输出多采样反馈控制器及系统稳定性

针对由连续被控对象和数字控制器构成的数字控制系统,将现有的线性系统输出多采样线性反馈数字控制器设计方法推广到非线性系统．并相应地研究了非线性输出多采样反馈控制器及摄动非线性系统．给出了这类非线性输出多采样数字控制系统及其摄动系统的稳定性和鲁棒性条件．     

Semiglobal stabilization of linearly uncontrollable and unobservable nonlinear systems via sampled‐data control

This article investigates the problem of using sampled‐data state/output feedback to semiglobally stabilize a class of uncertain nonlinear systems whose linearization around the origin is neither controllable nor observable. For any arbitrarily large bound of initial states, by employing homogeneous domination approach and a homogeneous version of Gronwall‐Bellman inequality, a sampled‐data state feedback controller with appropriate sampling period and scaling gain is constructed to semiglobally stabilize the system. In the case when not all states are available, a reduced‐order sampled‐data observer is constructed to provide estimates for the control law, which can guarantee semiglobal stability of the closed‐loop system with carefully selected sampling period and scaling gain.     

Global output‐feedback stabilization for a class of stochastic nonlinear systems via sampled‐data control

In this paper, the global sampled‐data output‐feedback stabilization problem is considered for a class of stochastic nonlinear systems. First, based on output‐feedback domination technique and emulation approach, a systematic design procedure for sampled‐data output‐feedback controller is proposed for a class of stochastic lower‐triangular nonlinear systems. It is proved that the proposed sampled‐data output‐feedback controller will stabilize the given stochastic nonlinear system in the sense of mean square exponential stability. Because of the domination nature of the proposed control approach, it is shown that the proposed control approach can also be used to handle the global sampled‐data output‐feedback stabilization problems for a more general class of stochastic non‐triangular nonlinear systems. Finally, simulation examples are given to demonstrate the effectiveness of the proposed method. Copyright © 2017 John Wiley & Sons, Ltd.     

Exponential dissipativeness of the random-structure diffusion processes and problems of robust stabilization

Consideration was given to the class of systems described by a finite set of the controllable control-affine diffusion Ito processes with stepwise transitions defined by the evolution of the uniform Markov chain (Markov switchings). For these systems, the notion of exponential dissipativity was introduced, and its theory was developed and used to estimate the possible variations of the output feedback law under which the system retains its robust stability. For the set of linear systems with uncertain parameters, proposed was a two-step procedure for determination of the output feedback control based on comparison with the stochastic model and providing their simultaneous robust stabilization. At the first step, the robust stabilizing control is established by means of an iterative algorithm. Then, the possible variations of the feedback law for which the robust stability is retained are estimated by solving a system of matrix linear inequalities. An example was presented.     

Bounded control of feedforward time‐delay systems with linearized systems consisting of chain of oscillators

For the global stabilization of a family of feedforward nonlinear time‐delay systems whose linearized systems consist of a chain of identical oscillators, a saturated feedback control is established based on a special canonical form. The proposed control laws use not only the current states but also the delayed states for feedback, which helps maintain the decoupling property in the recursive design. Moreover, explicit conditions guaranteeing the stability of the closed‐loop system are provided. When the nonlinear terms vanish and even the oscillators are distinct, a modified saturated feedback control can still be established for the corresponding global stabilization problem. Two numerical examples are given to illustrate the effectiveness of the proposed approaches.     

