Output‐feedback control of a class of stochastic nonlinear systems with linearly bounded unmeasurable states

In this paper, the problems of stochastic disturbance attenuation and asymptotic stabilization via output feedback are investigated for a class of stochastic nonlinear systems with linearly bounded unmeasurable states. For the first problem, under the condition that the stochastic inverse dynamics are generalized stochastic input‐to‐state stable, a linear output‐feedback controller is explicitly constructed to make the closed‐loop system noise‐to‐state stable. For the second problem, under the conditions that the stochastic inverse dynamics are stochastic input‐to‐state stable and the intensity of noise is known to be a unit matrix, a linear output‐feedback controller is explicitly constructed to make the closed‐loop system globally asymptotically stable in probability. Using a feedback domination design method, we construct these two controllers in a unified way. Copyright © 2007 John Wiley & Sons, Ltd.     

Partially decoupled approach of extended non-minimal state space predictive functional control for MIMO processes

This paper presents a partially decoupled design of the state space predictive functional control for MIMO processes. The multivariable process is first treated into MISO process by a simple Cramer's rule solution to linear equations which provides a balance between model complexity and control system design, and then the derived MISO process based extended state space predictive functional control is presented. The overall design of the controller enables the controller to consider both the process state dynamics and the output dynamics, thus improved control performance for tracking set-points and disturbance rejection is resulted. The proposed controller is tested on both model match and model mismatch cases to demonstrate its superiority. In addition, a closed-form of transfer function representation that facilitates frequency analysis of the control system is provided to give further insight into the proposed method.     

Time-scale separation and robust controller design for uncertain nonlinear singularly perturbed systems under perfect state measurements

We study time-scale separation and robust controller design for a class of singularly perturbed nonlinear systems under perfect state measurements. The system dynamics are taken to be jointly linear in the fast state variables, control and disturbance inputs, but nonlinear in the slow state variables. Since global timescale separation may not always be possible for nonlinear singularly perturbed systems, we restrict our attention here to some closed subset of the state space, on which a timescale separation holds for sufficiently small values of the singular perturbation parameter. We construct a slow controller and a composite controller based on the solutions of particular slow and fast games obtained using time-scale separation. For the class of systems for which the slow controller can be selected to be robust with respect to small regular structural perturbations on the slow subsystem, we show under some growth conditions that the composite controller can achieve any desired level of performance that is larger than the maximum of the performance levels for the slow and fast subsystems,. A slow controller, however, is not generally as robust as the composite controller; but, still under some conditions which are delineated in the paper, the fast dynamics can be totally ignored. The paper also presents a numerical example to illustrate the theoretical results.     

Safety and Reachability of Piecewise Linear Hybrid Dynamical Systems Based on Discrete Abstractions

In this paper, a novel methodology for analysis of piecewise linear hybrid systems based on discrete abstractions of the continuous dynamics is presented. An important characteristic of the approach is that the available control inputs are taken into consideration in order to simplify the continuous dynamics. Control specifications such as safety and reachability specifications are formulated in terms of partitions of the state space of the system. The approach provides a convenient general framework not only for analysis, but also for controller synthesis of hybrid systems. The research contributions of this paper impact the areas of analysis, verification, and synthesis of piecewise linear hybrid systems.     

基于随机通信逻辑的网络控制器设计

设计具有带宽约束的网络控制器,采用带时倚强度的泊松过程形成随机通信逻辑调度策略,实现系统状态的有限次更新,根据其马尔科夫跳变本质,基于更新时刻特性,协同设计控制器。仿真结果表明,引入随机通信逻辑能减少状态更新的次数,降低网络带宽对控制性能的影响,提高系统的动态性能。     

Model-based periodic event-triggered stabilization for continuous-time stochastic nonlinear systems

In this paper, we investigate a model-based periodic event-triggered control framework for continuous-time stochastic nonlinear systems. In this framework, an auxiliary approximate discrete-time model of stochastic nonlinear systems is constructed in the controller module, which is utilized not only to design a discrete-time controller but also as a state predictor within trigger intervals. This discrete controller design approach, the strategy of state prediction, and the periodic detection strategy for the trigger rule not only provide a manner of more direct and easier implementation on the digital platform but also effectively reduce the communication load while a satisfactory control performance is maintained. Additionally, the mean-square exponentially stabilization for continuous-time stochastic nonlinear systems is achieved, in which a guideline for determining the maximum admissible sampling period is provided and the periodic event trigger rule is designed. The final numerical simulation also supports the effectiveness of our proposed framework.     

