Identification and robust control for systems with ellipsoidal parametric uncertainty by convex optimization

In this paper, sufficient conditions for robust output feedback controller design for systems with ellipsoidal parametric uncertainty are given in terms of solutions to a set of linear matrix inequalities (LMIs) Performance specifications are in terms of combined pole placement with sensitivity function shaping in the H₂ or H_∞ norm. Furthermore, an optimal input design technique for parameter estimation that is integrated into the robust control design is employed in this paper. This means that performance specifications on the closed‐loop transfer functions are translated into the requirements on the input signal spectrum. The simulation results show the effectiveness of the proposed method. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

A two‐degree‐of‐freedom ℋ︁∞ control design method for robust model matching

We propose an ??_∞ controller design method which achieves a closed‐loop transfer function equal or otherwise sensibly close to a desired transfer function, viz. a model reference design. The proposed controller design method inherits the model reference feature of the internal model control design method and incorporates the weighting scheme of the ??_∞ loop‐shaping. It utilizes Youla–Kucera parameterization in a two‐degree‐of‐freedom scheme to achieve robust model reference and high performance design while ensuring a sensible robust stability margin, and can be readily applied to the generic class of LTI systems (SISO, MIMO, stable, unstable). Copyright © 2006 John Wiley & Sons, Ltd.     

Robust FOPID controller design for fractional‐order delay systems using positive stability region analysis

In this paper, a robust fractional‐order PID (FOPID) controller design method for fractional‐order delay systems is proposed based on positive stability region (PSR) analysis. Firstly, the PSR is presented to improve the existing stability region (SR) in D‐decomposition method. Then, the optimal fractional orders λ and μ of FOPID controller are achieved at the biggest three‐dimensional PSR, which means the best robustness. Given the optimal λ and μ, the other FOPID controller parameters k_p, k_i, k_d can be solved under the control specifications, including gain crossover frequency, phase margin, and an extended flat phase constraint. In addition, the steps of the proposed robust FOPID controller design process are listed at length, and an example is given to illustrate the corresponding steps. At last, the control performances of the obtained robust FOPID controller are compared with some other controllers (PID and FOPI). The simulation results illustrate the superior robustness as well as the transient performance of the proposed control algorithm.     

Robust multiple model adaptive control: Modified using ν‐gap metric

A new robust adaptive control method is proposed, which removes the deficiencies of the classic robust multiple model adaptive control (RMMAC) using benefits of the ν‐gap metric. First, the classic RMMAC design procedure cannot be used for systematic design for unstable plants because it uses the Baram Proximity Measure, which cannot be calculated for open‐loop unstable plants. Next, the %FNARC method which is used as a systematic approach for subdividing the uncertainty set makes the RMMAC structure being always companion with the µ‐synthesis design method. Then in case of two or more uncertain parameters, the model set definition in the classic RMMAC is based on cumbersome ad hoc methods. Several methods based on ν‐gap metric for working out the mentioned problems are presented in this paper. To demonstrate the benefits of the proposed RMMAC method, two benchmark problems subject to unmodeled dynamics, stochastic disturbance input and sensor noise are considered as case studies. The first case‐study is a non‐minimum‐phase (NMP) system, which has an uncertain NMP zero; the second case‐study is a mass‐spring‐dashpot system that has three uncertain real parameters. In the first case‐study, five robust controller design methods (H₂, H_∞, QFT, H_∞ loop‐shaping and µ‐synthesis) are implemented and it is shown via extensive simulations that RMMAC/ν/QFT method improves disturbance‐rejection, when compared with the classic RMMAC. In the second case‐study, two robust controller design methods (QFT and mixed µ‐synthesis) are applied and it is shown that the RMMAC/ν/QFT method improves disturbance‐rejection, when compared with RMMAC/ν/mixed?µ. Copyright © 2010 John Wiley & Sons, Ltd.     