Robust control of a family of uncertain nonminimum‐phase systems via continuous‐time and sampled‐data output feedback

The problem of global robust stabilization is studied by both continuous‐time and sampled‐data output feedback for a family of nonminimum‐phase nonlinear systems with uncertainty. The uncertain nonlinear system considered in this paper has an interconnect structure consisting of a driving system and a possibly unstable zero dynamics with uncertainty, ie, the uncertain driven system. Under a linear growth condition on the uncertain zero dynamics and a Lipschitz condition on the driving system, we show that it is possible to globally robustly stabilize the family of uncertain nonminimum‐phase systems by a single continuous‐time or a sampled‐data output feedback controller. The sampled‐data output feedback controller is designed by using the emulated versions of a continuous‐time observer and a state feedback controller, ie, by holding the input/output signals constant over each sampling interval. The design of either continuous‐time or sampled‐data output compensator uses only the information of the nominal system of the uncertain controlled plant. In the case of sampled‐data control, global robust stability of the hybrid closed‐loop system with uncertainty is established by means of a feedback domination method together with the robustness of the nominal closed‐loop system if the sampling time is small enough.     

Sampled‐data control under magnitude and rate saturating actuators

This paper addresses the problems of stability analysis and stabilization of sampled‐data control systems under magnitude and rate saturating actuators. A position‐type feedback modeling for the actuator is considered. Based on the use of a quadratic Lyapunov function, a looped‐functional, and generalized sector relations (to cope with nested saturation functions), LMI‐based conditions are derived to assess local (regional) and global stability of the closed‐loop systems under aperiodic sampling strategies and also to synthesize stabilizing sampled‐data state feedback control laws. These conditions are then incorporated in convex optimization problems aiming at maximizing estimates of the region of attraction of the origin or maximizing the inter‐sampling time for which the stability is ensured regionally or, when possible, globally. Copyright © 2016 John Wiley & Sons, Ltd.     

A new optimal multirate control of linear periodic andtime-invariant systems

The optimal multirate design of linear, continuous-time, periodic and time-invariant systems is considered. It is based on solving the continuous linear quadratic regulation (LQR) problem with the control being constrained to a certain piecewise constant feedback. Necessary and sufficient conditions for the asymptotic stability of the resulting closed-loop system are given. An explicit multirate feedback law that requires the solution of an algebraic discrete Riccati equation is presented. Such control is simple and can be easily implemented by digital computers. When applied to linear time-invariant systems, multirate optimal feedback optimal control provides a satisfactory response even if the state is sampled relatively slowly. Compared to the classical single-rate sampled-data feedback in which the state is always sampled at the same rate, the multirate system can provide a better response with a considerable reduction in the optimal cost. In general, the multirate scheme offers more flexibility in choosing the sampling rates     

Global output feedback sampled‐data stabilization for upper‐triangular nonlinear systems with improved maximum allowable transmission delay

This paper addresses the problem of output feedback sampled‐data stabilization for upper‐triangular nonlinear systems with improved maximum allowable transmission delay. A class of hybrid systems are firstly introduced. The transmission delay may be larger than the sampling period. Then, sufficient conditions are proposed to guarantee global exponential stability of the hybrid systems. Based on these sufficient conditions and a linear continuous‐discrete observer, an output feedback control law is presented to globally exponentially stabilize the feedforward nonlinear system. The improved maximum allowable transmission delay is also given. The results are also extended to output feedback sampled‐data stabilization for lower‐triangular nonlinear systems. Finally, illustrative examples are used to verify the effectiveness of the proposed design methods. Copyright © 2016 John Wiley & Sons, Ltd.     

SYSTEMS WITH NONEQUIDISTANT SAMPLING: CONTROLLABLE? OBSERVABLE? STABLE?

Some qualitative properties of systems with nonequidistant sampling are investigated. First, it is proved that the nonequidistant sampling pattern mentioned in [1] does not affect the controllability and observability of time‐varying linear systems during discretization. The result is claimed to be true for linear systems with periodic behavior and time‐varying sampling. Second, closed‐loop stability conditions are established, respectively, for linear and nonlinear sampled‐data systems consisting of continuous plants and linear digital feedback controllers. The stability results are extended to general systems consisting of nonlinear continuous plants and nonlinear digital controllers with time‐varying sampling periods.     

