Showing papers in "International Journal of Robust and Nonlinear Control in 2009"

Delay-dependent stability and stabilization of neutral time-delay systems

Abstract: This paper is concerned with the problem of stability and stabilization of neutral time-delay systems. A new delay-dependent stability condition is derived in terms of linear matrix inequality by constructing a new Lyapunov functional and using some integral inequalities without introducing any free-weighting matrices. On the basis of the obtained stability condition, a stabilizing method is also proposed. Using an iterative algorithm, the state feedback controller can be obtained. Numerical examples illustrate that the proposed methods are effective and lead to less conservative results. Copyright © 2008 John Wiley & Sons, Ltd.

Average consensus on networks with quantized communication

Abstract: This work presents a contribution to the solution of the average agreement problem on a network with quantized links. Starting from the well-known linear diffusion algorithm, we propose a simple and effective adaptation that is able to preserve the average of states and to drive the system near to the consensus value, when a uniform quantization is applied to communication between agents. The properties of this algorithm are investigated both by a worst-case analysis and by a probabilistic analysis, and are shown to depend on the spectral properties of the evolution matrix. A special attention is devoted to the issue of the dependence of the performance on the number of agents, and several examples are given. Copyright © 2008 John Wiley & Sons, Ltd.

H∞ control for discrete‐time Markovian jump linear systems with partly unknown transition probabilities

Abstract: In this paper, the problem of H∞ control for a class of discrete-time Markovian jump linear system with partly unknown transition probabilities is investigated. The class of systems under consideration is more general, which covers the systems with completely known and completely unknown transition probabilities as two special cases. Moreover, in contrast to the uncertain transition probabilities studied recently, the concept of partly unknown transition probabilities proposed in this paper does not require any knowledge of the unknown elements. The H∞ controllers to be designed include state feedback and dynamic output feedback, since the latter covers the static one. The sufficient conditions for the existence of the desired controllers are derived within the matrix inequalities framework, and a cone complementary linearization algorithm is exploited to solve the latent equation constraints in the output-feedback control case. Two numerical examples are provided to show the validness and potential of the developed theoretical results. Copyright © 2008 John Wiley & Sons, Ltd.

Feedback–feedforward individual pitch control for wind turbine load reduction

Abstract: This paper focuses on the problem of wind turbine fatigue load reduction by means of individual pitch control (IPC). The control approach has a two-degree-of-freedom structure, consisting of an optimal multivariable LQG controller and a feedforward disturbance rejection controller based on estimated wind speed signals. To make the control design problem time invariant, all signals are transformed to the non-rotating reference frame using the Coleman transformation. In the Coleman domain, the LQG control objective is minimization of the rotor tilt and yaw moments, whereas the feedforward controller tries to achieve even further improvement by rejecting the influence of the low-frequency components of the wind on the rotor moments. To this end, the tilt- and yaw-oriented components of the blade-effective wind speeds are approximated using stochastic random walk models, the states of which are then augmented with the turbine states and estimated using a Kalman filter. The effects of these (estimated) disturbances on the controlled outputs are then reduced using stable dynamic model inversion. The approach is tested and compared with the conventional IPC method in simulation studies with models of different complexities. The results demonstrate very good load reduction at not only low frequencies (1p blade fatigue load reduction) but also at the 3p frequency, giving rise to fatigue load reduction of the non-rotating turbine components. Copyright © 2008 John Wiley & Sons, Ltd.

A piecewise analysis method to stability analysis of linear continuous/discrete systems with time‐varying delay

Abstract: The delay-dependent stability problem of linear continuous/discrete systems with time-varying delay is investigated based on a piecewise analysis method (PAM). In the method, the variation interval of the time delay is firstly divided into several subintervals. By checking the variation of the Lyapunov functional in every subinterval, some new delay-dependent stability criteria are derived. Several numerical examples show that our method can lead to much less conservative results than those in the existing references. Moreover, when the number of the divided subintervals increases, the corresponding criteria can provide an improvement on the results. Copyright © 2008 John Wiley & Sons, Ltd.

Linear parameter varying control of wind turbines covering both partial load and full load conditions

Abstract: This paper considers the design of linear parameter varying (LPV) controllers for wind turbines in order to obtain a multivariable control law that covers the entire nominal operating trajectory. The paper first presents a controller structure for selecting a proper operating trajectory as a function of estimated wind speed. The dynamic control law is based on LPV controller synthesis with general parameter dependency by gridding the parameter space. The controller construction can, for medium- to large-scale systems, be difficult from a numerical point of view, because the involved matrix operations tend to be ill-conditioned. The paper proposes a controller construction algorithm together with various remedies for improving the numerical conditioning the algorithm. The proposed algorithm is applied to the design of a LPV controller for wind turbines, and a comparison is made with a controller designed using classical techniques to conclude that an improvement in performance is obtained for the entire operating envelope. Copyright © 2008 John Wiley & Sons, Ltd.