Partially‐observable stochastic hybrid systems (poshss) state estimation and optimal control

This paper discusses the state estimation and optimal control problem of a class of partially‐observable stochastic hybrid systems (POSHS). The POSHS has interacting continuous and discrete dynamics with uncertainties. The continuous dynamics are given by a Markov‐jump linear system and the discrete dynamics are defined by a Markov chain whose transition probabilities are dependent on the continuous state via guard conditions. The only information available to the controller are noisy measurements of the continuous state. To solve the optimal control problem, a separable control scheme is applied: the controller estimates the continuous and discrete states of the POSHS using noisy measurements and computes the optimal control input from the state estimates. Since computing both optimal state estimates and optimal control inputs are intractable, this paper proposes computationally efficient algorithms to solve this problem numerically. The proposed hybrid estimation algorithm is able to handle state‐dependent Markov transitions and compute Gaussian‐ mixture distributions as the state estimates. With the computed state estimates, a reinforcement learning algorithm defined on a function space is proposed. This approach is based on Monte Carlo sampling and integration on a function space containing all the probability distributions of the hybrid state estimates. Finally, the proposed algorithm is tested via numerical simulations.     

Non-linear generalised minimum variance control state space design for a second-order Volterra series model

This paper presents a non-linear generalised minimum variance (NGMV) controller for a second-order Volterra series model with a general linear additive disturbance. The Volterra series models provide a natural extension of a linear convolution model with the nonlinearity considered in an additive term. The design procedure is entirely carried out in the state space framework, which facilitates the application of other analysis and design methods in this framework. First, the non-linear minimum variance (NMV) controller is introduced and then by changing the cost function, NGMV controller is defined as an extended version of the linear cases. The cost function is used in the simplest form and can be easily extended to the general case. Simulation results show the effectiveness of the proposed non-linear method.     

Coordinate frame free Dubins vehicle circumnavigation using only range‐based measurements

The paper presents a feedback control design that allows a Dubins vehicle to enter a circular trajectory using only range‐based measurements from the vehicle to the center of the trajectory. The controller is derived and analyzed based on a novel state space kinematic model, with the state that is composed of two continuous and one discrete state variables.The evolution of the discrete state variable is not completely defined by the model and the control design has to deal with the ambiguity of this value. Based on the conditions that need to be satisfied for the controller to work, the closed loop dynamics analysis can be performed based on 2D phase portraits, and it can be shown that the controller can work in the case of the bounded turning rate of the vehicle. The conditions define only bounds for the controller parameters and not their specific values. Therefore, the parameters can be selected based on the maximal working range of the controller and linear quadratic regulator design. The proposed control design is illustrated by 2D phase portraits and simulations describing the control implementation, which is based only on range measurements. Copyright © 2016 John Wiley & Sons, Ltd.     

Servo controller design using neural networks

The dynamics of a physical plant may be difficult to express as concise mathematical equations. In practice there exist uncertainties that cannot be modeled with the system equations. Hence, robustness against system uncertainties is essential in a control system design. In this article, multilayered neural networks (MNNs) are used to compensate for model uncertainties of a dynamical system. Neural network models are used along with a classical linear servo controller derived from the linear state space equations. These models are trained so that system uncertainties are compensated. The design of a servo system indicates the enhanced performance of the neural-network-based servo controller as compared to the classical servo controller.     

