Asymptotic Stability and Finite‐Time Stability of Networked Control Systems: Analysis and Synthesis

This paper focuses on the problems of asymptotic stability and finite‐time stability (FTS) analysis, along with the state feedback controller design for networked control systems (NCSs) with consideration of both network‐induced delay and packet dropout. The closed‐loop NCS is modeled as a discrete‐time linear system with a time‐varying, bounded state delay. Sufficient conditions for the asymptotic stability and the FTS of the closed‐loop NCS are provided, respectively. Based on the stability analysis results, a mixed controller design method, which guarantees the asymptotic stability of the closed‐loop NCS in the usual case and the FTS of the closed‐loop NCS in the unusual case (that is, in some particular time intervals, large state delay occurs), is presented. A numerical example is provided to illustrate the effectiveness of the proposed mixed controller design method.     

Global stabilizability of an anaerobic biodegradation process via piecewise constant feedback

We consider a nonlinear model of an anaerobic digestion process with methane production. We propose a stabilizing control law involving piecewise constant feedback and study the asymptotic stability of the obtained closed‐loop system. An extremum seeking algorithm is applied to maximize the output. Numerical simulation results are also presented to illustrate the theoretical investigations.     

On the addition of integral action to port-controlled Hamiltonian systems

A technique that provides closed loop integral action depending on the passive outputs of port-controlled Hamiltonian systems is already available. This paper addresses a new method that allows us to add integral action also on system variables having relative degree higher than one, while still preserving the Hamiltonian form and, thus, closed loop stability. The new approach is applied to design speed regulation controllers for the permanent magnet synchronous motor. Closed loop stability and asymptotic rejection of unknown piecewise constant load torques are formally proved. This theoretically predicted control system performance is illustrated via simulation experiments, which also show that the properties hold under parameter uncertainties. This is in line with the usual practice of including integral action in a controller with the aim of improving its closed loop robustness. The fact that the method enhances the range of possible integral actions in the controller, enriched with this robustness property, allows us to assess it as a practically important complement to the well-known interconnection and damping assignment techniques developed in the framework of port-controlled Hamiltonian systems.     

Model reference adaptive control of discrete‐time piecewise linear systems

This article presents a switched model reference adaptive controller for discrete‐time piecewise linear systems. In the spirit of the work by Landau in the late seventies, proof of asymptotic stability of the closed‐loop error system is obtained, recasting its dynamics as a feedback system and showing the feedforward and the feedback paths are both passive. The challenge is that both paths can be piecewise linear. Numerical results show excellent performance of the proposed controller even in the face of sudden variations of the plant parameters. Copyright © 2012 John Wiley & Sons, Ltd.     

Robust Constrained Model Predictive Control for Discrete‐Time Uncertain System in Takagi‐Sugeno's Form

In this paper, we investigate a robust constrained model predictive control synthesis approach for discrete‐time Takagi‐Sugeno's (T‐S) fuzzy system with structured uncertainty. The key idea is to determine, at each sampling time, a state feedback fuzzy predictive controller that minimizes the performance objective function in the infinite time horizon by solving a class of linear matrix inequalities (LMIs) optimization problem. To do this, the fuzzy predictive controller is designed on the basis of non‐parallel distributed compensation (non‐PDC) control law, relaxed stability conditions of the closed‐loop fuzzy system are developed by employing an extended nonquadratic Lyapunov function and introducing additional slack and collection matrices. In addition, the presented approach is capable of ensuring the robust asymptotic stability as well as the recursive feasibility of the closed‐loop fuzzy system. Simulations on a highly nonlinear continuous stirred tank reactor (CSTR) are eventually presented to demonstrate the effectiveness of the developed theoretical approach.     

