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Showing papers on "Robust control published in 2006"


Journal ArticleDOI
TL;DR: A rich family of control problems which are in general hard to solve in a deterministically robust sense is therefore amenable to polynomial-time solution, if robustness is intended in the proposed risk-adjusted sense.
Abstract: This paper proposes a new probabilistic solution framework for robust control analysis and synthesis problems that can be expressed in the form of minimization of a linear objective subject to convex constraints parameterized by uncertainty terms. This includes the wide class of NP-hard control problems representable by means of parameter-dependent linear matrix inequalities (LMIs). It is shown in this paper that by appropriate sampling of the constraints one obtains a standard convex optimization problem (the scenario problem) whose solution is approximately feasible for the original (usually infinite) set of constraints, i.e., the measure of the set of original constraints that are violated by the scenario solution rapidly decreases to zero as the number of samples is increased. We provide an explicit and efficient bound on the number of samples required to attain a-priori specified levels of probabilistic guarantee of robustness. A rich family of control problems which are in general hard to solve in a deterministically robust sense is therefore amenable to polynomial-time solution, if robustness is intended in the proposed risk-adjusted sense.

1,122 citations


Book
21 Apr 2006
TL;DR: This document describes the design and development of the Markovian Jump Systems, as well as some of the systems used in the production of these systems, which were developed and tested in the field.
Abstract: Introduction and Preview.- Stability.- Stabilization.- Robust Control.- H1 Control.- Guaranteed Cost Control.- Positive Real Control.- H1 Filtering.- Delay Systems.- Markovian Jump Systems.

840 citations


Proceedings ArticleDOI
14 Jun 2006
TL;DR: In this paper, it is shown that the unknown dynamics and disturbance can be actively estimated and compensated in real time and this makes the feedback control more robust and less dependent on the detailed mathematical model of the physical process.
Abstract: The question addressed in this paper is: just what do we need to know about a process in order to control it? With active disturbance rejection, perhaps we don't need to know as much as we were told. In fact, it is shown that the unknown dynamics and disturbance can be actively estimated and compensated in real time and this makes the feedback control more robust and less dependent on the detailed mathematical model of the physical process. In this paper we first examine the basic premises in the existing paradigms, from which it is argued that a paradigm shift is necessary. Using a motion control metaphor, the basis of such a shift, the active disturbance rejection control, is introduced. Stability analysis and applications are presented. Finally, the characteristics and significance of the new paradigm are discussed.

803 citations


Journal ArticleDOI
TL;DR: It is shown that the class of admissible affine state feedback control policies with knowledge of prior states is equivalent to the classOf admissible feedback policies that are affine functions of the past disturbance sequence, which implies that a broad class of constrained finite horizon robust and optimal control problems can be solved in a computationally efficient fashion using convex optimization methods.

617 citations


Journal ArticleDOI
TL;DR: The proposed control framework provides humans with extended physiological proprioception, so that s/he can affect and sense the remote slave environments mainly relying on her/his musculoskeletal systems.
Abstract: We propose a novel control framework for bilateral teleoperation of a pair of multi-degree-of-freedom nonlinear robotic systems under constant communication delays. The proposed framework uses the simple proportional-derivative control, i.e., the master and slave robots are directly connected via spring and damper over the delayed communication channels. Using the controller passivity concept, the Lyapunov-Krasovskii technique, and Parseval's identity, we can passify the combination of the delayed communication and control blocks altogether robustly, as long as the delays are finite constants and an upper bound for the round-trip delay is known. Having explicit position feedback through the delayed P-action, the proposed framework enforces master-slave position coordination, which is often compromised in the conventional scattering-based teleoperation. The proposed control framework provides humans with extended physiological proprioception, so that s/he can affect and sense the remote slave environments mainly relying on her/his musculoskeletal systems. Simulation and experiments are performed to validate and highlight properties of the proposed control framework

551 citations


Journal ArticleDOI
TL;DR: This note shows how to select the projection matrix in such a way that the euclidean norm of the resulting perturbation is minimal, which is particularly useful if integral sliding-mode control is to be combined with other methods to further robustify against unmatched perturbations.
Abstract: The robustness properties of integral sliding-mode controllers are studied. This note shows how to select the projection matrix in such a way that the euclidean norm of the resulting perturbation is minimal. It is also shown that when the minimum is attained, the resulting perturbation is not amplified. This selection is particularly useful if integral sliding-mode control is to be combined with other methods to further robustify against unmatched perturbations. H/sub /spl infin// is taken as a special case. Simulations support the general analysis and show the effectiveness of this particular combination.

