Robust semiglobal swarm tracking of coupled harmonic oscillators with input saturation and external disturbance

The robust semiglobal swarm tracking problem of N coupled harmonic oscillators and 1 actual leader with input saturation and external disturbance on a directed communication topology is considered, in which the N coupled harmonic oscillators are referred to followers. First, the low‐and‐high gain feedback technique is introduced to construct a relative state‐dependent control algorithm. Then, an observer‐based control algorithm is designed based on the low‐and‐high gain feedback technique and the high‐gain observer design methodology. Sufficient conditions are derived to guarantee robust semiglobal swarm tracking for state‐feedback control and output‐feedback control, respectively. Numerical simulations are finally provided to verify the theoretic results.     

Time‐varying input delay compensation for nonlinear systems with additive disturbance: An output feedback approach

This paper addresses the output feedback tracking control of a class of multiple‐input and multiple‐output nonlinear systems subject to time‐varying input delay and additive bounded disturbances. Based on the backstepping design approach, an output feedback robust controller is proposed by integrating an extended state observer and a novel robust controller, which uses a desired trajectory‐based feedforward term to achieve an improved model compensation and a robust delay compensation feedback term based on the finite integral of the past control values to compensate for the time‐varying input delay. The extended state observer can simultaneously estimate the unmeasurable system states and the additive disturbances only with the output measurement and delayed control input. The proposed controller theoretically guarantees prescribed transient performance and steady‐state tracking accuracy in spite of the presence of time‐varying input delay and additive bounded disturbances based on Lyapunov stability analysis by using a Lyapunov‐Krasovskii functional. A specific study on a 2‐link robot manipulator is performed; based on the system model and the proposed design procedure, a suitable controller is developed, and comparative simulation results are obtained to demonstrate the effectiveness of the developed control scheme.     

Optimality of robust disturbance‐feedback strategies

In this paper, robust disturbance‐feedback strategies for finite time‐horizon problems are studied. Linear discrete‐time systems subject to linear control, state constraints, and quadratic objective functions are considered. In addition, persistent disturbances, which enter the system additively and are contained in a polytopic set, act on the system. The synthesis of robust strategies leads in the case of the traditional robust state‐feedback and open‐loop min–max strategies to, respectively, nonconvex problems or conservatism. However, robust disturbance‐feedback problems can easily be reformulated as convex problems and solved by tractable linear matrix inequalities. Hence this approach bypasses the nonconvexity issue while maintaining the advantages of feedback strategies. As a key result, it is shown that both sources of conservatism attributed to this approach, namely, the relaxation method and the affine parametrization, can be removed at the expense of an increase in computational effort. Copyright © 2015 John Wiley & Sons, Ltd.     

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 consensus tracking for a class of high‐order multi‐agent systems

In this paper, we study the robust consensus tracking problem for a class of high‐order multi‐agent systems with unmodelled dynamics and unknown disturbances. A continuous robust state feedback control algorithm is proposed to enable the agents to achieve robust consensus tracking of a desired trajectory. By utilizing Lyapunov analysis methods and an invariance‐like theorem, sufficient conditions for semi‐global asymptotic consensus tracking are established. A robust output feedback control algorithm is designed to obtain a uniformly ultimately bounded consensus tracking result. Numerical simulations are provided to show the effectiveness of the proposed algorithms. Copyright © 2015 John Wiley & Sons, Ltd.     

Synthesis of Mixed Objective Output Feedback Robust Model Predictive Control

Aiming at the constrained polytopic uncertain system with energy‐bounded disturbance and unmeasurable states, a novel synthesis scheme to design the output feedback robust model predictive control(MPC)is put forward by using mixed H₂/H_∞ design approach. The proposed scheme involves an offline design of a robust state observer using linear matrix inequalities(LMIs)and an online output feedback robust MPC algorithm using the estimated states in which the desired mixed objective robust output feedback controllers are cast into efficiently tractable LMI‐based convex optimization problems. In addition, the closed‐loop stability and the recursive feasibility of the proposed robust MPC are guaranteed through an appropriate reformulation of the estimation error bound (EEB). A numerical example subject to input constraints illustrates the effectiveness of the proposed controller.     

Improved robust stability criteria and design of robust stabilizing controller for uncertain linear time‐delay systems

In this paper, an improved linear matrix inequality (LMI)‐based robust delay‐dependent stability test is introduced to ensure a larger upper bound for time‐varying delays affecting the state vector of an uncertain continuous‐time system with norm‐bounded‐type uncertainties. A quasi‐full‐size Lyapunov–Krasovskii functional is chosen and free‐weighting matrix approach is employed. Less restrictive sufficient conditions are derived for robust stability of time‐varying delay systems with norm‐bounded‐type uncertainties. Moreover, the investigation of the stabilization problem with memoryless state‐feedback control is presented such that the stabilizability criteria are obtained in terms of matrix inequalities, which can be solved via utilizing a cone complementarity minimization algorithm. Finally, the problem of output feedback stabilization for square systems is also taken into consideration. The output feedback stabilizability criteria are derived in the form of linear matrix inequalities, which are convex and can be easily solved using interior point algorithms. A plenty of numerical examples are presented indicating that the proposed stability and stabilization methods effectively improve the existing results. Copyright © 2006 John Wiley & Sons, Ltd.     

