# Showing papers in "IEEE Transactions on Automatic Control in 1999"

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TL;DR: In this article, a fractional-order PI/sup/spl lambda/D/sup /spl mu/controller with fractionalorder integrator and fractional order differentiator is proposed.

Abstract: Dynamic systems of an arbitrary real order (fractional-order systems) are considered. The concept of a fractional-order PI/sup /spl lambda//D/sup /spl mu//-controller, involving fractional-order integrator and fractional-order differentiator, is proposed. The Laplace transform formula for a new function of the Mittag-Leffler-type made it possible to obtain explicit analytical expressions for the unit-step and unit-impulse response of a linear fractional-order system with fractional-order controller for both open- and closed-loops. An example demonstrating the use of the obtained formulas and the advantages of the proposed PI/sup /spl lambda//D/sup /spl mu//-controllers is given.

2,479 citations

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TL;DR: A new class of feedback control problems is introduced, which cannot be asymptotically stabilized if the underlying dynamics are unstable, and a weaker stability concept called containability is introduced.

Abstract: For part I, see ibid., vol.42, p.1294-8, 1997. In this paper a new class of feedback control problems is introduced. Unlike classical models, the systems considered here have communication channel constraints. As a result, the issue of coding and communication protocol becomes an integral part of the analysis. Since these systems cannot be asymptotically stabilized if the underlying dynamics are unstable, a weaker stability concept called containability is introduced. A key result connects containability with an inequality equation involving the communication data rate and the rate of change of the state.

923 citations

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TL;DR: It is shown that the estimation error remains bounded if the system satisfies the nonlinear observability rank condition and the initial estimation error as well as the disturbing noise terms are small enough.

Abstract: The authors analyze the error behavior for the discrete-time extended Kalman filter for general nonlinear systems in a stochastic framework. In particular, it is shown that the estimation error remains bounded if the system satisfies the nonlinear observability rank condition and the initial estimation error as well as the disturbing noise terms are small enough. This result is verified by numerical simulations for an example system.

867 citations

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TL;DR: A new delay-dependent robust stability criterion for systems with time-invariant uncertain delays is derived, which is shown by an example less conservative than existing stability criteria.

Abstract: This paper provides a new stability criterion for systems with time-invariant uncertain delays. Based on an improved upper bound for the inner product of two vectors, a new delay-dependent robust stability criterion is derived, which is shown by an example less conservative than existing stability criteria.

844 citations

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TL;DR: Discusses analysis and synthesis techniques for robust pole placement in linear matrix inequality (LMI) regions, a class of convex regions of the complex plane that embraces most practically useful stability regions, and describes the effectiveness of this robust pole clustering technique.

Abstract: Discusses analysis and synthesis techniques for robust pole placement in linear matrix inequality (LMI) regions, a class of convex regions of the complex plane that embraces most practically useful stability regions. The focus is on linear systems with static uncertainty on the state matrix. For this class of uncertain systems, the notion of quadratic stability and the related robustness analysis tests are generalized to arbitrary LMI regions. The resulting tests for robust pole clustering are all numerically tractable because they involve solving linear matrix inequalities (LMIs) and cover both unstructured and parameter uncertainty. These analysis results are then applied to the synthesis of dynamic output-feedback controllers that robustly assign the closed-loop poles in a prescribed LMI region. With some conservatism, this problem is again tractable via LMI optimization. In addition, robust pole placement can be combined with other control objectives, such as H/sub 2/ or H/sub /spl infin// performance, to capture realistic sets of design specifications. Physically motivated examples demonstrate the effectiveness of this robust pole clustering technique.

743 citations

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TL;DR: The authors prove that, although the state dimension is not preserved, the number of input channels is kept fixed and it is proved that a Lie-Backlund isomorphism can be realized by an endogenous feedback.