基于分段Lyapunov 函数的Hammerstein-Wiener 非线性预测控制

针对输入和输出受约束的Hammerstein-Wiener型非线性系统,建立T-S模糊模型,并提出一种基于分段Lyapunov函数的非线性预测控制算法.通过构造分段二次Lyapunov函数,分析非线性系统的稳定性,降低普通二次Lyapunov函数的保守性;通过离线设计分段反馈控制律,在线实施符合条件的反馈控制律,极大程度地提高了在线计算效率.仿真结果验证了该方法的有效性.     

H ∞ control of networked control systems with state quantisation

This article addresses the problem of controller design for networked control systems over digital communication. The systems under consideration are stabilised via state feedback, where the effects of sampled signal, state quantisation, network-induced delay and packet dropout are considered. The proposed delay-dependent stability criteria are formulated in the form of a linear matrix inequality, which ensure asymptotic stability and a prescribed H _∞ performance level for networked control systems with admissible uncertainties. Maximum allowable delay bound of networked control systems is obtained by solving a convex optimisation problem. Furthermore, a numerical example is given to illustrate the effectiveness of the main result.     

Output feedback stabilization for a general class of nonlinear systems via sampled‐data control

This paper considers global output feedback stabilization via sampled‐data control for a general class of nonlinear systems, which admit unknown control coefficients and nonderivable output function. A sector region of the output function is given by utilizing a technical lemma, and a sampled‐data controller is designed by combining a robust state stabilizer and a reduced‐order sampled‐data observer. By carefully choosing an appropriate sampling period, the proposed controller guarantees the globally asymptotical stability of the closed‐loop systems.     

Coning motion stability and decoupling methods analysis of spinning missiles with angle-of-attack feedback autopilot

The angle-of-attack (AOA) three-loop feedback autopilot is an improved three-loop autopilot that has been widely employed in missile control systems. For spinning missiles, however, unstable coning motion can be induced by the cross-couple effect. For spinning missiles with an AOA feedback autopilot, this paper analyzes the coning motion stability with the consideration of the augmentation loop and the position of the accelerometer and compares the performance of three decoupling methods. First, a novel double-channel actuator AOA three-loop autopilot is established, and the sufficient and necessary condition of coning motion stability is proposed analytically on account of the complex system equations. The stability condition shows that the stable region of the design parameters for the autopilot shrinks as a result of the spinning condition. Moreover, methods associated with actuator dynamics, control coupling, static stability, and the decoupling method of setting the lead angle to the control system are presented to improve the stability of spinning missiles. Numerical simulations are implemented to demonstrate the accuracy of the proposed methods, whose results illustrate that the stability conditions can guide AOA autopilot design for the flight stabilization of spinning missiles.     

多输出非线性系统在数据截断协议下的 时滞多采样率输出反馈镇定

本文研究一类多输出非线性系统基于一类数据截断协议的时滞多采样率输出反馈控制. 所考虑的非线性 系统的输出以异步方式进行采集, 通过网络传输到输出反馈控制端后立即用于构造输出反馈控制器. 当控制输入 信号可用时, 立即用来更新被控制系统. 这样, 就存在两种传输时滞, 一种是非线性系统输出端到输出反馈控制器端 的传输时滞, 另一种是输出反馈控制器端到非线性系统输入端的传输时滞. 从而被控系统的更新和输出反馈控制 器的更新不在同一个时间区间. 利用区间分解, 可以在同一个区间考虑被控系统和输出反馈控制器并分析闭环系 统的稳定性. 最后, 一个算例用来验证所提方法的有效性.     

基于区间二型T-S模糊模型的网络控制系统的输出反馈预测控制

针对干扰作用下的非线性网络控制系统,给出了带一个自由控制作用的输出反馈预测控制方法.首先,利用区间二型T-S模糊模型描述具有参数不确定性的非线性对象,采用马尔科夫链描述系统中的随机丢包过程,由此建立了丢包网络环境下的非线性网络控制系统的数学模型.然后,通过引入二次有界技术得到了干扰作用下网络控制系统的稳定性描述方法,并在此基础上给出了状态观测器的线性矩阵不等式条件.最后,基于估计状态,通过将无穷时域控制作用参数化为一个自由控制作用加一个线性反馈律得到了输出反馈预测控制方法.论文的特色在于构建了在线更新误差椭圆集合的基本方法,满足了约束条件下输出反馈预测控制保证稳定性的要求.仿真例子验证了所提方法的有效性.     

