Robust stability of Switched Boolean Networks with function perturbation

In genetic regulatory networks, gene mutations are one of natural phenomena, which attract much attention by biological researchers. In modeling gene networks using switched Boolean networks (SBNs), gene mutations can be described by function perturbations, which is a meaningful issue in analyzing function perturbation of SBNs. This paper studies robust stability of SBNs with function perturbation. With the help of semi-tensor product (STP) of matrices, one equivalent algebraic form of SBNs is established. By constructing two state sets, a criterion for global stability of SBNs under arbitrary switching signals is proposed. In order to relax the conditions of global stability, pointwise stabilizability and consistent stabilizability of SBNs are further considered. Based on state reachable sets, several criteria are established for the proposed kinds of stability. Finally, the obtained results are verified by two examples and lac operon in the Escherichia coli, respectively.     

Global convergence of serial Boolean networks based on algebraic representation

This paper analyzes the global convergence of serial Boolean networks (SBNs) via the semi-tensor product of matrices, and presents some new results. Firstly, an algebraic representation is obtained for SBNs, and an algorithm is established for the conversion between the algebraic representations of SBNs and the corresponding Boolean networks. Secondly, the non-equivalence of global convergence between SBNs and the corresponding Boolean networks is revealed, although they have the same fixed points. Thirdly, a necessary and sufficient condition is presented for the global convergence of SBNs. Finally, the obtained results are applied to the evolutionary behaviour analysis of evolutionary networked games with cascading myopic best response adjustment.     

Modeling and SPM-dependent control of multi-rate networked control system with long time delay

In this paper, an efficient approach of modeling and control is presented for Multi-Rate Networked Control System (MRNCS) with considering long time delay. Firstly, the system is modeled as a switched system with a random switching signal which is subject to random networked-induced delay. For this, time delay is defined as a Markov chain and the model of MRNCS is obtained as a Markovian jump linear system. Afterward, a dynamic output feedback controller is designed for output tracking as well as stabilization of closed-loop system. The modeling and control of MRNCS are presented for two structures. At first, a new model of single-side MRNCS is proposed and a mode-independent controller is designed for stabilizing the system. Then the proposed modeling method is generalized to double-side MRNCS and by introducing the Set of Possible Modes (SPM) concept, an SPM-dependent controller is proposed for double-side MRNCS. To show the effectiveness of the proposed methods, some numerical results are provided on the quadruple-tank process.     

Adaptive tracking control for a class of switched uncertain nonlinear systems under a new state-dependent switching law

This paper deals with the problem of adaptive fuzzy tracking control for a class of switched uncertain nonlinear systems. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and the adaptive backstepping and dynamic surface control techniques are adopted. First, a new state-dependent switching method is proposed. By introducing convex combination technique and designing a state-dependent switching law, only the solvability of the adaptive tracking control problem for a convex combination of the subsystems is necessary. Second, a new common Lyapunov function with switched adaptive parameters is constructed to reduce the conservatism. Third, to avoid Zeno behavior, a modified state-dependent switching law with dwell time is proposed. It is shown that under the proposed control and switching laws, all the signals of the closed-loop system are bounded and all the state tracking errors can converge to a priori accuracy, even if some subsystems are uncontrollable. Finally, the effectiveness of the proposed method is illustrated through two simulation examples.     

Synchronization of drive–response singular Boolean networks

Network synchronization, explicating typical collective behaviors of coupled systems, plays a crucial role in social production and life. This paper addresses the synchronization problem of drive–response singular Boolean networks (SBNs). The solvability of drive–response SBNs is investigated based on the matrix representation. In view of the existence and uniqueness of the solutions to drive–response SBNs, three types of concepts, synchronization, strong synchronization and weak synchronization, are put forward for the first time. By two new systems, a restricted BN and a switched restricted BN, which are constructed from the considered systems, several synchronization conditions are provided to deal with the circumstances of unique solutions and multiple solutions, respectively. Besides, the synchronous ratio is defined to characterize the synchronization capability of drive–response SBNs for the case of multiple solutions. Finally, several examples are given to illustrate the effectiveness of the obtained results.     

Tracking consensus of nonlinear MASs with asymmetric communication delays in noisy environments

This paper investigates the tracking consensus problem of nonlinear multi-agent systems (MASs) with asymmetric time-varying communication delays in noisy environments under the conditions of fixed and switching directed topologies. A novel stochastic analysis approach is proposed, which guarantees that the designed two distributed tracking protocols can guide the controlled systems to achieve tracking consensus in the sense of mean square. In order to further reveal the influence of asymmetric communication delays on the tracking consensus ability for MASs, some new delay-dependent sufficient conditions for mean-square consensus are also developed. A simple example is finally given to illustrate the effectiveness of the proposed theoretical results.     