Abstract: A new system equivalence relation, using the framework of differential geometry of jets and prolongations of infinite order, is studied. In this setting, two systems are said to be equivalent if any variable of one system may be expressed as a function of the variables of the other system and of a finite number of their time derivatives. This is a Lie-Backlund isomorphism. The authors prove that, although the state dimension is not preserved, the number of input channels is kept fixed. They also prove that a Lie-Backlund isomorphism can be realized by an endogenous feedback. The differentially flat nonlinear systems introduced by the authors (1992) via differential algebraic techniques, are generalized and the new notion of orbitally flat systems is defined. They correspond to systems which are equivalent to a trivial one, with time preservation or not. The endogenous linearizing feedback is explicitly computed in the case of the VTOL aircraft to track given reference trajectories with stability.

742 citations

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TL;DR: It is shown that the performance of a globally bounded partial state feedback control of an input-output linearizable system can be recovered by a sufficiently fast high-gain observer.

Abstract: It is shown that the performance of a globally bounded partial state feedback control of a certain class of nonlinear systems can be recovered by a sufficiently fast high-gain observer. The performance recovery includes recovery of asymptotic stability of the origin, the region of attraction, and trajectories.

655 citations

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TL;DR: Two suboptimal MPC schemes are presented and analyzed that are guaranteed to be stabilizing, provided an initial feasible solution is available and for which the computational requirements are more reasonable.

Abstract: Practical difficulties involved in implementing stabilizing model predictive control laws for nonlinear systems are well known. Stabilizing formulations of the method normally rely on the assumption that global and exact solutions of nonconvex, nonlinear optimization problems are possible in limited computational time. In the paper, we first establish conditions under which suboptimal model predictive control (MPC) controllers are stabilizing; the conditions are mild holding out the hope that many existing controllers remain stabilizing even if optimality is lost. Second, we present and analyze two suboptimal MPC schemes that are guaranteed to be stabilizing, provided an initial feasible solution is available and for which the computational requirements are more reasonable.

641 citations

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TL;DR: The focus of this paper is to prove a converse Lyapunov theorem for this class of systems in which the dynamics at any instant in time will follow one of a fixed set of vector fields.

Abstract: The authors investigate the stability of a system in which the dynamics at any instant in time will follow one of a fixed set of vector fields. They allow switching between members of the family of vector fields to be completely random. The focus of this paper is to prove a converse Lyapunov theorem for this class of systems.

572 citations

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TL;DR: This paper addresses the problem of robust state feedback control in which both robust stochastic stability and a prescribed H/sub /spl infin// performance are required to be achieved irrespective of the uncertainty and time delay.

Abstract: This paper studies the problem of control for discrete time delay linear systems with Markovian jump parameters. The system under consideration is subjected to both time-varying norm-bounded parameter uncertainty and unknown time delay in the state, and Markovian jump parameters in all system matrices. We address the problem of robust state feedback control in which both robust stochastic stability and a prescribed H/sub /spl infin// performance are required to be achieved irrespective of the uncertainty and time delay. It is shown that the above problem can be solved if a set of coupled linear matrix inequalities has a solution.

521 citations

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TL;DR: A theoretical framework for the dynamics and control of underactuated mechanical systems, defined as systems with fewer inputs than degrees of freedom, is presented and controlability and stabilizability results are derived.

Abstract: This paper presents a theoretical framework for the dynamics and control of underactuated mechanical systems, defined as systems with fewer inputs than degrees of freedom. Control system formulation of underactuated mechanical systems is addressed and a class of underactuated systems characterized by nonintegrable dynamics relations is identified. Controllability and stabilizability results are derived for this class of underactuated systems. Examples are included to illustrate the results; these examples are of underactuated mechanical systems that are not linearly controllable or smoothly stabilizable.

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TL;DR: The authors present linear matrix inequality (LMI) conditions for output feedback control problems and their approach can be used for designing decentralized controllers and is easily extended to H/sub 2/, H/ sub /spl infin// and mixed H/ Sub 2//H/sub /spl Infin// problems via standard LMI techniques.