Exponential H∞ filtering for switched linear systems with interval time‐varying delay

Abstract: This paper deals with the problem of exponential H∞ filtering for a class of continuous-time switched linear system with interval time-varying delay. The time delay under consideration includes two cases: one is that the time delay is differentiable and bounded with a constant delay-derivative bound, whereas the other is that the time delay is continuous and bounded. Switched linear filters are designed to ensure that the filtering error systems under switching signal with average dwell time are exponentially stable with a prescribed H∞ noise attenuation level. Based on the free-weighting matrix approach and the average dwell technology, delay-dependent sufficient conditions for the existence of such a filter are derived and formulated in terms of linear matrix inequalities (LMIs). By solving that corresponding LMIs, the desired filter parameterized matrices and the minimal average dwell time are obtained. Finally, two numerical examples are presented to demonstrate the effectiveness of the developed results

Delay-distribution-dependent robust stability of uncertain systems with time-varying delay

Abstract: By employing the information of the probability distribution of the time delay, this paper investigates the problem of robust stability for uncertain systems with time-varying delay satisfying some probabilistic properties. Different from the common assumptions on the time delay in the existing literatures, it is assumed in this paper that the delay is random and its probability distribution is known a priori. In terms of the probability distribution of the delay, a new type of system model with stochastic parameter matrices is proposed. Based on the new system model, sufficient conditions for the exponential mean square stability of the original system are derived by using the Lyapunov functional method and the linear matrix inequality (LMI) technique. The derived criteria, which are expressed in terms of a set of LMIs, are delay-distribution-dependent, that is, the solvability of the criteria depends on not only the variation range of the delay but also the probability distribution of it. Finally, three numerical examples are given to illustrate the feasibility and effectiveness of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.

Global stability results for systems under sampled-data control

Abstract: In this work sufficient conditions for uniform input-to-output stability and uniform input-to-state stability are presented for finite-dimensional systems under feedback control with zero-order hold. The conditions are expressed by means of single and vector Lyapunov functions. Copyright © 2008 John Wiley & Sons, Ltd.

Tracking control for sampled-data systems with uncertain time-varying sampling intervals and delays

Abstract: SUMMARY In this paper, a solution to the approximate tracking problem of sampled-data systems with uncertain, time-varying sampling intervals and delays is presented. Such time-varying sampling intervals and delays can typically occur in the field of networked control systems. The uncertain, time-varying sampling and network delays cause inexact feedforward, which induces a perturbation on the tracking error dynamics, for which a model is presented in this paper. Sufficient conditions for the input-to-state stability (ISS) of the tracking error dynamics with respect to this perturbation are given. Hereto, two analysis approaches are developed: a discrete-time approach and an approach in terms of delay impulsive differential equations. These ISS results provide bounds on the steady-state tracking error as a function of the plant properties, the control design and the network properties. Moreover, it is shown that feedforward preview can significantly improve the tracking performance and an online extremum seeking (nonlinear programming) algorithm is proposed to online estimate the optimal preview time. The results are illustrated on a mechanical motion control example showing the effectiveness of the proposed strategy and providing insight into the differences and commonalities between the two analysis approaches. Copyright q 2009 John Wiley & Sons, Ltd.

Kalman filter‐based adaptive control for networked systems with unknown parameters and randomly missing outputs

Abstract: This paper investigates the problem of adaptive control for networked control systems with unknown model parameters and randomly missing outputs. In particular, for a system with the autoregressive model with exogenous input placed in a network environment, the randomly missing output feature is modeled as a Bernoulli process. Then, an output estimator is designed to online estimate the missing output measurements, and further a Kalman filter-based method is proposed for parameter estimation. Based on the estimated output and the available output, and the estimated model parameters, an adaptive control is designed to make the output track the desired signal. Convergence properties of the proposed algorithms are analyzed in detail. Simulation examples illustrate the effectiveness of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.