A closed‐loop nonlinear control and sliding mode estimation strategy for fluid flow regulation

Novel sliding mode observer (SMO) and robust nonlinear control methods are presented, which are shown to achieve finite‐time state estimation and asymptotic regulation of a fluid flow system. To facilitate the design and analysis of the closed‐loop active flow control (AFC) system, proper orthogonal decomposition–based model order reduction is utilized to express the Navier‐Stokes partial differential equations as a set of nonlinear ordinary differential equations. The resulting reduced‐order model contains a measurement equation that is in a nonstandard mathematical form. This challenge is mitigated through the detailed design and analysis of an SMO. The observer is shown to achieve finite‐time estimation of the unmeasurable states of the reduced‐order model using direct sensor measurements of the flow field velocity. The estimated states are utilized as feedback measurements in a closed‐loop AFC system. To address the practical challenge of actuator bandwidth limitations, the control law is designed to be continuous. A rigorous Lyapunov‐based stability analysis is presented to prove that the closed‐loop flow estimation and control method achieves asymptotic regulation of a fluid flow field to a prescribed state. Numerical simulation results are also provided to demonstrate the performance of the proposed closed‐loop AFC system, comparing 2 different designs for the SMO.     

Adaptive Nonlinear Control of Wind Energy Conversion System Involving Induction Generator

This paper presents a theoretical framework for adaptive control of a wind energy conversion system (WECS), involving a squirrel cage induction generator (SIG) connected with an AC/DC/AC IGBT‐based PWM converter. A multi‐loop nonlinear controller is designed to meet two main control objectives, i.e., (i) speed reference optimization in order to extract a maximum wind energy whatever the wind speed, and (ii) power factor correction (PFC) to avoid net harmonic pollution. These objectives must be achieved despite the mechanical parameters uncertainty. First, a nonlinear model of the whole controlled system is developed within the Park coordinates. Then, a multi‐loop nonlinear controller is synthesized using the adaptive backstepping design. A formal analysis based on Lyapunov stability is carried out to describe the control system performances. In addition to closed‐loop global asymptotic stability, it is proven that all control objectives (induction generator speed tracking, rotor flux regulation, DC link voltage regulation and unitary power factor) are asymptotically achieved.     

Necessary and Sufficient Stability Criterion and Stabilization for Positive 2‐D Continuous‐Time Systems with Multiple Delays

This paper addresses the stability and control problem of the linear positive two‐dimensional (2‐D) continuous‐time systems in Roesser model with multiple time delays. The contribution lies in two aspects. First, a simple novel proof is provided to establish necessary and sufficient conditions of asymptotic stability for 2‐D continuous delayed systems. It turns out that the magnitude of delays has no any impact on the stability of these systems, which is completely determined by the system matrices. Second, a necessary and sufficient condition for the existence of state‐feedback controllers is proposed for general delayed 2‐D systems, which ensures the non‐negativity and the stability of the resulting closed‐loop systems. Two examples are given to validate the proposed methods.     

Sampled‐data control of networked nonlinear systems with variable delays and drops

This paper investigates the stabilization problem of the nonlinear networked control systems (NCSs) with drops and variable delays. The NCS is modeled as a sampled‐data system. For such a sampled‐data NCS, the stability properties are studied for delay that can be both shorter and longer than one sampling period, respectively. The exponential stability conditions are derived in terms of the parameters of the plant and time delay. On the other hand, a model‐based control scheme based on an approximate discrete‐time model of the plant is presented to guarantee the stability of the closed‐loop system subject to variable time delays and packet losses. The performance of the proposed control schemes are examined through numerical simulations of an automated rendezvous and docking of spacecraft system. Moreover, the simulations show that by employing the model‐based controller, a higher closed‐loop control performance can be achieved. Copyright © 2013 John Wiley & Sons, Ltd.     

High‐order mismatched disturbance rejection control for small‐scale unmanned helicopter via continuous nonsingular terminal sliding‐mode approach

In this paper, the problem of finite‐time control for small‐scale unmanned helicopter system with high‐order mismatched disturbance is investigated via continuous nonsingular terminal sliding‐mode control approach. The key idea is to design a novel nonlinear dynamic sliding‐mode surface based on finite‐time disturbance observer. Then, the finite‐time convergence and chattering attenuation capability is guaranteed by the continuous nonsingular terminal sliding‐mode control law. Additionally, rigorous finite‐time stability analysis for the closed‐loop helicopter system is given by means of the Lyapunov theory. Finally, some simulation results demonstrate the effectiveness and predominant properties of the proposed control method for the small‐scale unmanned helicopter even in the presence of high‐order mismatched disturbance.     

