Showing papers in "IEEE Transactions on Automatic Control in 2002"

Stability analysis and control synthesis for switched systems: a switched Lyapunov function approach

Abstract: This paper addresses the problem of stability analysis and control synthesis of switched systems in the discrete-time domain. The approach followed in this paper looks at the existence of a switched quadratic Lyapunov function to check asymptotic stability of the switched system under consideration. Two different linear matrix inequality-based conditions allow to check the existence of such a Lyapunov function. The first one is classical while the second is new and uses a slack variable, which makes it useful for design problems. These two conditions are proved to be equivalent for stability analysis. Investigating the static output feedback control problem, we show that the second condition is, in this case, less conservative. The reduction of the conservatism is illustrated by a numerical evaluation.

Synthesis of mechanical networks: the inerter

Abstract: The paper is concerned with the problem of synthesis of (passive) mechanical one-port networks. One of the main contributions of the paper is the introduction of a device, which win be called the inerter, which is the true network dual of the spring. This contrasts with the mass element which, by definition, always has one terminal connected to ground. The inerter allows electrical circuits to be translated over to mechanical ones in a completely analogous way. The inerter need not have large mass. This allows any arbitrary positive-real impedance to be synthesized mechanically using physical components which may be assumed to have small mass compared to other structures to which they may be attached. The possible application of the inerter is considered to a vibration absorption problem, a suspension strut design, and as a simulated.

Distributed control of spatially invariant systems

Abstract: We consider distributed parameter systems where the underlying dynamics are spatially invariant, and where the controls and measurements are spatially distributed. These systems arise in many applications such as the control of vehicular platoons, flow control, microelectromechanical systems (MEMS), smart structures, and systems described by partial differential equations with constant coefficients and distributed controls and measurements. For fully actuated distributed control problems involving quadratic criteria such as linear quadratic regulator (LQR), H/sub 2/ and H/sub /spl infin//, optimal controllers can be obtained by solving a parameterized family of standard finite-dimensional problems. We show that optimal controllers have an inherent degree of decentralization, and this provides a practical distributed controller architecture. We also prove a general result that applies to partially distributed control and a variety of performance criteria, stating that optimal controllers inherit the spatial invariance structure of the plant. Connections of this work to that on systems over rings, and systems with dynamical symmetries are discussed.

Analysis and design of controllers for AQM routers supporting TCP flows

Abstract: In active queue management (AQM), core routers signal transmission control protocol (TCP) sources with the objective of managing queue utilization and delay. It is essentially a feedback control problem. Based on a recently developed dynamic model of TCP congestion-avoidance mode, this paper does three things: 1) it relates key network parameters such as the number of TCP sessions, link capacity and round-trip time to the underlying feedback control problem; 2) it analyzes the present de facto AQM standard: random early detection (RED) and determines that REDs queue-averaging is not beneficial; and 3) it recommends alternative AQM schemes which amount to classical proportional and proportional-integral control. We illustrate our results using ns simulations and demonstrate the practical impact of proportional-integral control on managing queue utilization and delay.

An improved stabilization method for linear time-delay systems

Abstract: In this paper, we combine a new approach for linear time delay systems based on a descriptor representation with a recent result on bounding of cross products of vectors. A delay-dependent criterion for determining the stability of systems with time-varying delays is obtained. This criterion is used to derive an efficient stabilizing state-feedback design method for systems with parameter uncertainty, of either the polytopic or the norm-bounded types.

Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment

Abstract: We consider the application of a formulation of passivity-based control (PBC), known as interconnection and damping assignment (IDA) to the problem of stabilization of underactuated mechanical systems, which requires the modification of both the potential and the kinetic energies. Our main contribution is the characterization of a class of systems for which IDA-PBC yields a smooth asymptotically stabilizing controller with a guaranteed domain of attraction. The class is given in terms of solvability of certain partial differential equations. One important feature of IDA-PBC, stemming from its Hamiltonian formulation, is that it provides new degrees of freedom for the solution of these equations. Using this additional freedom, we are able to show that the method of "controlled Lagrangians"-in its original formulation-may be viewed as a special case of our approach. As illustrations we design asymptotically stabilizing IDA-PBCs for the classical ball and beam system and a novel inertia wheel pendulum.

