stabilizability condition for PFSMs is derived. Next, the feedback stabilization problem of PFSMs is transformed into an optimization problem. Finally, by using the stabilizability condition and deep Q-network, an algorithm for solving the optimization problem (equivalently, computing a state feedback stabilizer) is provided. Discussion: Compared with the traditional Q learning, DQN avoids the limited capacity problem. So our method can deal with high-dimensional complex systems efficiently. The effectiveness of our method is further demonstrated through an illustrative example.

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In network systems, control using minimum nodes or pinning control can be effectively used for stabilization problems to cut down the cost of control. In this paper, we investigate the set stabilization problem of logical control networks. In particular, we study the set stabilization problem of probabilistic Boolean networks (PBNs) and probabilistic Boolean control networks (PBCNs) via controlling minimal nodes. Firstly, an algorithm is given to search for the minimum index set of pinning nodes. Then, based on the analysis of its high computational complexity, we present optimized algorithms with lower computational complexity to ascertain the network control using minimum node sets. Moreover, some sufficient and necessary conditions are proposed to ensure the feasibility and effectiveness of the proposed algorithms. Furthermore, a theorem is presented for PBCNs to devise all state-feedback controllers corresponding to the set of pinning nodes. Finally, two models of gene regulatory networks are considered to show the efficacy of obtained results.

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In this paper, some new approaches for stability and stabilizability determination as well as state feedback stabilization controllers of linear time-invariant (LTI) interval systems are proposed. The presented stability conditions are less conservative than those of Kharitonov's theorem, and Gerschgorin's disc theorem methods. Moreover, some of the proposed stability, stabilizability, and feedback stabilization control methods for LTI interval systems are proved to be sufficient and necessary conditions. Compared with some traditional stability analysis and feedback stabilization design methods for LTI interval systems, these new approaches have lower computational complexity because of a special form of parameter vertex matrices developed in this work. Some numerical and practical examples are given to demonstrate the effectiveness and advantages of the proposed methods.

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Finite-time stabilization of strict-feedback switched systems with asymmetric output constraints (AOCs) via state feedback is investigated. First, an elaborately constructed fraction-type barrier Lyapunov function (BLF) is presented. Then, with a mild assumption on strict-feedback switched systems, state feedback laws are constructed by revamping the adding a power integrator approach (AAPIA) and meanwhile a common Lyapunov function (CLF) is also obtained. The resultant closed-loop systems are finite-time stable (FTS) and the asymmetric output constraint is satisfied too. The approach, proposed in this note, can make strict-feedback switched systems with/without AOCs finite-time stable in a unified frame.

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Information fusion integrates aspects of data and knowledge mostly on the basis that system information is accumulative/distributive, but a subtle case emerges for a system with bifurcations, which is always un-linearizable and exacerbates information acquisition and presents a control problem. In this paper, the problem of an un-linearizable system related to system observation and control is addressed, and Andronov-Hopf bifurcation is taken as a typical example of an un-linearizable system and detailed. Firstly, the properties of a linear/linearized system is upon commented. Then, nonlinear degeneracy for the normal form of Andronov-Hopf bifurcation is analyzed, and it is deduced that the cubic terms are an integral part of the system. Afterwards, the theoretical study on feedback stabilization is conducted between the normal-form Andronov-Hopf bifurcation and its linearized counterpart, where stabilization using washout-filter-aided feedback is compared, and it is found that by synergistic controller design, the dual-conjugate-unstable eigenvalues can be stabilized by single stable washout filter. Finally, the high-dimensional ethanol fermentation model is taken as a case study to verify the proposed bifurcation control method.

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In this paper the robust pole assignment problem using combined velocity and acceleration feedback for second-order linear systems with singular mass matrix is illustrated. This is promising for better applicability in several practical applications where the acceleration signals are easier to obtain than the proportional ones. First, the explicit parametric expressions of both the feedback gain controller and the eigenvector matrix are derived. The parametric solution involves manipulations only on the original second-order model. The available degrees of freedom offered by the velocity-acceleration feedback in selecting the associated eigenvectors are utilized to improve robustness of the closed-loop system. Straight-forward computational algorithms are introduced to demonstrate the effectiveness of the proposed approach. These algorithms are applicable for a dynamical system with mass matrices that can be either singular or nonsingular. Numerical examples are provided to illustrate the application of the proposed procedure.

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This paper considers a single sensor and single actuator approach to the static feedback stabilization of nonlinear systems. This is essentially a remote control problem that is present in many engineering applications. The proposed method solves this problem that is less expensive to implement and more reliable in practice. Significant results are obtained on the design of controllers for stabilizing the nonlinear systems. Important issues on control implementation are also discussed. The proposed design method is validated through its application to nonlinear control of aircraft engines.