535 citations


Journal ArticleDOI
TL;DR: In this paper, the authors classified robust design into three methods: the Taguchi method, robust optimization, and robust design with the axiomatic approach, and examined them from a theoretical viewpoint and discussed from an application viewpoint.
Abstract: Robust design has been developed with the expectation that an insensitive design can be obtained. That is, a product designed by robust design should be insensitive to external noises or tolerances. An insensitive design has more probability to obtain a target value, although there are uncertain noises. Theories of robust design have been developed by adopting the theories of other fields. Based on the theories, robust design can be classified into three methods: 1) the Taguchi method, 2) robust optimization, and 3) robust design with the axiomatic approach. Each method is reviewed and investigated. The methods are examined from a theoretical viewpoint and are discussed from an application viewpoint. The advantages and drawbacks of each method are discussed, and future directions for development are proposed.

489 citations


Journal ArticleDOI
TL;DR: The robust Hinfin filtering problem is studied for stochastic uncertain discrete time-delay systems with missing measurements and filters such that, for all possible missing observations and all admissible parameter uncertainties, the filtering error system is exponentially mean-square stable.
Abstract: In this paper, the robust Hinfin filtering problem is studied for stochastic uncertain discrete time-delay systems with missing measurements. The missing measurements are described by a binary switching sequence satisfying a conditional probability distribution. We aim to design filters such that, for all possible missing observations and all admissible parameter uncertainties, the filtering error system is exponentially mean-square stable, and the prescribed Hinfin performance constraint is met. In terms of certain linear matrix inequalities (LMIs), sufficient conditions for the solvability of the addressed problem are obtained. When these LMIs are feasible, an explicit expression of a desired robust Hinfin filter is also given. An optimization problem is subsequently formulated by optimizing the Hinfin filtering performances. Finally, a numerical example is provided to demonstrate the effectiveness and applicability of the proposed design approach

474 citations


Journal ArticleDOI
TL;DR: This paper provides a solution to the problem of robust output feedback model predictive control of constrained, linear, discrete-time systems in the presence of bounded state and output disturbances by combining a simple, stable Luenberger state estimator and a recently developed, robustly stabilizing, tube-based, model predictive controller.

472 citations


Journal ArticleDOI
TL;DR: Alternative sequential and nonsequential versions of robust control theory imply identical robust decision rules that are dynamically consistent in a useful sense.

354 citations


Journal ArticleDOI
Il-Song Kim1
TL;DR: In this article, a simple resistor-capacitor battery model was used in order to reduce calculation time and system resource and the structure of the proposed system is simple, but it shows robust control property against modeling errors and uncertainties.

Journal ArticleDOI
TL;DR: It is reviewed how various classical relaxations based on the S-procedure can be subsumed to a unified framework based on Lagrange duality for semi-definite programs, and the systematic construction of families of relaxations which can be shown to be asymptotically exact.

Journal ArticleDOI
TL;DR: In this article, a discrete-time current controller is proposed to damp LCL resonance, combining deadbeat current control with optimal state-feedback pole assignment to achieve transient overcurrent protection.
Abstract: Inductance-capacitor-inductance (LCL)-filters installed at converter outputs offer higher harmonic attenuation than L-filters, but careful design is required to damp LCL resonance, which can cause poorly damped oscillations and even instability. A new topology is presented for a discrete-time current controller which damps this resonance, combining deadbeat current control with optimal state-feedback pole assignment. By separating the state feedback gains into deadbeat and damping feedback loops, transient overcurrent protection is realizable while preserving the desired pole locations. Moreover, the controller is shown to be robust to parameter uncertainty in the grid inductance. Experimental tests verify that fast well-damped transient response and overcurrent protection is possible at low switching frequencies relative to the resonant frequency

01 Jan 2006
TL;DR: This paper describes the implementation of Rational Implementation Inspired by the Bilinear Transformation of the 2DOF Controller Parameterisation and its application to time-delay systems.
Abstract: Controller design.- Classical Control of Time-delay Systems.- Preliminaries.- J-spectral Factorisation of Regular Para-Hermitian Transfer Matrices.- The Delay-type Nehari Problem.- An Extended Nehari Problem.- The Standard H? Problem.- A Transformed Standard H? Problem.- 2DOF Controller Parameterisation.- Unified Smith Predictor.- Controller Implementation.- Discrete-delay Implementation of Distributed Delay in Control Laws.- Rational Implementation Inspired by the ?-operator.- Rational Implementation Based on the Bilinear Transformation.