A descriptor system approach to H/sub /spl infin// control of linear time-delay systems

Abstract: The output-feedback H/sub /spl infin// control problem is solved for continuous-time, linear, retarded and neutral-type systems. A delay-dependent solution is obtained in terms of linear matrix inequalities (LMIs) by using a descriptor model transformation of the system and by applying P. Park's inequality (1999) for bounding cross-terms. A state-feedback solution is derived for systems with polytopic parameter uncertainties. An output-feedback controller is then found by solving two LMIs, one of which is associated with a descriptor time-delay "innovation filter". The cases of instantaneous and delayed measurements are considered. Numerical examples are given which illustrate the effectiveness of the new theory.

Model predictive control based on linear programming - the explicit solution

Abstract: We study model predictive control (MPC) schemes for discrete-time linear time-invariant systems with constraints on inputs and states, that can be formulated using a linear program (LP). In particular, we focus our attention on performance criteria based on a mixed 1 -norm, namely, 1-norm with respect to time and -norm with respect to space. First we provide a method to compute the terminal weight so that closed-loop stability is achieved. We then show that the optimal control profile is a piecewise affine and continuous function of the initial state and briefly describe the algorithm to compute it. The piecewise affine form allows to eliminate online LP, as the computation associated with MPC becomes a simple function evaluation. Besides practical advantages, the availability of the explicit structure of the MPC controller provides an insight into the type of control action in different regions of the state space, and highlights possible conditions of degeneracies of the LP, such as multiple optima.

Robust stability and stabilization for singular systems with state delay and parameter uncertainty

Abstract: Considers the problems of robust stability and stabilization for uncertain continuous singular systems with state delay. The parametric uncertainty is assumed to be norm bounded. The purpose of the robust stability problem is to give conditions such that the uncertain singular system is regular, impulse free, and stable for all admissible uncertainties, while the purpose of the robust stabilization is to design a state feedback control law such that the resulting closed-loop system is robustly stable. These problems are solved via the notions of generalized quadratic stability and generalized quadratic stabilization, respectively. Necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are derived. A strict linear matrix inequality (LMI) design approach is developed. An explicit expression for the desired robust state feedback control law is also given. Finally, a numerical example is provided to demonstrate the application of the proposed method.

A Lyapunov approach to incremental stability properties

Abstract: Deals with several notions of incremental stability. In other words, the focus is on stability of trajectories with respect to one another, rather than with respect to some attractor. The aim is to present a framework for understanding such questions fully compatible with the well-known input-to-state stability approach. Applications of the newly introduced stability notions are also discussed.

An exact method for the stability analysis of time-delayed linear time-invariant (LTI) systems

Abstract: A general class of linear time invariant systems with time delay is studied. Recently, they attracted considerable interest in the systems and control community. The complexity arises due to the exponential type transcendental terms in their characteristic equation. The transcendentality brings infinitely many characteristic roots, which are cumbersome to elaborate as evident from the literature. A number of methodologies have been suggested with limited ability to assess the stability in the parametric domain of time delay. This study offers an exact, structured and robust methodology to bring a closure to the question at hand. Ultimately we present a unique explicit analytical expression in terms of the system parameters which not only reveals the stability regions (pockets) in the domain of time delay, but it also declares the number of unstable characteristic roots at any given pocket. The method starts with the determination of all possible purely imaginary (resonant) characteristic roots for any positive time delay. To achieve this a simplifying substitution is used for the transcendental terms in the characteristic equation. It is proven that the number of such resonant roots for a given dynamics is finite. Each one of these roots is created by infinitely many time delays, which are periodically distributed. An interesting property is also claimed next, that the root crossing directions at these locations are invariant with respect to the delay and dependent only on the crossing frequency. These two unique findings facilitate a simple and practical stability method, which is the highlight of the work.