Event-triggered-based integral reinforcement learning output feedback optimal control for partially unknown constrained-input nonlinear systems

In this paper, an adaptive output feedback event-triggered optimal control algorithm is proposed for partially unknown constrained-input continuous-time nonlinear systems. First, a neural network observer is constructed to estimate unmeasurable state. Next, an event-triggered condition is established, and only when the event-triggered condition is violated will the event be triggered and the state be sampled. Then, an event-triggered-based synchronous integral reinforcement learning (ET-SIRL) control algorithm with critic-actor neural networks (NNs) architecture is proposed to solve the event-triggered Hamilton–Jacobi–Bellman equation under the established event-triggered condition. The critic and actor NNs are used to approximate cost function and optimal event-triggered optimal control law, respectively. Meanwhile, the event-triggered-based closed-loop system state and all the neural network weight estimation errors are uniformly ultimately bounded proved by Lyapunov stability theory, and there is no Zeno behavior. Finally, two numerical examples are presented to show the effectiveness of the proposed ET-SIRL control algorithm.     

On exponential stability of linear networked control systems

This paper addresses exponential stability of linear networked control systems. More specifically, the paper considers a continuous‐time linear plant in feedback with a linear sampled‐data controller with an unknown time varying sampling rate, the possibility of data packet dropout, and an uncertain time varying delay. The main contribution of this paper is the derivation of new sufficient stability conditions for linear networked control systems taking into account all of these factors. The stability conditions are based on a modified Lyapunov–Krasovskii functional. The stability results are also applied to the case where limited information on the delay bounds is available. The case of linear sampled‐data systems is studied as a corollary of the networked control case. Furthermore, the paper also formulates the problem of finding a lower bound on the maximum network‐induced delay that preserves exponential stability as a convex optimization program in terms of linear matrix inequalities. This problem can be solved efficiently from both practical and theoretical points of view. Finally, as a comparison, we show that the stability conditions proposed in this paper compare favorably with the ones available in the open literature for different benchmark problems. Copyright © 2012 John Wiley & Sons, Ltd.     

Input-to-state stability of exponentially stabilized semilinear control systems with inhomogeneous perturbations

In this paper we investigate the robustness of state feedback stabilized semilinear systems subject to inhomogeneous perturbations in terms of input-to-state stability. We consider a general class of exponentially stabilizing feedback controls which covers sampled discrete feedbacks and discontinuous mappings as well as classical feedbacks and derive a necessary and sufficient condition for the corresponding closed-loop systems to be input-to-state stable with exponential decay and linear dependence on the perturbation. This condition is easy to check and admits a precise estimate for the constants involved in the input-to-state stability formulation. Applying this result to an optimal control based discrete feedback yields an equivalence between (open-loop) asymptotic null controllability and robust input-to-state (state feedback) stabilizability.     

离散Markov跳变系统事件触发H∞量化输出反馈控制

主要研究了基于事件触发机制的离散Markov跳变系统的量化H∞输出反馈控制问题,对系统的建模、稳定性分析、控制器设计等三个方面进行了研究。首先,提出了事件触发通信机制来确定当前采样数据是否能够传输到控制器当中。其次,在传感器与控制器之间引入对数量化器,利用扇形有界方法,量化采样数据达到降低网络中的数据传输速率的目的。接下来,考虑网络诱导时延建立一种具有外部扰动的Markov跳变时滞系统。构造Lyapunov-Krasovskii 泛函,得到使闭环系统渐近稳定且满足H∞性能指标的充分条件,在此基础上设计相应的输出反馈控制器。最后通过数值仿真来证明本文所提方法的有效性。