A dual‐observer design for global output feedback stabilization of nonlinear systems with low‐order and high‐order nonlinearities

Abstract: This paper employs a dual-observer design to solve the problem of global output feedback stabilization for a class of nonlinear systems whose nonlinearities are bounded by both low-order and high-order terms. We show that the dual-observer comprised of two individual homogeneous observers, can be implemented together to estimate low-order and high-order states in parallel. The proposed dual observer, together with a state feedback controller, which has both low-order and high-order terms, will lead to a new result combining and generalizing two recent results (Li J, Qian C. Proceedings of the 2005 IEEE Conference on Decision and Control, 2005; 2652–2657) and (Qian C. Proceedings of the 2005 American Control Conference, June 2005; 4708–4715). Copyright © 2008 John Wiley & Sons, Ltd.

Robust monotone gradient-based discrete-time iterative learning control

Abstract: This paper considers the use of matrix models and the robustness of a gradient-based iterative learning control (ILC) algorithm using both fixed learning gains and nonlinear data-dependent gains derived from parameter optimization. The philosophy of the paper is to ensure monotonic convergence with respect to the mean-square value of the error time series. The paper provides a complete and rigorous analysis for the systematic use of the well-known matrix models in ILC. Matrix models provide necessary and sufficient conditions for robust monotonic convergence. They also permit the construction of accurate sufficient frequency domain conditions for robust monotonic convergence on finite time intervals for both causal and non-causal controller dynamics. The results are compared with recently published results for robust inverse-model-based ILC algorithms and it is seen that the algorithm has the potential to improve the robustness to high-frequency modelling errors, provided that resonances within the plant bandwidth have been suppressed by feedback or series compensation. Copyright © 2008 John Wiley & Sons, Ltd.

LMI optimization approach to robust H∞ observer design and static output feedback stabilization for discrete-time nonlinear uncertain systems

Abstract: A new approach for the design of robust H∞ observers for a class of Lipschitz nonlinear systems with time-varying uncertainties is proposed based on linear matrix inequalities (LMIs). The admissible Lipschitz constant of the system and the disturbance attenuation level are maximized simultaneously through convex multiobjective optimization. The resulting H∞ observer guarantees asymptotic stability of the estimation error dynamics and is robust against nonlinear additive uncertainty and time-varying parametric uncertainties. Explicit norm-wise and element-wise bounds on the tolerable nonlinear uncertainty are derived. Also, a new method for the robust output feedback stabilization with H∞ performance for a class of uncertain nonlinear systems is proposed. Our solution is based on a noniterative LMI optimization and is less restrictive than the existing solutions. The bounds on the nonlinear uncertainty and multiobjective optimization obtained for the observer are also applicable to the proposed static output feedback stabilizing controller. Copyright © 2008 John Wiley & Sons, Ltd.

Robust control of uncertain systems with polynomial nonlinearity by output feedback

Abstract: The problem of global robust stabilization by output feedback is investigated for two classes of uncertain systems with polynomial nonlinearity—one is with controllable/observable linearization and the other is not. The uncertainties in the systems are assumed to be dominated by both lower- and higher-order nonlinearities multiplying by an output-dependent growth rate. There are two ingredients in this study. One is to exploit the idea of how to handle polynomial growth conditions via homogeneity and domination without introducing an observer gain updated law. The other is the development of a recursive design algorithm for the construction of reduced-order observers, which is not only interesting in its own right but also has a valid counterpart, capable of dealing with strongly nonlinear systems, even lack of uniform observability and smooth stabilizability. Copyright © 2008 John Wiley & Sons, Ltd.

Adjustment of high-order sliding-mode controllers

Abstract: Long-lasting problems of high-order sliding-mode (HOSM) design are solved. Only local uncertainty suppression was previously obtained in the case when the dynamic system uncertainties are unbounded. This restriction is removed in this paper. A universal method is proposed for the proper controller parameter adjustment based on the homogeneity approach. The method allows making the finite-time convergence arbitrarily fast or slow. In addition, a HOSM regularization procedure is proposed diminishing chattering. Computer simulation confirms the theoretical results. Copyright © 2008 John Wiley & Sons, Ltd.

Direct adaptive control of a utility-scale wind turbine for speed regulation

Abstract: The accurate modeling of wind turbines is an extremely challenging problem due to the tremendous complexity of the machines and the turbulent and unpredictable conditions in which they operate. Adaptive control techniques are well suited to nonlinear applications, such as wind turbines, which are difficult to accurately model and which have effects from poorly known operating environments. In this paper, we extended the direct model reference adaptive control (DMRAC) approach to track a reference point and to reject persistent disturbances. This approach was then used to design an adaptive collective pitch controller for a high-fidelity simulation of a variable-speed horizontal axis wind turbine. The objective of the adaptive pitch controller was to regulate generator speed in Region 3 and to reject step disturbances. The control objective was accomplished by collectively pitching the turbine blades. The turbine simulation models the controls advanced research turbine (CART) of the National Renewable Energy Laboratory in Golden, Colorado. The CART is a utility-scale wind turbine that has a well-developed and extensively verified simulator. This novel application of adaptive control was compared in simulations with a classical proportional integrator (PI) collective pitch controller. In the simulations, the adaptive pitch controller showed improved speed regulation in Region 3 when compared with the PI pitch controller. Copyright © 2008 John Wiley & Sons, Ltd.