A robust detection and isolation scheme for abrupt and incipient faults in nonlinear systems

Abstract: This paper presents a robust fault diagnosis scheme for abrupt and incipient faults in nonlinear uncertain dynamic systems. A detection and approximation estimator is used for online health monitoring. Once a fault is detected, a bank of isolation estimators is activated for the purpose of fault isolation. A key design issue of the proposed fault isolation scheme is the adaptive residual threshold associated with each isolation estimator. A fault that has occurred can be isolated if the residual associated with the matched isolation estimator remains below its corresponding adaptive threshold, whereas at least one of the components of the residuals associated with all the other estimators exceeds its threshold at some finite time. Based on the class of nonlinear uncertain systems under consideration, an isolation decision scheme is devised and fault isolability conditions are given, characterizing the class of nonlinear faults that are isolable by the robust fault isolation scheme. The nonconservativeness of the fault isolability conditions is illustrated by deriving a subclass of nonlinear systems and of faults for which these conditions are also necessary for fault isolability. Moreover, the analysis of the proposed fault isolation scheme provides rigorous analytical results concerning the fault isolation time. Two simulation examples are given to show the effectiveness of the fault diagnosis methodology.

Adaptive control of nonlinearly parameterized systems: the smooth feedback case

Abstract: Studies global adaptive control of nonlinearly parameterized systems with uncontrollable linearization. Using a parameter separation technique and the tool of adding a power integrator, we develop a feedback domination design approach for the explicit construction of a smooth adaptive controller that solves the problem of global state regulation. In contrast to the existing results in the literature, a key feature of our adaptive regulator is its minimum-order property, namely, no matter how big the number of unknown parameters is, the order of the dynamic compensator is identical to one, and is therefore minimal. As a consequence, global state regulation of feedback linearizable systems with nonlinear parameterization is achieved by one-dimensional adaptive controllers, without imposing any extra (e.g., convex/concave) conditions on the unknown parameters.

Exponential stability of stochastic delay interval systems with Markovian switching

Abstract: In the past few years, a lot of research has been dedicated to the stability of interval systems as well as the stability of systems with Markovian switching. However, little research has been on the stability of interval systems with Markovian switching, which is the topic of this paper. The system discussed is the stochastic delay interval system with Markovian switching. It is a very advanced system and takes all the features of interval systems, Ito equations, and Markovian switching, as well as time lag, into account. The theory developed is applicable in many different and complicated situations so the importance of the paper is clear.

Output feedback control of a class of nonlinear systems: a nonseparation principle paradigm

Abstract: Considers the problem of global stabilization by output feedback, for a family of nonlinear systems that are dominated by a triangular system satisfying a linear growth condition. The problem has remained unsolved due to the violation of the commonly assumed conditions in the literature. Using a feedback domination design method which is not based on the separation principle, we explicitly construct a linear output compensator making the closed-loop system globally exponentially stable.

Adaptive observer for multiple-input-multiple-output (MIMO) linear time-varying systems

Abstract: For joint state-parameter estimation in linear time-varying (LTV) multiple-input-multiple-output (MIMO) systems, an approach to the design of adaptive observers is proposed. It is conceptually simple and computationally efficient. Its global exponential convergence is established for noise-free systems. In the presence of noises, it is proved that the estimation errors are bounded and converge in the mean to zero if the noises are bounded and have zero means. Potential applications are fault detection and isolation, and adaptive control.

New results on the synthesis of PID controllers

Abstract: This paper considers the problem of stabilizing a first-order plant with dead time using a proportional-integral-derivative (PID) controller. Using a version of the Hermite-Biehler theorem that is applicable to quasi-polynomials, the complete set of stabilizing PID parameters is determined for both open-loop stable and unstable plants. The range of admissible proportional gains is first determined in closed form. For each proportional gain in this range, the stabilizing set in the space of the integral and derivative gains is shown to be either a trapezoid, a triangle or a quadrilateral. For the case of an open-loop unstable plant, a necessary and sufficient condition on the time delay is determined for the existence of stabilizing PID controllers.

Single state elastoplastic friction models

Abstract: For control applications involving small displacements and velocities, friction modeling and compensation can be very important. In particular, the modeling of presliding displacement (motion prior to fully developed slip) can play a pivotal role. In this paper, it is shown that existing single-state friction models exhibit a nonphysical drift phenomenon which results from modeling presliding as a combination of elastic and plastic displacement. A new class of single state models is defined in which presliding is elastoplastic: under loading, frictional displacement is first purely elastic and then transitions to plastic. The new model class is demonstrated to substantially reduce drift while preserving the favorable properties of existing models (e.g., dissipativity) and to provide a comparable match to experimental data.