Abstract: The authors present linear matrix inequality (LMI) conditions for output feedback control problems. The results are based on sufficient conditions because they are dependent on the particular state-space representation used for describing the system. Nevertheless, the conditions are not sensitive to a certain class of state-space transformations, and if the control problem is feasible then there exists some state-space transformation leading the conditions to be necessary and sufficient for the problem. The authors approach can be used for designing decentralized controllers and is easily extended to H/sub 2/, H/sub /spl infin// and mixed H/sub 2//H/sub /spl infin// problems via standard LMI techniques. The continuous- and discrete-time cases are considered and numerical examples are given to illustrate the results.

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TL;DR: A recursive technique is proposed which appears to be an extension of the currently popular integrator backstepping idea to the tracking of nonholonomic control systems.

Abstract: The authors address the tracking problem for a class of nonholonomic chained form control systems. A recursive technique is proposed which appears to be an extension of the currently popular integrator backstepping idea to the tracking of nonholonomic control systems. Conditions are given under which the problems of semiglobal tracking and global path-following are solved for a nonholonomic system in chained form and its dynamic extension. Results on local exponential tracking are also obtained. Two physical examples of an articulated vehicle and a knife edge are provided to demonstrate the effectiveness of our algorithm through simulations.

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TL;DR: The authors present the first result on global output-feedback stabilization (in probability) for stochastic nonlinear continuous-time systems, a stochastically counterpart of the broadest class of deterministic systems for which globally stabilizing controllers are currently available.

Abstract: The authors present the first result on global output-feedback stabilization (in probability) for stochastic nonlinear continuous-time systems. The class of systems that they consider is a stochastic counterpart of the broadest class of deterministic systems for which globally stabilizing controllers are currently available. Their controllers are "inverse optimal" and possess an infinite gain margin. A reader of the paper needs no prior familiarity with techniques of stochastic control.

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TL;DR: The design of a residual generator for fault detection and isolation (FDI) in nonlinear systems which are affine in the control signals and in the failure modes is studied.

Abstract: The design of a residual generator for fault detection and isolation (FDI) in nonlinear systems which are affine in the control signals and in the failure modes is studied, First, the problem statement used for linear systems is extended, and a set of sufficient conditions for the existence of a solution is given. Next, circumstances under which high-gain observers for uniformly observable systems can be used in the synthesis of the residual generator are provided.

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TL;DR: A state estimator is designed such that the covariance of the estimation error is guaranteed to be within a certain bound for all admissible uncertainties, which is in terms of solutions of two sets of coupled algebraic Riccati equations.

Abstract: Studies the problem of Kalman filtering for a class of uncertain linear continuous-time systems with Markovian jumping parameters. The system under consideration is subjected to time-varying norm-bounded parameter uncertainties in the state and measurement equations. Stochastic quadratic stability of the above system is analyzed. A state estimator is designed such that the covariance of the estimation error is guaranteed to be within a certain bound for all admissible uncertainties, which is in terms of solutions of two sets of coupled algebraic Riccati equations.

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TL;DR: The authors propose a stochastic approximation algorithm that tunes weights of a linear combination of basis functions in order to approximate a value function and prove that this algorithm converges and that the limit of convergence has some desirable properties.

Abstract: The authors develop a theory characterizing optimal stopping times for discrete-time ergodic Markov processes with discounted rewards. The theory differs from prior work by its view of per-stage and terminal reward functions as elements of a certain Hilbert space. In addition to a streamlined analysis establishing existence and uniqueness of a solution to Bellman's equation, this approach provides an elegant framework for the study of approximate solutions. In particular, the authors propose a stochastic approximation algorithm that tunes weights of a linear combination of basis functions in order to approximate a value function. They prove that this algorithm converges (almost surely) and that the limit of convergence has some desirable properties. The utility of the approximation method is illustrated via a computational case study involving the pricing of a path dependent financial derivative security that gives rise to an optimal stopping problem with a 100-dimensional state space.