A backstepping controller for path‐tracking of an underactuated autonomous airship

Abstract: In this paper we propose a nonlinear control approach for the path-tracking of an autonomous underactuated airship. A backstepping controller is designed from the airship nonlinear dynamic model including wind disturbances, and further enhanced to consider actuators saturation. Control implementation issues related to airship underactuation are also addressed, namely control allocation and an attitude reference shaping to obtain a faster error correction with smoother input requests. The results obtained demonstrate the capacity of an underactuated unmanned airship to execute a realistic mission including vertical take-off and landing, stabilization and path-tracking, in the presence of wind disturbances, with a single robust control law. Copyright © 2008 John Wiley & Sons, Ltd.

A delay decomposition approach to delay-dependent stability for linear systems with time-varying delays

Abstract: SUMMARY This paper is concerned with delay-dependent stability for linear systems with time-varying delays. By decomposing the delay interval into multiple equidistant subintervals, on which different Lyapunov functionals are chosen, and new LyapunovKrasvskii functionals are then constructed. Employing these new Lyapunov-Krasvskii functionals, some new delay-dependent stability criteria are established. The numerical examples show that the obtained results are less conservative than some existing ones in the literature. Copyright q 2009 John Wiley & Sons, Ltd. Received 5 December 2007; Revised 23 October 2008; Accepted 25 October 2008

On linear-parameter-varying (LPV) slip-controller design for two-wheeled vehicles

Abstract: This paper describes the application of linear-parameter-varying (LPV) control design techniques to the problem of slip control for two-wheeled vehicles. A nonlinear multi-body motorcycle simulator is employed to derive a control-oriented dynamic model. It is shown that, in order to devise a robust controller with good performance, it is necessary to take into account the dependence of the model on the velocity and on the wheel slip. This dependence is modeled via an LPV system constructed from Jacobian linearizations at different velocities and slip values. The control problem is formulated as a model-matching control problem within the LPV framework; a specific modification of the LPV control synthesis algorithm is proposed to alleviate controller interpolation problems. Linear and nonlinear simulations indicate that the synthesized controller achieves the required robustness and performance. Copyright © 2008 John Wiley & Sons, Ltd.

Fault‐tolerant control synthesis for a class of nonlinear systems: Sum of squares optimization approach

Abstract: This paper studies the fault-tolerant control (FTC) problem for nonlinear systems, with guaranteed cost or H∞ performance objective in the presence of actuator faults. The faulty mode is built as a multi-model framework of the typical aberration in actuator effectiveness. The novelty of this paper is that the effect of the nonlinear terms is described as an index in order to transform the FTC design problem into a semi-definite programming. The proposed optimization approach is to find zero optimum for this index. Combined with other performance indexes, the conceived multi-objective optimization problem is solved by using sum of squares method in a reliable and efficient manner. Numerical examples are included to verify the applicability of this new approach for the nonlinear FTC synthesis. Copyright © 2008 John Wiley & Sons, Ltd.

A backstepping design for directed formation control of three‐coleader agents in the plane

Abstract: This paper deals with a directed formation control problem of three agents moving in the plane, where the agents have a cyclic ordering with each one required to maintain a nominated distance from its neighbor, and each agent is described by a double integrator Firstly, a directed formation control law based on the knowledge only of the neighbor's direction is designed by using the integrator backstepping technique, which can not only accomplish the desired triangle formation but also ensure that speeds of all agents converge to a common value without collision between each other during the motion Then, with the purpose of relaxing and even overcoming the restriction of initial conditions of the agents owing to collision avoidance, we introduce the inter-agent potential functions into the design The convergence of the proposed control algorithms is proved by using tools from LaSalle's invariance principle Simulation results are provided to illustrate the effectiveness of the control laws Copyright © 2008 John Wiley & Sons, Ltd

Kalman filtering over unreliable communication networks with bounded Markovian packet dropouts

Abstract: We address the peak covariance stability of time-varying Kalman filter with possible packet losses in transmitting measurement outputs to the filter via a packet-based network. The packet losses are assumed to be bounded and driven by a finite-state Markov process. It is shown that if the observability index of the discrete-time linear time-invariant (LTI) system under investigation is one, the Kalman filter is peak covariance stable under no additional condition. For discrete LTI systems with observability index greater than one, a sufficient condition for peak covariance stability is obtained in terms of the system dynamics and the probability transition matrix of the Markov chain. Finally, the validity of these results is demonstrated by numerical simulations. Copyright © 2008 John Wiley & Sons, Ltd.