Adaptive fuzzy backstepping control design for a class of pure-feedback switched nonlinear systems

In this paper, an adaptive fuzzy output tracking control approach is proposed for a class of single input and single output (SISO) uncertain pure-feedback switched nonlinear systems under arbitrary switchings. Fuzzy logic systems are used to identify the unknown nonlinear system. Under the framework of the backstepping control design and fuzzy adaptive control, a new adaptive fuzzy output tracking control method is developed. It is proved that the proposed control approach can guarantee that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and the tracking error remains an adjustable neighborhood of the origin. A numerical example is provided to illustrate the effectiveness of the proposed approach.     

Adaptive fuzzy backstepping control for a class of MIMO switched nonlinear systems with unknown control directions

In this article, an adaptive fuzzy output tracking control approach is proposed for a class of multiple‐input and multiple‐output uncertain switched nonlinear systems with unknown control directions and under arbitrary switchings. In the control design, fuzzy logic systems are used to identify the unknown switched nonlinear systems. A Nussbaum gain function is introduced into the control design and the unknown control direction problem is solved. Under the framework of the backstepping control design, fuzzy adaptive control and common Lyapunov function stability theory, a new adaptive fuzzy output tracking control method is developed. It is proved that the proposed control approach can guarantee that all the signals in the closed‐loop system are bounded and the tracking error remains an adjustable neighborhood of the origin. A numerical example is provided to illustrate the effectiveness of the proposed approach. © 2015 Wiley Periodicals, Inc. Complexity 21: 155–166, 2016     

自组织结构的变论域模糊控制

针对变论域模糊控制,提出一种新的自组织结构的变论域模糊控制方法。自组织结构算法可以调整变论域模糊系统结构以及动态获得模糊规则,进一步减小变论域模糊控制项的稳态逼近误差。通过进一步理论分析可知,自组织结构算法仅仅保证了系统瞬时的切换是平稳的,但不能保证系统的闭环稳定性。给出了所提出控制方法的适用条件。通过与固定模糊系统结构的变论域模糊控制比较,仿真结果表明,所提出控制方法不仅使得系统的稳态跟踪误差更平稳,而且使得输入控制信号更加平滑。     

Output feedback dynamic control for trajectory tracking and vibration suppression

A new output feedback dynamic tracking control scheme for multiple and variable excitation frequency vibration suppression in mechanical systems is proposed. Dynamic vibration absorbers, differential flatness, Taylor polynomials and dynamic error compensation are integrated into the control synthesis. In this fashion, significant control capabilities are added to physical or virtual dynamic vibration absorbers to simultaneously perform multiple-frequency forced vibration suppression and trajectory tracking on the primary mechanical system. Parametric uncertainty and unmodeled dynamics are also considered to be actively compensated. Real-time estimations of periodic or aperiodic dynamic perturbation forces, excitation frequencies, unavailable state variables and parametric uncertainty are not necessary. Thus, measurements of the output position variable of the controlled primary mechanical system are only required. Analytical and numerical results on three case studies prove the efficiency and robustness of the proposed control method.     

Output feedback control for MIMO nonlinear systems using factorization

A new output feedback adaptive control scheme for multi-input and multi-output (MIMO) nonlinear systems is presented based on the high frequency gain matrix factorization and the backstepping approach with vector form. The only required prior knowledge about the high frequency gain matrix of the linear part of the system is the signs of its leading principal minors. The proposed controller is a dynamic one that only needs the measurement of the system output, and the observer and the filters are introduced in order to construct a virtual estimate of the unmeasured system states. The global stability of the closed-loop systems is guaranteed through this control scheme, and the tracking error converges to zero. Finally, the numerical simulation results illustrate the effectiveness of the proposed scheme.     

Switched safe tracking control design for unmanned autonomous helicopter with disturbances

In this paper, the switched safe tracking control scheme is investigated for the attitude and altitude system of a medium-scale unmanned autonomous helicopter with output constraints and unknown external disturbances. To keep the attitude angles and altitude within the desired constrained range, an output boundary protection approach is adopted to generate an output constrained trajectory which is piecewise differentiable. The disturbance observer-based control method is employed to handle the unknown external disturbances of the system. Because of the piecewise differentiability of the output constrained trajectory, the closed-loop error system with the safe tracking controller can be seen as a switched system with jump dynamics. The multiple Lyapunov function method is adopted to guarantee the tracking performance with designed average dwell time. Simulation results of an example are provided to illustrate the effectiveness of the proposed control scheme for the unmanned autonomous helicopter system.     