Network‐based robust H∞ control of continuous‐time systems with uncertainty

This paper studies the problem of robust H_∞ control for continuous‐time networked control systems (NCSs). A new type of Lyapunov functionals is exploited to derive sufficient conditions for guaranteeing the robust exponential stability and H_∞ performance of the considered system. It is shown that the new result is less conservative than the existing corresponding ones. Meanwhile, a method of eliminating redundant variables to reduce computational complexity is given, which is also applied to design state feedback H_∞ controllers, and the design condition is given in terms of solutions to a set of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the proposed methods. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Multiple robust H∞ controller design using the nonsmooth optimization method

This paper proposes a systematic technique to design multiple robust H_∞ controllers. The proposed technique achieves a desired robust performance objective, which is impossible to achieve with a single robust controller, by dividing the uncertainty set into several subsets and by designing a robust controller to each subset. To achieve this goal with a small number of divisions of the uncertainty set, an optimization problem is formulated. Since the cost function of this optimization problem is not a smooth function, a numerical nonsmooth optimization algorithm is proposed to solve this problem. This method avoids the use of Lyapunov variables, and therefore it leads to a moderate size optimization problem. A numerical example shows that the proposed multiple robust control method can improve the closed‐loop performance when a single robust controller cannot achieve satisfactory performance. Copyright © 2009 John Wiley & Sons, Ltd.     

Robust H2/H∞ control for time‐delay systems with polytopic uncertainty

In this paper, new separated H_∞ and H₂ performance criteria are derived for a class of time‐delay systems. When used in robust performance analysis and synthesis for real polytopic uncertainty and in multiobjective controller synthesis, they can partially rule out the technical restriction of using a single Lyapunov function, and therefore, lead to potentially less conservative linear matrix inequality (LMI) characterizations. Based on the criteria, robust multiobjective H₂/H_∞ controller is designed for time‐delay systems with polytopic uncertainty. All the conditions are given in terms of LMIs. Numerical examples are given to illustrate the proposed method. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust nonlinear ship course‐keeping control by H∞ I/O linearization and μ‐synthesis

In this paper, the H_∞ input/output (I/O) linearization formulation is applied to design an inner‐loop nonlinear controller for a nonlinear ship course‐keeping control problem. Due to the ship motion dynamics are non‐minimum phase, it is impossible to use the ordinary feedback I/O linearization to resolve. Hence, the technique of H_∞ I/O linearization is proposed to obtain a nonlinear H_∞ controller such that the compensated nonlinear system approximates the linear reference model in I/O behaviour. Then a μ‐synthesis method is employed to design an outer‐loop robust controller to address tracking, regulation, and robustness issues. The time responses of the tracking signals for the closed‐loop system reveal that the overall robust nonlinear controller is able to provide robust stability and robust performance for the plant uncertainties and state measurement errors. Copyright © 2002 John Wiley & Sons, Ltd.     

On the synthesis of robust PID controllers for plants with structured and unstructured uncertainty

In this paper, we consider the problems of synthesizing PID controllers for robust stability and performance for a given linear time‐invariant plant subject to both parametric and H_∞‐norm‐bounded perturbations. Using results from the area of parametric robust control, synthesis problems are converted into simultaneous stabilization of a family of complex segment polynomials. The results on H_∞ PID synthesis are then used to devise a design procedure for determining the admissible PID gain values. One of the important features of the proposed method is that it constructively characterizes the approximated set of all admissible PID controllers. This characterization can facilitate the optimal design of any additional design requirements. Copyright © 2005 John Wiley & Sons, Ltd.     

Fixed‐Structure ℋ∞ Controller Design for Systems with Polytopic Uncertainty: An LMI Solution

This note provides a new method for fixed‐structure H_∞ controller design for discrete‐time single input single output (SISO) systems with polytopic uncertainty. New conditions are derived based on the concept of robust strict positive realness (SPRness) of an uncertain polynomial with respect to a parameter‐dependent polynomial. The quality of this approximation depends on this SPR‐maker. A procedure is proposed for choosing the parameter‐dependent SPR‐maker that guarantees the improvement of the performance for the designed controller in comparison with the traditional approaches employed fixed SPR‐makers. The proposed conditions are given in terms of solutions to a set of linear matrix inequalities. The effectiveness of the proposed approach is demonstrated by comparing with the existing results.     