Integrated fault detection and control for LPV systems

Abstract: This paper studies the integrated fault detection and control problem for linear parameter-varying systems. A parameter-dependent detector/controller is designed to generate two signals: residual and control signals that are used to detect faults and simultaneously meet some control objectives. The low-frequency faults and certain finite-frequency disturbances are considered. With the aid of the newly developed linearization techniques, the design methods are presented in terms of solutions to a set of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed methods. Copyright © 2008 John Wiley & Sons, Ltd.

A switching system approach to actuator assignment with limited channels

Abstract: The problem of integrated design of controller and communication sequences is addressed for networked control systems with simultaneous consideration of medium access limitations and network-induced delays, packet dropouts and measurement quantization. By exploiting a Lyapunov–Krasovskii functional and by making use of novel techniques for switching delay systems, it is shown that linear time invariant systems can be stabilized with delay-dependent state feedback controllers and communication sequences satisfying appropriate delay-dependent conditions in terms of linear matrix inequalities. Illustrative examples are provided to show the usefulness and advantage of the developed results. Copyright © 2009 John Wiley & Sons, Ltd.

Global continuous finite-time tracking of robot manipulators

Abstract: This paper addresses the global finite-time tracking of robot manipulators. The commonly used linear proportional-derivative (PD) plus (PD+) scheme is extended to achieve the global finite-time tracking by replacing the linear errors with nonsmooth but continuous exponential errors. The global finite-time stability of the closed loop with the proposed nonlinear PD plus control is shown using Lyapunov's direct method and finite-time stability. Simulations performed on a two-degree-of-freedom manipulator are provided to illustrate the effectiveness and the improved performance of the formulated algorithm. Copyright © 2008 John Wiley & Sons, Ltd.

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

Abstract: 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

Semiautonomous control of multiple networked lagrangian systems

Abstract: In this paper we study the problem of coordinating the positions of a group of Lagrangian systems with communication constraints exhibited through delays and limited data rates. We show that in a bidirectional connected communication graph structure, it is possible to design PD-type control laws that render the overall nonnetworked system input-to-state stable. Then, we exploit the robustness property of these control laws along with a small-gain condition on the allowable delays to infer the stability of the overall networked system. We illustrate how the obtained results can be specialized to handle the problem of position–position control for three networked 2DOF manipulators as well as teleoperation of robotic formations. Copyright © 2008 John Wiley & Sons, Ltd.

Model predictive control for networked control systems

Abstract: This paper investigates the problem of model predictive control for a class of networked control systems. Both sensor-to-controller and controller-to-actuator delays are considered and described by Markovian chains. The resulting closed-loop systems are written as jump linear systems with two modes. The control scheme is characterized as a constrained delay-dependent optimization problem of the worst-case quadratic cost over an infinite horizon at each sampling instant. A linear matrix inequality approach for the controller synthesis is developed. It is shown that the proposed state feedback model predictive controller guarantees the stochastic stability of the closed-loop system. Copyright © 2008 John Wiley & Sons, Ltd.

Fuzzy model‐based fault detection for Markov jump systems

Abstract: The robust fault detection filter (RFDF) design problems are studied for nonlinear stochastic time-delay Markov jump systems. By means of the Takagi–Sugeno fuzzy models, the fuzzy RFDF system and the dynamics of filtering error generator are constructed. Moreover, taking into account the sensitivity to faults while guaranteeing robustness against unknown inputs, the H∞ filtering scheme is proposed to minimize the influences of the unknown inputs and another new performance index is introduced to enhance the sensitivity to faults. A sufficient condition is first established on the stochastic stability using stochastic Lyapunov–Krasovskii function. Then in terms of linear matrix inequalities techniques, the sufficient conditions on the existence of fuzzy RFDF are presented and proved. Finally, the design problem is formulated as a two-objective optimization algorithm. Simulation results illustrate that the proposed RFDF can detect the faults shortly after the occurrences. Copyright © 2008 John Wiley & Sons, Ltd.