Polynomial-time verification of diagnosability of partially observed discrete-event systems

Abstract: The problem of verifying the properties of diagnosability and I-diagnosability is considered. We present new polynomial-time algorithms for deciding diagnosability and I-diagnosability. These algorithms are based on the construction of a nondeterministic automaton called a verifier.

Robust H/spl infin/ control for uncertain stochastic systems with state delay

Abstract: This note deals with the problems of robust stochastic stabilization and robust H ∞ control for uncertain stochastic systems with a time-varying delay in the state. The parameter uncertainties are assumed to be time-varying norm-bounded appearing in both the state and input matrices. The purpose of the robust stochastic stabilization problem is the design of a memoryless state feedback controller such that the closed-loop system is mean-square asymptotically stable for all admissible uncertainties. In the robust H ∞ control problem, in addition to the mean-square asymptotic stability requirement, a prescribed H ∞ performance is required to be achieved. In terms of a linear matrix inequality, sufficient conditions for the solvability of these problems are proposed respectively; the expressions of desired state feedback controllers are given. An example illustrating the proposed approach is provided.

Adaptive control of nonlinearly parameterized systems: a nonsmooth feedback framework

Abstract: This paper introduces a nonsmooth framework for global adaptive control of a significant class of nonlinearly parameterized systems with uncontrollable unstable linearization. While there may not exist any smooth static or dynamic stabilizer due to the violation of the well-known necessary condition, we give sufficient conditions for the existence of non-Lipschitz continuous adaptive regulators that achieve global stability with asymptotic state regulation. A constructive design method is developed based on an effective coupling of a new parameter separation technique and the tool of adding a power integrator, leading to C/sup 0/ adaptive regulators with minimal parameterization. Indeed, the dimension of the proposed dynamic compensator can always be one, irrespective of the number of unknown parameters. The power of our continuous adaptive control strategy is demonstrated by solving a number of challenging adaptive stabilization problems that have remained open for more than a decade.

Impulse differential inclusions: a viability approach to hybrid systems

Abstract: Impulse differential inclusions are introduced as a framework for modeling hybrid phenomena. Connections to standard problems in the area of hybrid systems are discussed. Conditions are derived that allow one to determine whether a set of states is viable or invariant under the action of an impulse differential inclusion. For sets that violate these conditions, methods are developed for approximating their viability and invariance kernels, that is the largest subset that is viable or invariant under the action of the impulse differential inclusion. The results are demonstrated on examples.

Technical Note: modification of the Leuven integrated friction model structure

Abstract: This note presents a modification of the integrated friction model structure proposed by Swevers et al. (2000), called the Leuven model. The Leuven model structure allows accurate modeling both in the presliding and the sliding regimes without the use of a switching function. The model incorporates a hysteresis function with nonlocal memory and arbitrary transition curves. This note presents two modifications of the Leuven model. A first modification overcomes a recently detected shortcoming of the original Leuven model: a discontinuity in the friction force which occurs during certain transitions in presliding. A second modification, using the general Maxwell slip model to implement the hysteresis force, eliminates the problem of stack overflow, which can occur with the implementation of the hysteresis force.

A new approach to state observation of nonlinear systems with delayed output

Abstract: The article presents a new approach for the construction of a state observer for nonlinear systems when the output measurements are available for computations after a nonnegligible time delay. The proposed observer consists of a chain of observation algorithms reconstructing the system state at different delayed time instants (chain observer). Conditions are given for ensuring global exponential convergence to zero of the observation error for any given delay in the measurements. The implementation of the observer is simple and computer simulations demonstrate its effectiveness.

Modification of the Leuven integrated friction model structure

Abstract: This note presents a modification of the integrated friction model structure proposed by Swevers et al. (2000), called the Leuven model. The Leuven model structure allows accurate modeling both in the presliding and the sliding regimes without the use of a switching function. The model incorporates a hysteresis function with nonlocal memory and arbitrary transition curves. This note presents two modifications of the Leuven model. A first modification overcomes a recently detected shortcoming of the original Leuven model: a discontinuity in the friction force which occurs during certain transitions in presliding. A second modification, using the general Maxwell slip model to implement the hysteresis force, eliminates the problem of stack overflow, which can occur with the implementation of the hysteresis force.