Journal ArticleDOI
TL;DR: Experiments show that good and robust performance is achieved in a limited development time by avoiding the design of ad hoc supervisory and logical constructs usually required by controllers developed according to standard techniques.
Abstract: This paper describes a hybrid model and a model predictive control (MPC) strategy for solving a traction control problem. The problem is tackled in a systematic way from modeling to control synthesis and implementation. The model is described first in the Hybrid Systems Description Language to obtain a mixed-logical dynamical (MLD) hybrid model of the open-loop system. For the resulting MLD model, we design a receding horizon finite-time optimal controller. The resulting optimal controller is converted to its equivalent piecewise affine form by employing multiparametric programming techniques, and finally experimentally tested on a car prototype. Experiments show that good and robust performance is achieved in a limited development time by avoiding the design of ad hoc supervisory and logical constructs usually required by controllers developed according to standard techniques.

Journal ArticleDOI
TL;DR: A less conservative delay-dependent linear matrix inequality (LMI) method is presented based on a new Lyapunov-Krasovskii functional that incorporates a relaxed parameter-dependent technique combined with a recently proposed idea of introducing free-weighting matrices.
Abstract: This note concerns with the robust stability of linear uncertain systems with state-delay. The uncertainty is assumed to be of polytopic type. A less conservative delay-dependent linear matrix inequality (LMI) method is presented based on a new Lyapunov-Krasovskii functional. The present method incorporates a relaxed parameter-dependent technique combined with a recently proposed idea of introducing free-weighting matrices. When confined to delay-free case, the present result is also less conservative than existing stability tests using parameter-dependent methods. Numerical examples are given to show the less conservativeness of the results.

Proceedings ArticleDOI
14 Jun 2006
TL;DR: In this article, a fractional order PID controller is investigated for a position servomechanism control system considering actuator saturation and the shaft torsional flexibility, and a modified approximation method is introduced to realize the designed fractional-order PID controller.
Abstract: In this paper, a fractional order PID controller is investigated for a position servomechanism control system considering actuator saturation and the shaft torsional flexibility. For actually implementation, we introduced a modified approximation method to realize the designed fractional order PID controller. Numerous simulation comparisons presented in this paper indicate that, the fractional order PID controller, if properly designed and implemented, will outperform the conventional integer order PID controller.

Journal ArticleDOI
TL;DR: A stability criterion is derived by introducing some relaxation matrices that can be used to reduce the conservatism of the criteria, based on the Lyapunov-Krasovskii functional approach.

Journal ArticleDOI
TL;DR: This note develops methods of robust stability analysis and robust stabilization in the mean square sense which are dependent on the system uncertainty.
Abstract: This note deals with robust stability and control of uncertain discrete-time linear systems with Markovian jumping parameters. Systems with polytopic-type parameter uncertainty in either the state-space model matrices, or in the transition probability matrix of the Markov process, are considered. This note develops methods of robust stability analysis and robust stabilization in the mean square sense which are dependent on the system uncertainty. The design of both mode-dependent and mode-independent control laws is addressed. The proposed methods are given in terms of linear matrix inequalities. Numerical examples are provided to demonstrate the effectiveness of the derived results.

Journal ArticleDOI
TL;DR: In this paper, the robust multiple model adaptive control (RMMAC) architecture is proposed to combine robust non-adaptive mixed µ-synthesis designs and stochastic hypothesis-testing concepts.
Abstract: We overview recent progress in the field of robust adaptive control with special emphasis on methodologies that use multiple-model architectures. We argue that the selection of the number of models, estimators and compensators in such architectures must be based on a precise definition of the robust performance requirements. We illustrate some of the concepts and outstanding issues by presenting a new methodology that blends robust non-adaptive mixed µ-synthesis designs and stochastic hypothesis-testing concepts leading to the so-called robust multiple model adaptive control (RMMAC) architecture. A numerical example is used to illustrate the RMMAC design methodology, as well as its strengths and potential shortcomings. The later motivated us to develop a variant architecture, denoted as RMMAC/XI, that can be effectively used in highly uncertain exogenous plant disturbance environments. Copyright © 2006 John Wiley & Sons, Ltd.