Robust and nonfragile consensus of positive multiagent systems via observer‐based output‐feedback protocols

This article investigates the consensus problem for positive multiagent systems via an observer‐based dynamic output‐feedback protocol. The dynamics of the agents are modeled by linear positive systems and the communication topology of the agents is expressed by an undirected connected graph. For the consensus problem, the nominal case is studied under the semidefinite programming framework while the robust and nonfragile cases are investigated under the linear programming framework. It is required that the distributed state‐feedback controller and observer gains should be structured to preserve the positivity of multiagent systems. Necessary and/or sufficient conditions for the analysis of consensus are obtained by using positive systems theory and graph theory. For the nominal case, necessary and sufficient conditions for the codesign of state‐feedback controller and observer of consensus are derived in terms of matrix inequalities. Sufficient conditions for the robust and nonfragile consensus designs are derived and the codesign of state‐feedback controller and observer can be obtained in terms of solving a set of linear programs. Numerical simulations are provided to show the effectiveness and applicability of the theoretical results and algorithms.     

Robust nonlinear control of atomic force microscope via immersion and invariance

This paper reports an immersion and invariance (I&I)–based robust nonlinear controller for atomic force microscope (AFM) applications. The AFM dynamics is prone to chaos, which, in practice, leads to performance degradation and inaccurate measurements. Therefore, we design a nonlinear tracking controller that stabilizes the AFM dynamics around a desired periodic orbit. To this end, in the tracking error state space, we define a target invariant manifold, on which the system dynamics fulfills the control objective. First, considering a nominal case with full state measurement and no modeling uncertainty, we design an I&I controller to render the target manifold exponentially attractive. Next, we consider an uncertain AFM dynamics, in which only the displacement of the probe cantilever is measured. In the framework of the I&I method, we recast the robust output feedback control problem as the immersion of the output feedback closed‐loop system into the nominal full state one. For this purpose, we define another target invariant manifold that recovers the performance of the nominal control system. Moreover, to handle large uncertainty/disturbances, we incorporate the method of active disturbance rejection into the I&I output feedback control. Through Lyapunov‐based analysis of the closed‐loop stability and robustness, we show the semiglobal practical stability and convergence of the tracking error dynamics. Finally, we present a set of detailed, comparative software simulations to assess the effectiveness of the control method.     

Adaptive Linear Quadratic Regulator for Continuous-Time Systems With Uncertain Dynamics

In this paper, adaptive linear quadratic regulator (LQR) is proposed for continuous-time systems with uncertain dynamics. The dynamic state-feedback controller uses input-output data along the system trajectory to continuously adapt and converge to the optimal controller. The result differs from previous results in that the adaptive optimal controller is designed without the knowledge of the system dynamics and an initial stabilizing policy. Further, the controller is updated continuously using input-output data, as opposed to the commonly used switched/intermittent updates which can potentially lead to stability issues. An online state derivative estimator facilitates the design of a model-free controller. Gradient-based update laws are developed for online estimation of the optimal gain. Uniform exponential stability of the closed-loop system is established using the Lyapunov-based analysis, and a simulation example is provided to validate the theoretical contribution.      

Electrical energy quality: Modeling and H<Superscript>∞</Superscript> control of a three-phase shunt active filter

The main contribution of the paper is the modeling approach used to describe a pure threephase shunt active filter, and the application of the H^∞ control design tool in order to improve the quality of electrical energy. Advanced power electronics devices have widely contributed to the degradation of power quality due to the injection of non-sinusoïdal currents into the utility system. Therefore, it is essential to use an active compensator which can attenuate current harmonics to an acceptable level on the line side of the power source. In this work, a three-phase active filter connected in parallel to a supply system feeding a non-linear load is described, in a complex framework, by a linear multivariable state space representation in order to guarantee that the system is mathematically decoupled and therefore to simplify the controller design. This representation includes a sensor to measure perturbations, and allows one to calculate a linear robust control law. The originality of this paper is that a Linear Matrix Inequality based H^∞ synthesis is performed to design a static state feedback controller with complex-valued parameters. The robustness of this controller with respect to network impedance uncertainties is investigated. Moreover, simulation and experimental results are given to reveal the effectiveness of the synthesized control law.     