Fast terminal sliding mode controller design for nonlinear second‐order systems with time‐varying uncertainties

This article investigates a novel fast terminal sliding mode control approach combined with global sliding surface structure for the robust tracking control of nonlinear second‐order systems with time‐varying uncertainties. The suggested control technique is formulated based on the Lyapunov stability theory and guarantees the existence of the sliding mode around the sliding surface in a finite time. Using the new form of switching surface, the reaching phase elimination and the robustness improvement of the whole system are satisfied. Simulation results demonstrate the efficiency of the proposed technique. © 2014 Wiley Periodicals, Inc. Complexity 21: 239–244, 2015     

含多重时滞非线性系统的分数阶迭代学习控制的收敛性分析

本文研究了含多重时滞非线性系统的分数阶迭代学习控制(FOILC).它包含了外部干扰和输出控制噪音,通过引入λ—范数,获得在开环和闭环迭代学习控制作用下,系统控制输入以及跟踪误差收敛的充分条件.最后,通过数值仿真验证所提方法的有效性.     

Output Feedback Model Predictive Tracking Control Using a Slope Bounded Nonlinear Model

In this paper, an output feedback model predictive tracking control method is proposed for constrained nonlinear systems, which are described by a slope bounded model. In order to solve the problem, we consider the finite horizon cost function for an off-set free tracking control of the system. For reference tracking, the steady state is calculated by solving by quadratic programming and a nonlinear estimator is designed to predict the state from output measurements. The optimized control input sequences are obtained by minimizing the upper bound of the cost function with a terminal weighting matrix. The cost monotonicity guarantees that tracking and estimation errors go to zero. The proposed control law can easily be obtained by solving a convex optimization problem satisfying several linear matrix inequalities. In order to show the effectiveness of the proposed method, a novel slope bounded nonlinear model-based predictive control method is applied to the set-point tracking problem of solid oxide fuel cell systems. Simulations are also given to demonstrate the tracking performance of the proposed method.     

Hybrid control for tracking of invariant manifolds

This paper presents a hybrid control method that controls to unstable equilibria of nonlinear systems by taking advantage of systems’ free dynamics. The approach uses a stable manifold tracking objective in a computationally efficient, optimization-based switching control design. Resulting nonlinear controllers are closed-loop and can be computed in real-time. Our method is validated for the cart–pendulum and the pendubot inversion problems. Results show the proposed approach conserves control effort compared to tracking the desired equilibrium directly. Moreover, the method avoids parameter tuning and reduces sensitivity to initial conditions. The resulting feedback map for the cart–pendulum has a switching structure similar to existing energy based swing-up strategies. We use the Lyapunov function from these prior works to numerically verify local stability for our feedback map. However, unlike the energy based swing-up strategies, our approach does not rely on pre-derived, system-specific switching controllers. We use hybrid optimization to automate switching control synthesis on-line for nonlinear systems.     

Dynamic Release Control Policy for the Semiconductor Wafer Fabrication Lines

We propose a policy for controlling the release of raw wafers into semiconductor wafer fabrication lines. The proposed policy exploits up-to-date factory floor information gathered by tracking systems in order to calculate the timing and amount of new releases to minimize mean flow times and mean tardiness while maintaining the maximum output rates of the system. Extensive computer experiments show that the proposed policy results in at least 23.0 and 17.9% improvements on average in mean waiting time and mean tardiness respectively compared to existing release rules.     

Adaptive compensation of uncertain Euler–Lagrange systems with multiple time-varying actuator faults

This work proposes the command tracking problem for uncertain Euler–Lagrange (EL) systems with multiple partial loss of effectiveness (PLOE) actuator faults. Compared to existing fault-tolerant controllers for EL systems, the proposed adaptive controller accounts for parametric uncertainties in the system and multiple time-varying actuator fault parameters. The proposed method can also handle an infinite number of fault cases. The closed-loop fault-tolerant system is treated as a switched dynamical system, and a switched system stability is established using multiple Lyapunov functions. It is shown that all signals are bounded in each sub-interval and at the switching instances, and asymptotic tracking can be obtained only for a finite number of fault occurrences, whereas tracking error is bounded for the infinite case. Finally, a simulation example on a robotic manipulator is presented to show the effectiveness of the proposed method.     

一类时滞非完整系统的反馈控制问题的研究

针对一类具有时滞项的非完整系统,研究了其反馈控制器的设计问题.采用状态转换技术和反推方法,设计了不依赖于时滞的反馈控制器.同时为了处理初值为零的情况,提出了一种新颖的基于第一个子系统输出值的切换控制策略,最后通过仿真算例说明了控制器的有效性.