Approaches to robust ℋ︁∞ static output feedback control of discrete‐time piecewise‐affine systems with norm‐bounded uncertainties

This paper investigates the problem of robust ??_∞ static output feedback controller design for a class of discrete‐time piecewise‐affine systems with norm‐bounded time‐varying parametric uncertainties. The objective is to design a piecewise‐linear static output feedback controller guaranteeing the asymptotic stability of the resulting closed‐loop system with a prescribed ??_∞ disturbance attenuation level. Based on a piecewise Lyapunov function combined with S‐procedure, Projection lemma, and some matrix inequality convexifying techniques, several novel approaches to the static output feedback controller analysis and synthesis are developed for the underlying piecewise‐affine systems. It is shown that the controller gains can be obtained by solving a set of strict linear matrix inequalities (LMIs) or a family of LMIs parameterized by one or two scalar variables, which are numerically efficient with commercially available software. Finally, three simulation examples are provided to illustrate the effectiveness of the proposed approaches. Copyright © 2010 John Wiley & Sons, Ltd.     

DIRECT ADAPTIVE CONTROL FOR NONLINEAR MATRIX SECOND‐ORDER SYSTEMS WITH TIME‐VARYING AND SIGN‐INDEFINITE DAMPING AND STIFFNESS OPERATORS

A direct adaptive control framework for a class of nonlinear matrix second‐order systems with time‐varying and sign‐indefinite damping and stiffness operators is developed. The proposed framework guarantees global asymptotic stability of the closed‐loop system states associated with the plant dynamics without requiring any knowledge of the system nonlinearities other than the assumption that they are continuous and bounded. The proposed adaptive control approach is used to design adaptive controllers for suppressing thermoacoustic oscillations in combustion chambers.     

Event‐Based Consensus Controller for Linear Multi‐Agent Systems Over Directed Communication Topologies: A Co‐Design Approach

The paper addresses the distributed event‐triggered consensus problem in directed topologies for multi‐agent systems (MAS) with general linear dynamic agents. A co‐design approach is proposed to determine parameters of the consensus controller and its event‐triggered mechanism (ETM), simultaneously. This approach guarantees asymptotic stability along with decreasing data transmission among agents. In the proposed event‐based consensus controller, each agent broadcasts data to the neighbors only at its own triggering instants; this differs from previous studies in which continuous data streams among agents were required. Furthermore, the proposed control law is based on the piecewise constant functions of the measurement values, which are updated at triggering instants. In this case the control scheme decreases the communication network usage, energy consumption, and wear of the actuator. As a result, it facilitates distributed implementation of the proposed consensus controller for real‐world applications. A theorem is proved to outline sufficient conditions to guarantee the asymptotic stability of the closed‐loop system with the event‐based consensus controller. Another theorem is also proved to show the Zeno behavior exclusion. As a case study, the proposed event‐based controller is applied for a diving consensus problem to illustrate the effectiveness of the method.     

Adaptive Control of Piecewise Linear Systems with State Feedback for Output Tracking

A piecewise linear system consists of a set of linear time‐invariant (LTI) subsystems, with a switching sequence specifying an active subsystem at each time instant. This paper studies the adaptive control problem of single‐input, single‐output (SISO) piecewise linear systems. By employing the knowledge of the time instant indicator functions of system parameter switches, a new controller structure parametrization is proposed for the development of a stable adaptive control scheme with reduced modeling error in the estimation error signal used for parameter adaptive laws. This key feature is achieved by the new control scheme's ability to avoid a major parameter swapping term in the error model, with the help of indicator functions whose knowledge is available in many applications. A direct state feedback model reference adaptive control (MRAC) scheme is presented for such systems to achieve closed‐loop signal boundedness and small output tracking error in the mean square sense, under the usual slow system parameter switching condition. Simulation results on linearized NASA GTM models are presented to demonstrate the effectiveness of the proposed scheme.     

脉宽调制控制系统的适定性

不连续动态系统的适定性(即解的唯一存在性)问题是混合系统研究的基本问题之一.脉 宽调制控制系统可以表示成具有时变仿射不等式约束的分段仿射系统.该文首先在Carathéodory 的解定义下导出了脉宽调制控制系统无滑模和跳跃的解的适定性的充分必要条件.然后利用该 结果对PWM型DC-DC降压变换器的适定性的研究表明当载波信号h(t)=O时闭环PWM DC-DC 变换器总是不适定的,当载波信号h(t)的参数和比例控制器的参数满足一定的条件时，比例 控制的闭环PWM DC-DC变换器是适定的.     