Functional observer-based sliding mode control for linear discrete-time-delayed stochastic systems

Functional observers are the primary solution to sundry estimation problems, wherein full- or reduced-order observer cannot be directly applied. This paper presents a functional observer-based sliding mode control method for the linear discrete-time delayed stochastic system. Stability analysis of sliding function is presented for the delayed stochastic system with a linear matrix inequality approach. The functional observer method for the linear discrete-time-delayed stochastic system is proposed based on the Kronecker product approach. Sliding mode controller is estimated using the functional observer method. Finally, to demonstrate the efficacy of the proposed design, comparison of its performance with some of the well-known existing state feedback controller is presented.     

DoS干扰攻击下的信息物理系统状态反馈稳定

基于网络的工业控制系统作为信息物理系统(CPSs)的一种重要应用正迅猛发展.然而,近年来针对工业控制系统的恶意网络攻击引起了人们对CPS安全问题的广泛关注.拒绝服务(DoS)干扰攻击作为CPS中最容易发生的攻击方式得到了深入研究.对此,提出一种能量受限的、周期的DoS干扰攻击模型,攻击的目的是增大无线信道发生数据包随机丢包的概率.基于一类CPS简化模型,考虑CPS中传感器与控制器(S-C)之间无线信道同时存在DoS干扰攻击和固有随机数据包丢失的情况,采用状态反馈,基于随机Lyapunov函数和线性矩阵不等式方法得到可以保证系统稳定的充分条件,并利用系统稳定的充分条件和锥补线性化算法设计控制器.最后,通过两个数值仿真例子验证所提出控制策略的有效性.     

Asynchronous H ∞ Control for Positive Discrete-time Markovian Jump Systems

This paper deals with the asynchronous H∞ control for discrete-time positive Markovian jump systems (PMJSs). In previous results about PMJSs, asynchronous behaviors are always overlooked and the designed controller is based on the synchronization between the system modes and controller modes. Sufficient conditions for stochastic stability are proposed by the use of Lyapunov-Krasovskii functional. The asynchronous controller is designed to ensure the closed-loop system stochastically stable with a prescribed H∞ performance index. All the conditions are given in linear matrix inequality framework. Finally, a pest’s age-structured population dynamic model is illustrated to show the validity of the present design.     

带马尔科夫跳的模态相关时变时滞随机系统的状态反馈控制器设计

针对带马尔科夫跳的模态相关时变时滞系统得到了一个改进的均方指数稳定结果并设计了状态反馈控制器. 首先, 通过构造一个改进的Lyapunov-Krasovskii泛函, 以线性矩阵不等式的形式给出一个均方指数稳定性条件; 这里, 衰减率可以是一个在区间内取值的有限常数, 同时, 时变时滞的导数上界不要求小于1; 基于得到的稳定性条件, 设计了状态反馈的控制器. 最后, 通过两个仿真算例验证了所得理论的结果的有效性, 并与已有结果相比较, 保守性较弱.     

Static and output-feedback of discrete-time LTI systems with state multiplicative noise

A parameter dependent approach for designing static output-feedback controller for linear time-invariant systems with state-multiplicative noise is introduced which achieves a minimum bound on either the stochastic H₂ or the H_∞ performance levels. A solution is obtained also for the case where, in addition to the stochastic parameters, the system matrices reside in a given polytope. In this case, a parameter dependent Lyapunov function is described which enables the derivation of the required constant feedback gain via a solution of a set of linear matrix inequalities that correspond to the vertices of the uncertainty polytope.The stochastic parameters appear in both the dynamics and the input matrices of the state space model of the system. The problems are solved using the expected value of the standard performance indices over the stochastic parameters. The theory developed is demonstrated by a simple example.     

Decentralized overlapping control of a formation of unmanned aerial vehicles

Decentralized overlapping feedback laws are designed for a formation of unmanned aerial vehicles. The dynamic model of the formation with an information structure constraint in which each vehicle, except the leader, only detects the vehicle directly in front of it, is treated as an interconnected system with overlapping subsystems. Using the mathematical framework of the inclusion principle, the interconnected system is expanded into a higher dimensional space in which the subsystems appear to be disjoint. Then, at each subsystem, a static state feedback controller is designed to robustly stabilize the perturbed nominal dynamics of the subsystem. The design procedure is based on the application of convex optimization tools involving linear matrix inequalities. As a final step, the decentralized controllers are contracted back to the original interconnected system for implementation.