Robust Reliable H∞ Control for Discrete‐Time Systems with Actuator Delays

This article focuses on the robust state feedback reliable H_∞ control problem for discrete‐time systems. Discrete‐time systems with time‐varying delayed control input are formulated. Based on the Lyapunov–Krasovskii method and linear matrix inequality (LMI) approach, delay‐dependent sufficient conditions are developed for synthesizing the state feedback controller for an uncertain discrete‐time system. The parameter uncertainty is assumed to be norm bounded. A design scheme for the state feedback reliable H_∞ controller is proposed in terms of LMIs, which can guarantee the global asymptotic stability and the minimum disturbance attenuation level. Finally, numerical examples are provided to illustrate the effectiveness and reduced conservatism of the proposed methods.     

Iterative learning control for uncertain systems: Noncausal finite time interval robust control design

In this paper, we present a novel robust Iterative Learning Control (ILC) control strategy that is robust against model uncertainty as given by an additive uncertainty model. The design methodology hinges on ??_∞ optimization, but formulated such that the obtained ILC controller is not restricted to be causal, and inherently operates on a finite time interval. Optimization of the robust ILC (R‐ILC) solution is accomplished for the situation where any information about structure in the uncertainty is discarded, and for the situation where the information about the structure in the uncertainty is explicitly taken into account. Subsequently, the convergence and performance properties of resulting R‐ILC controlled system are analyzed. On an experimental set‐up, we show that the presented R‐ILC control strategy can outperform an existing linear‐quadratic norm‐optimal ILC approach and an existing causal R‐ILC approach based on frequency domain ??_∞ synthesis. Copyright © 2010 John Wiley & Sons, Ltd.     

An Improved Anti‐Windup Bumpless Transfer Structures Design for Controllers Switching

In this paper, an anti‐windup bumpless transfer (AWBT) control structure combined with linear interpolation method is proposed for smooth switching control. By choosing an appropriate scheduling signal, different controllers can be switched smoothly under a unified framework. Meanwhile, some robust specifications including H₂/H_∞ performance, pole placement constraint, and passivity of the closed‐loop system can be preserved through controller switching. Furthermore, for the linear system subject to input saturation, the stability and L₂ gain of the closed‐loop system can be guaranteed. Finally, a cart‐spring pendulum system is simulated to demonstrate the effectiveness of the proposed scheme.     

Design of an RMPC with a time‐varying terminal constraint set for tracking problem

This paper presents a robust model predictive control algorithm with a time‐varying terminal constraint set for systems with model uncertainty and input constraints. In this algorithm, the nonlinear system is approximated by a linear model where the approximation error is considered as an unstructured uncertainty that can be represented by a Lipschitz nonlinear function. A continuum of terminal constraint sets is constructed off‐line, and robust stability is achieved on‐line by using a variable control horizon. This approach significantly reduces the computational complexity. The proposed robust model predictive controller with a terminal constraint set is used in tracking set‐points for nonlinear systems. The effectiveness of the proposed method is illustrated with a numerical example. Copyright © 2015 John Wiley & Sons, Ltd.     

NETWORK‐INDUCED DELAY‐DEPENDENT H∞ CONTROLLER DESIGN FOR A CLASS OF NETWORKED CONTROL SYSTEMS

This paper is concerned with the problem of robust H_∞ controller design for a class of uncertain networked control systems (NCSs). The network‐induced delay is of an interval‐like time‐varying type integer, which means that both lower and upper bounds for such a kind of delay are available. The parameter uncertainties are assumed to be normbounded and possibly time‐varying. Based on Lyapunov‐Krasovskii functional approach, a robust H_∞ controller for uncertain NCSs is designed by using a sum inequality which is first introduced and plays an important role in deriving the controller. A delay‐dependent condition for the existence of a state feedback controller, which ensures internal asymptotic stability and a prescribed H_∞ performance level of the closed‐loop system for all admissible uncertainties, is proposed in terms of a nonlinear matrix inequality which can be solved by a linearization algorithm, and no parameters need to be adjusted. A numerical example about a balancing problem of an inverted pendulum on a cart is given to show the effectiveness of the proposed design method.     