Journal ArticleDOI
TL;DR: A delay-dependent condition for the existence of a state feedback controller, which ensures asymptotic stability and a prescribed H"~ performance level of the closed-loop system for all admissible uncertainties, is proposed in terms of a matrix inequality.

Journal ArticleDOI
TL;DR: A new condition of robust right coprime factorization of non linear systems with unknown bounded perturbations is derived, and a broader class of nonlinear plants can be controlled robustly.
Abstract: In this note, robust stabilization and tracking performance of operator based nonlinear feedback control systems are studied by using robust right coprime factorization. Specifically, a new condition of robust right coprime factorization of nonlinear systems with unknown bounded perturbations is derived. Using the new condition, a broader class of nonlinear plants can be controlled robustly. When the spaces of the nonlinear plant output and the reference input are different, a space change filter is designed, and in this case this note considers tracking controller design using the exponential iteration theorem.

Journal ArticleDOI
TL;DR: This paper presents an adaptive nonsingular terminal sliding mode (NTSM) tracking control design for robotic systems using fuzzy wavelet networks, which requires no prior knowledge about the dynamics of the robot and no off-line learning phase.
Abstract: This paper presents an adaptive nonsingular terminal sliding mode (NTSM) tracking control design for robotic systems using fuzzy wavelet networks. Compared with linear hyperplane-based sliding control, terminal sliding mode controller can provide faster convergence and higher precision control. Therefore, a terminal sliding controller combined with the fuzzy wavelet network, which can accurately approximate unknown dynamics of robotic systems by using an adaptive learning algorithm, is an attractive control approach for robots. In addition, the proposed learning algorithm can on-line tune parameters of dilation and translation of fuzzy wavelet basis functions and hidden-to-output weights. Therefore, a robust control law is used to eliminate uncertainties including the inevitable approximation errors resulted from the finite number of fuzzy wavelet basis functions. The proposed controller requires no prior knowledge about the dynamics of the robot and no off-line learning phase. Moreover, both tracking performance and stability of the closed-loop robotic system can be guaranteed by Lyapunov theory. Finally, the effectiveness of the fuzzy wavelet network-based control approach is illustrated through comparative simulations on a six-link robot manipulator

Journal ArticleDOI
TL;DR: Simulation results verify that the proposed WABC can achieve favorable tracking performance by incorporating of WNN identification, adaptive backstepping control, and L2 robust control techniques.
Abstract: This paper proposes a wavelet adaptive backstepping control (WABC) system for a class of second-order nonlinear systems. The WABC comprises a neural backstepping controller and a robust controller. The neural backstepping controller containing a wavelet neural network (WNN) identifier is the principal controller, and the robust controller is designed to achieve L2 tracking performance with desired attenuation level. Since the WNN uses wavelet functions, its learning capability is superior to the conventional neural network for system identification. Moreover, the adaptation laws of the control system are derived in the sense of Lyapunov function and Barbalat's lemma, thus the system can be guaranteed to be asymptotically stable. The proposed WABC is applied to two nonlinear systems, a chaotic system and a wing-rock motion system to illustrate its effectiveness. Simulation results verify that the proposed WABC can achieve favorable tracking performance by incorporating of WNN identification, adaptive backstepping control, and L2 robust control techniques

Journal ArticleDOI
TL;DR: A new architecture is introduced, which builds upon the traditional passivity-based configuration by using additional position control on both the master and slave robots, to solve the steady-state position and force-tracking problem in bilateral teleoperation.
Abstract: This paper addresses the problem of steady-state position and force tracking in bilateral teleoperation. Passivity-based control schemes for bilateral teleoperation provide robust stability against network delays in the feedback loop and velocity tracking, but do not guarantee steady-state position and force tracking in general. Position drift due to data loss and offset of initial conditions is a well-known problem in such systems. In this paper, we introduce a new architecture, which builds upon the traditional passivity-based configuration by using additional position control on both the master and slave robots, to solve the steady-state position and force-tracking problem. Lyapunov stability methods are used to establish the range of the position control gains on the master and slave sides. Experimental results using a single-degree-of-freedom master/slave system are presented, showing the performance of the resulting system

Journal ArticleDOI
TL;DR: A method for designing a global robust adaptive controller that forces an underactuated ship to follow a reference path under both constant and time-varying disturbances induced by waves, wind and ocean-currents is proposed.