Robust H∞ control for uncertain discrete‐time stochastic bilinear systems with Markovian switching

This paper is concerned with the problems of robust stochastic stabilization and robust H_∞ control for uncertain discrete‐time stochastic bilinear systems with Markovian switching. The parameter uncertainties are time‐varying norm‐bounded. For the robust stochastic stabilization problem, the purpose is the design of a state feedback controller which ensures the robust stochastic stability of the closed‐loop system irrespective of all admissible parameter uncertainties; while for the robust H_∞ control problem, in addition to the robust stochastic stability requirement, a prescribed level of disturbance attenuation is required to be achieved. Sufficient conditions for the solvability of these problems are obtained in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, explicit expressions of the desired state feedback controllers are also given. An illustrative example is provided to show the effectiveness of the proposed approach. Copyright © 2005 John Wiley & Sons, Ltd.     

基于卡尔曼滤波的液压主动悬架控制研究

汽车的液压主动悬架系统在控制过程中不可避免的受到噪声的影响。应用卡尔曼滤波对系统的状态向量做最优估计,并应用到系统的全状态反馈控制中,可以有效的提高系统的鲁棒性。文章给出了卡尔曼滤波的应用条件,对单一LQR调节器系统和基于LQG理论的调节器系统做了仿真对比。在LQR调节器系统中前置卡尔曼滤波,能得到更好的振动控制效果。     

Switched state feedback for uncertain continuous‐time systems with interval delays

The objective of this paper is to design a switched robust control for a class of continuous‐time systems subject to linear fractional uncertainty and interval time delays. The controller is based on state feedback and the LMI‐based stability conditions are derived using an improved Lyapunov–Krasovskii functional. Moreover, the switching rule as well as the state feedback gains are determined from the minimization of a guaranteed cost function. The theoretical results are illustrated with a numerical example. Copyright © 2010 John Wiley & Sons, Ltd.     

Robust Stability and Stabilization of Positive Interval Systems Subject to Actuator Saturation

This paper addresses the stabilization problem for a class of uncertain positive linear systems (PLSs) in the presence of saturating actuators. The objective is to obtain sufficient conditions for the robust stability of PLSs and to design robust state feedback control laws such that the closed‐loop uncertain system is asymptotically stable and positive at the origin with a large domain of attraction. Several sufficient conditions for robust stabilization and positivity are derived via the Lyapunov function approach and convex analysis method for both the discrete‐time and the continuous‐time cases, respectively. The state feedback controller design and the estimation of the domain of attraction are presented by solving a convex optimization problem with linear matrix inequalities (LMIs) constraints. A numerical example is given to show the effectiveness of the proposed methods.     

A modified dynamic surface approach for control of nonlinear systems with unknown input dead zone

This paper focuses on the robust output precise tracking control problem of uncertain nonlinear systems in pure‐feedback form with unknown input dead zone. By designing an extended state observer, the states unmeasurable problem in traditional feedback control is solved, and the lumped uncertainty, which is caused by system unknown functions and input dead zone, is estimated. In order to apply separation principle, finite‐time extended state observer is designed to obtain system states and estimate the lumped uncertainty. Then, by introducing tracking differentiator, a modified dynamic surface control approach is developed to eliminate the ‘explosion of complexity’ problem and guarantee the tracking performance of system output. Because tracking differentiator is a fast precise signal filter, the closed‐loop control performance is significantly improved when it is used in dynamic surface control instead of first‐order filters. The L _∞ stability of the whole closed‐loop system, which guarantees both the transient and steady‐state performance, is shown by the Lyapunov method and initialization technique. Numerical and experiment examples are performed to illustrate our proposed control scheme with satisfactory results. Copyright © 2013 John Wiley & Sons, Ltd.     

Robust control and fault detection for continuous‐time switched systems subject to a dwell time constraint

This paper is concerned with the simultaneous robust control and fault detection problem for continuous‐time switched systems subject to a dwell time constraint. To meet the control and detection objectives under the constraint, the controller/detectors matching different time intervals are first constructed in an output feedback framework. A state‐dependent switching law that obeys the dwell time constraint is then designed such that the closed‐loop switched system is asymptotically stable and also with the robust and detection performance. Further, the proposed switching law is dependent only on the partial measurable states of the closed‐loop system, which is applicable when the states of system mode are fully unavailable. Thus, our result extends the existing ones in state‐dependent switching and state‐feedback frameworks. Finally, a numerical example is given to illustrate the effectiveness of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.     