非均质Euler-bernoulli梁的局部反馈定问题

In this article, we study the locally distributed feedback stabilization problem of a nonuniform Euler-Bernoulli beam. Firstly, using the semi-group theory, we establish the well-posedness of the associated closed loop system. Then by proving the uniqueness of the solution to a related ordinary differential equation, we derive the asymptotic stability of the closed loop system. Finally, by means of the piecewise multiplier method, we prove that, by either one distributed force feedback or a distributed moment feedback control, the closed loop system can be exponentially stabilized.     

An augmented system approach to static output‐feedback stabilization with ℋ︁∞ performance for continuous‐time plants

This paper revisits the static output‐feedback stabilization problem of continuous‐time linear systems from a novel perspective. The closed‐loop system is represented in an augmented form, which facilitates the parametrization of the controller matrix. Then, new equivalent characterizations on stability and ??_∞ performance of the closed‐loop system are established in terms of matrix inequalities. On the basis of these characterizations, a necessary and sufficient condition with slack matrices for output‐feedback stabilizability is proposed, and an iteration algorithm is given to solve the condition. An extension to output‐feedback ??_∞ control is provided as well. The effectiveness and merits of the proposed approach are shown through several examples. Copyright © 2008 John Wiley & Sons, Ltd.     

Locally Distributed Feedback Stabilization of Nonuniform Euler-Bernoulli Beam

In this article,we study the locally distributed feedback stabilization problem of a nonuniform Euler-Bernoulli beam.Firstly,using the semi-group theory,we establish the well- posedness of the associated closed loop system.Then by proving the uniqueness of the solution to a related ordinary differential equation,we derive the asymptotic stability of the closed loop sys- tem.Finally,by means of the piecewise multiplier method,we prove that,by either one distributed force feedback or a distributed moment feedback control,the closed loop system can be exponentially stabilized.     

FLEXIBLE SPACECRAFT VIBRATION SUPPRESSION USING PWPF MODULATED INPUT COMPONENT COMMAND AND SLIDING MODE CONTROL

This paper presents a dual‐stage control system design method for the rotational maneuver and vibration stabilization of a spacecraft with flexible appendages. In this design approach, attitude control system and vibration suppression were designed separately using lower order model. The design of attitude controller was based on sliding mode control (SMC) theory leading to a discontinuous control law. This controller accomplishes asymptotic attitude maneuvering in the closed‐loop system and is insensitive to the interaction of elastic modes and uncertainty in the system. The shaped command input controller based on component synthesis vibration suppression (CSVS) method is designed for reduction of flexible mode vibration, which only requires information about natural frequency and damping of the closed system. Additionally, to extend the CSVS method to the system with on‐off actuators, pulse‐width pulse‐frequency (PWPF) modulation is employed to control the thruster firing and integrated with the CSVS method. Simulation results have been proven the potential of this technique to control flexible spacecraft.     

On estimation of the domain of attraction for sliding mode control of underactuated nonlinear systems

A system is considered underactuated if the number of the actuator inputs is less than the number of degrees of freedom for the system. Sliding mode control for underactuated systems has been shown to be an effective way to achieve system stabilization. It involves exponentially stable sliding surfaces so that when the closed‐loop system trajectory reaches the surface, it moves along the surface while converging to the origin. In this paper, a general framework that provides sufficient conditions for asymptotic stabilization of underactuated nonlinear systems using sliding mode control in the presence of system uncertainties is presented. Specifically, it is shown that the closed‐loop system trajectories reach the sliding surface in finite time, and a constructive methodology to determine exponential stability of the closed‐loop system on the sliding surface is developed, which ensures asymptotic stability of the overall closed‐loop system. Furthermore, the aforementioned framework provides the basis to determine an estimate of the domain of attraction for the closed‐loop system with uncertainties. Finally, the results developed in the paper are experimentally validated using a linear inverted pendulum testbed to show a good match between the actual domain of attraction of the upward equilibrium state of the pendulum and its analytical estimate.Copyright © 2012 John Wiley & Sons, Ltd.