Journal ArticleDOI
TL;DR: In this article, the authors consider the problem of finding the (constrained) input signal that minimizes a measure of a control-oriented model uncertainty set, where the control objective is disturbance rejection only.

Journal ArticleDOI
TL;DR: One of the key aims of this paper is to present results such that one can perform the relevant set computations using polyhedral algebra and computational geometry software, provided the system is piecewise affine and the constraints are polygonal.
Abstract: This paper presents new results that allow one to compute the set of states that can be robustly steered in a finite number of steps, via state feedback control, to a given target set. The assumptions that are made in this paper are that the system is discrete-time, nonlinear and time-invariant and subject to mixed constraints on the state and input. A persistent disturbance, dependent on the current state and input, acts on the system. Existing results are not able to address state- and input-dependent disturbances and the results in this paper are, therefore, a generalization of previously published results. One of the key aims of this paper is to present results such that one can perform the relevant set computations using polyhedral algebra and computational geometry software, provided the system is piecewise affine and the constraints are polygonal. Existing methods are only applicable to piecewise affine systems that either have no control inputs or no disturbances, whereas the results in this paper remove this limitation. Some simple examples are also given that show that, even if all the relevant sets are convex and the system is linear, convexity of the set of controllable states cannot be guaranteed.

Proceedings ArticleDOI
14 Jun 2006
TL;DR: The key idea behind the approach is that the probabilistic obstacle avoidance problem can be expressed as a disjunctive linear program using linear chance constraints, such that planning with uncertainty requires minimal additional computation.
Abstract: Autonomous vehicles need to plan trajectories to a specified goal that avoid obstacles. Previous approaches that used a constrained optimization approach to solve for finite sequences of optimal control inputs have been highly effective. For robust execution, it is essential to take into account the inherent uncertainty in the problem, which arises due to uncertain localization, modeling errors, and disturbances. Prior work has handled the case of deterministically bounded uncertainty. We present here an alternative approach that uses a probabilistic representation of uncertainty, and plans the future probabilistic distribution of the vehicle state so that the probability of collision with obstacles is below a specified threshold. This approach has two main advantages; first, uncertainty is often modeled more naturally using a probabilistic representation (for example in the case of uncertain localization); second, by specifying the probability of successful execution, the desired level of conservatism in the plan can be specified in a meaningful manner. The key idea behind the approach is that the probabilistic obstacle avoidance problem can be expressed as a disjunctive linear program using linear chance constraints. The resulting disjunctive linear program has the same complexity as that corresponding to the deterministic path planning problem with no representation of uncertainty. Hence the resulting problem can be solved using existing, efficient techniques, such that planning with uncertainty requires minimal additional computation. Finally, we present an empirical validation of the new method with a number of aircraft obstacle avoidance scenarios.

Journal ArticleDOI
TL;DR: This paper presents two novel sliding mode (SM) model reference adaptive system (MRAS) observers for speed estimation in a sensorless-vector-controlled induction-machine drive that use the flux estimated by the voltage model observer as the reference and construct SM flux observers that allow speed estimation.
Abstract: This paper presents two novel sliding mode (SM) model reference adaptive system (MRAS) observers for speed estimation in a sensorless-vector-controlled induction-machine drive. Both methods use the flux estimated by the voltage model observer as the reference and construct SM flux observers that allow speed estimation. Stability and dynamics of the two proposed SM flux observers are discussed. The observers are compared with the classical MRAS observer. The proposed estimators seem very robust and easy to tune. Unlike the classical MRAS, the speed-estimation process is based on algebraic calculations that do not exhibit underdamped poles or zeros on the right-hand plane. Simulations and experimental results on a 1/4-hp three-phase induction machine confirm the validity of the approaches.