Linear quadratic networked control of uncertain polytopic systems

This paper investigates the problem of designing robust linear quadratic regulators for uncertain polytopic continuous‐time systems over networks subject to delays. The main contribution is to provide a procedure to determine a discrete‐time representation of the weighting matrices associated to the quadratic criterion and an accurate discretized model, in such a way that a robust state feedback gain computed in the discrete‐time domain assures a guaranteed quadratic cost to the closed‐loop continuous‐time system. The obtained discretized model has matrices with polynomial dependence on the uncertain parameters and an additive norm‐bounded term representing the approximation residual error. A strategy based on linear matrix inequality relaxations is proposed to synthesize, in the discrete‐time domain, a digital robust state feedback control law that stabilizes the original continuous‐time system assuring an upper bound to the quadratic cost of the closed‐loop system. The applicability of the proposed design method is illustrated through a numerical experiment. Copyright © 2015 John Wiley & Sons, Ltd.     

Robust output regulation of linear time‐delay systems: A state predictor approach

This paper considers the robust output regulation problem for linear systems in the presence of state, input, and output delays. First, a state feedback control law is constructed from a state predictor, recently developed for systems with state and input delays. Necessary and sufficient conditions for the existence of a solution to the regulator equations are presented. Next, an error feedback control law for the output regulation problem is constructed by means of an error‐based state predictor. Finally, the proposed error feedback solution is extended to solve the output regulation problem in the presence of model uncertainty. Numerical examples demonstrate the effectiveness of the proposed predictor‐based solutions. Copyright © 2015 John Wiley & Sons, Ltd.     

Adaptive tracking and asymptotic rejection of unknown but bounded disturbances in nonlinear MIMO systems

The goal of this paper is global disturbance rejection in nonlinear systems. An output feedback controller with disturbance rejection is developed for a class of nonlinear multi input-multi output (MIMO) systems. The availability of state variables and the bound of disturbances are not required to be known in advance and reference tracking will is guaranteed. By the aid of designing an adaptive observer, a robust adaptive nonlinear state feedback controller using the estimated states is proposed. For tracking problem, an adaptive pre-compensator is used. The control methodology is robust against both constant and time varying bounded disturbances, maintaining effective performance. The adaptive laws are derived based on the Lyapunov synthesis method, therefore closed-loop asymptotic stability is also guaranteed. Moreover, for chattering reduction we use a low-pass filter. Consequently, small gain theorem is adopted to prove the stability of the closed-loop system. Simulation results are employed to illustrate the effectiveness of the proposed controller.     

GLOBAL ROBUST SERVOMECHANISM OF A CLASS OF NONLINEAR SYSTEMS USING OUTPUT FEEDBACK

The robust servomechanism problem (alternatively, output regulation problem) of the class of nonlinear systems in lower triangular form has been extensively studied in recent years. The semi‐global solution was first given by either state feedback or output feedback. The global solution by state feedback was given very recently. However, the global solution by output feedback has long been an open problem. In this paper, we present a set of solvability conditions of the global robust servomechanism problem for this class of nonlinear systems by output feedback.     

ROBUST CONTROL FOR A CLASS OF UNCERTAIN STATE‐DELAYED SINGULARLY PERTURBED SYSTEMS

This paper considers the problem of robust control for a class of uncertain state‐delayed singularly perturbed systems with norm‐bounded nonlinear uncertainties. The system under consideration involves state time‐delay and norm‐bounded nonlinear uncertainties in the slow state variable. It is shown that the state feedback gain matrices can be determined to guarantee the stability of the closed‐loop system for all ∞ ∞ (0, ∞00) and independently of the time‐delay. Based on this key result and some standard Riccati inequality approaches for robust control of singularly perturbed systems, a constructive design procedure is developed. We present an illustrative example to demonstrate the applicability of the proposed design approach.     

STABILIZATION AND H∞ CONTROL FOR UNCERTAIN STOCHASTIC TIME‐DELAY SYSTEMS VIA NON‐FRAGILE CONTROLLERS

This paper considers the problems of robust non‐fragile stochastic stabilization and H_∞ control for uncertain time‐delay stochastic systems with time‐varying norm‐bounded parameter uncertainties in both the state and input matrices. Attention is focused on the design of memoryless state feedback controllers which are subject to norm‐bounded uncertainties. For both the cases of additive and multiplicative controller uncertainties, delay‐independent sufficient conditions for the solvability of the above problems are obtained. The desired state feedback controller can be constructed by solving a certain linear matrix inequality.