Robust fault diagnosis and fault‐tolerant control for non‐Gaussian uncertain stochastic distribution control systems

The purpose of fault diagnosis of stochastic distribution control systems is to use the measured input and the system output probability density function to obtain the fault estimation information. A fault diagnosis and sliding mode fault‐tolerant control algorithms are proposed for non‐Gaussian uncertain stochastic distribution control systems with probability density function approximation error. The unknown input caused by model uncertainty can be considered as an exogenous disturbance, and the augmented observation error dynamic system is constructed using the thought of unknown input observer. Stability analysis is performed for the observation error dynamic system, and the H_∞ performance is guaranteed. Based on the information of fault estimation and the desired output probability density function, the sliding mode fault‐tolerant controller is designed to make the post‐fault output probability density function still track the desired distribution. This method avoids the difficulties of design of fault diagnosis observer caused by the uncertain input, and fault diagnosis and fault‐tolerant control are integrated. Two different illustrated examples are given to demonstrate the effectiveness of the proposed algorithm. Copyright © 2016 John Wiley & Sons, Ltd.     

Observer‐based adaptive robust control of a class of nonlinear systems with dynamic uncertainties

In this paper, a discontinuous projection‐based adaptive robust control (ARC) scheme is constructed for a class of nonlinear systems in an extended semi‐strict feedback form by incorporating a nonlinear observer and a dynamic normalization signal. The form allows for parametric uncertainties, uncertain nonlinearities, and dynamic uncertainties. The unmeasured states associated with the dynamic uncertainties are assumed to enter the system equations in an affine fashion. A novel nonlinear observer is first constructed to estimate the unmeasured states for a less conservative design. Estimation errors of dynamic uncertainties, as well as other model uncertainties, are dealt with effectively via certain robust feedback control terms for a guaranteed robust performance. In contrast with existing conservative robust adaptive control schemes, the proposed ARC method makes full use of the available structural information on the unmeasured state dynamics and the prior knowledge on the bounds of parameter variations for high performance. The resulting ARC controller achieves a prescribed output tracking transient performance and final tracking accuracy in the sense that the upper bound on the absolute value of the output tracking error over entire time‐history is given and related to certain controller design parameters in a known form. Furthermore, in the absence of uncertain nonlinearities, asymptotic output tracking is also achieved. Copyright © 2001 John Wiley & Sons, Ltd.     

Local input‐to‐state stabilization and ℓ ∞ ‐induced norm control of discrete‐time quadratic systems

This paper addresses the problems of local stabilization and control of open‐loop unstable discrete‐time quadratic systems subject to persistent magnitude bounded disturbances and actuator saturation. Firstly, for some polytopic region of the state‐space containing the origin, a method is derived to design a static nonlinear state feedback control law that achieves local input‐to‐state stabilization with a guaranteed stability region under nonzero initial conditions and persistent bounded disturbances. Secondly, the stabilization method is extended to deliver an optimized upper bound on the ? _∞ ‐induced norm of the closed‐loop system for a given set of persistent bounded disturbances. Thirdly, the stabilization and ? _∞ designs are adapted to cope with actuator saturation by means of a generalized sector bound constraint. The proposed controller designs are tailored via a finite set of state‐dependent linear matrix inequalities. Numerical examples are presented to illustrate the potentials of the proposed control design methods. Copyright © 2014 John Wiley & Sons, Ltd.     

Delay‐dependent robust H2/H∞ control for time‐delay systems with polytopic uncertainty

In this paper, new separated delay‐dependent H_∞ and H₂ performance criteria are derived for a class of time‐delay systems. Then they are extended to design a multiobjective robust H₂/H_∞ controller for polytopic uncertain systems with time delay. All the conditions are given in terms of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the proposed method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust H∞ fuzzy observer‐based tracking control design for a class of nonlinear stochastic Markovian jump systems

This paper investigates the stochastic H_∞ tracking control problem for a class of nonlinear stochastic Markovian jump systems. The attention is focused on the design of a fuzzy observer‐based fuzzy controller such that an H_∞ model reference tracking performance is guaranteed for admissible disturbances. A sufficient condition is established to guarantee the existence of the desired robust controller, which is given in terms of a set of coupled matrix inequalities. Moreover, a novel decoupled method is proposed to transform the sufficient condition into some linear matrix inequality (LMI) form such that observer gains and control gains can be simultaneously obtained by solving a set of LMIs. Finally, a simulation example is presented to illustrate the effectiveness of the proposed design method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society