An adaptive actuator failure compensation controller using output feedback

Abstract: An adaptive control scheme using output feedback for output tracking is developed for systems with unknown actuator failures. Such actuator failures are characterized by some unknown inputs stuck at some unknown fixed values at unknown time instants. An effective output feedback controller structure is proposed for actuator failure compensation. When implemented with true matching parameters, the controller achieves desired plant-model output matching. When implemented with adaptive parameter estimates, the controller achieves asymptotic output tracking. A stable adaptive law is derived for parameter adaptation in the presence of parameter uncertainties. Closed-loop signal boundedness and asymptotic output tracking, despite the uncertainties in actuator failures and plant parameters, are ensured analytically and verified by simulation results.

Comment on "A new method for the nonlinear transformation of means and covariances in filters and estimators" [with authors' reply]

Abstract: The above paper (Julier et al. IEEE Trans. Automat. Contr, vol. 45, pp. 477-82, 2000) generalizes the Kalman filter to nonlinear systems by transforming approximations of the probability distributions through the nonlinear process and measurement functions. This comment derives exactly the same estimator by linearizing the process and measurement functions by a statistical linear regression through some regression points (in contrast with the extended Kalman filter which uses an analytic linearization in one point). This insight allows one: 1) to understand/predict the performance of the estimator for specific applications, and 2) to make adaptations to the estimator (i.e., the choice of the regression points and their weights) in those cases where the original formulation does not assure good results. In reply the authors state that the commenters conclusion is unnecessarily narrow interpretation of results.

Should model-based inverse inputs be used as feedforward under plant uncertainty?

Abstract: Bounds on the size of the plant uncertainties are found such that the use of the inversion-based feedforward input improves the output-tracking performance when compared to the use of feedback alone. The output-tracking error is normalized by the size of the desired output and used as a measure of the output tracking performance. The worst-case performance is compared for two cases: (1) with the use of feedback alone and (2) with the addition of the feedforward input. It is shown that inversion-based feedforward controllers can lead to performance improvements at frequencies w where the uncertainty /spl Delta/ (jw) in the nominal plant is smaller than the size of the nominal plant G/sub 0/(jw) divided by its condition number K/sub G0/ (jw), i.e., /spl par//spl Delta/(jw)/spl par//sub 2/ < /spl par/G/sub 0/(jw) /spl par//sub 2//k/sub G0/ (jw). A modified feedforward input is proposed that only uses the model information in frequency regions where plant uncertainty is sufficiently small. The use of this modified inverse with (any) feedback results in improvement of the output tracking performance, when compared to the use of the feedback alone.

Underactuated ship global tracking under relaxed conditions

Abstract: A controller is developed for underactuated surface ships with only surge force and yaw moment available to globally asymptotically track a reference trajectory generated by a suitable virtual ship in a frame attached to the ship body. The reference trajectory is allowed too be a curve including a straight line. The control development is based on Lyapunov's direct method and backstepping technique, and utilizes several properties of ship dynamics and their interconnected structure. Numerical simulations are provided to validate the effectiveness of the proposed controller.

On stabilization of bilinear uncertain time-delay stochastic systems with Markovian jumping parameters

Abstract: In this paper, we investigate the stochastic stabilization problem for a class of bilinear continuous time-delay uncertain systems with Markovian jumping parameters. Specifically, the stochastic bilinear jump system under study involves unknown state time-delay, parameter uncertainties, and unknown nonlinear deterministic disturbances. The jumping parameters considered here form a continuous-time discrete-state homogeneous Markov process. The whole system may be regarded as a stochastic bilinear hybrid system that includes both time-evolving and event-driven mechanisms. Our attention is focused on the design of a robust state-feedback controller such that, for all admissible uncertainties as well as nonlinear disturbances, the closed-loop system is stochastically exponentially stable in the mean square, independent of the time delay. Sufficient conditions are established to guarantee the existence of desired robust controllers, which are given in terms of the solutions to a set of either linear matrix inequalities (LMIs), or coupled quadratic matrix inequalities. The developed theory is illustrated by numerical simulation.