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Supélec

^{1}TL;DR: The authors propose a new adaptive notch filter whose dynamic equations exhibit the following remarkable features: all signals are globally bounded and the estimated frequency is asymptotically correct for all initial conditions and all frequency values.

Abstract: Online estimation of the frequency of a sinusoidal signal is a classical problem in systems theory that has many practical applications. In this paper the authors provide a solution to the problem of ensuring a globally convergent estimation. More specifically, they propose a new adaptive notch filter whose dynamic equations exhibit the following remarkable features: 1) all signals are globally bounded and the estimated frequency is asymptotically correct for all initial conditions and all frequency values; 2) the authors obtain a simple tuning procedure for the estimator design parameters, which trades-off the adaptation tracking capabilities with noise sensitivity, ensuring (exponential) stability of the desired orbit; and 3) transient performance is considerably enhanced, even for small or large frequencies, as witnessed by extensive simulations. To reveal some of the stability-instability mechanisms of the existing algorithms and motivate our modifications the authors make appeal to a novel nonlinear (state-dependent) time scaling. The main advantage of working in the new time scale is that they remove the coupling between the parameter update law and the filter itself, decomposing the system into a feedback form where the required modifications to ensure stability become apparent. Even though they limit their attention here to the simplest case of a single constant frequency without noise the algorithm is able to track time-varying frequencies, preserve local stability in the presence of multiple sinusoids, and is robust with respect to noise.

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TL;DR: Asymptotic stability of a class of linear equations with arbitrary discrete and distributed delays is investigated and the approach of deriving various Riccati equations using the direct Lyapunov method is proposed.

Abstract: Asymptotic stability of a class of linear equations with arbitrary discrete and distributed delays is investigated. Both delay-independent and delay-dependent stability conditions are formulated in terms of existence of positive definite solutions to Riccati matrix equations. The approach of deriving various Riccati equations using the direct Lyapunov method is proposed.

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TL;DR: The authors present an approach for constructing optimal feedback control laws for regulation of a rotating rigid spacecraft using the inverse optimal control approach which circumvents the task of solving a Hamilton-Jacobi equation and results in a controller optimal with respect to a meaningful cost functional.

Abstract: The authors present an approach for constructing optimal feedback control laws for regulation of a rotating rigid spacecraft. They employ the inverse optimal control approach which circumvents the task of solving a Hamilton-Jacobi equation and results in a controller optimal with respect to a meaningful cost functional. The inverse optimality approach requires the knowledge of a control Lyapunov function and a stabilizing control law of a particular form. For the spacecraft problem, they are both constructed using the method of integrator backstepping. The authors give a characterization of (nonlinear) stability margins achieved with the inverse optimal control law.

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TL;DR: Stable direct and indirect decentralized adaptive radial basis neural network controllers are presented for a class of interconnected nonlinear systems that are able to adaptively compensate for disturbances and interconnections with unknown bounds.

Abstract: Stable direct and indirect decentralized adaptive radial basis neural network controllers are presented for a class of interconnected nonlinear systems. The feedback and adaptation mechanisms for each subsystem depend only upon local measurements to provide asymptotic tracking of a reference trajectory. Due to the functional approximation capabilities of radial basis neural networks, the dynamics for each subsystem are not required to be linear in a set of unknown coefficients as is typically required in decentralized adaptive schemes. In addition, each subsystem is able to adaptively compensate for disturbances and interconnections with unknown bounds.

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TL;DR: It is shown that the decreasing Lyapunov function condition leads to a linear matrix inequality (LMI) problem, which points out the connection between a good convergence behavior of the EKO and the instrumental matrices R/ sub k/ and Q/sub k/.

Abstract: The authors show how the extended Kalman filter, used as an observer for nonlinear discrete-time systems or extended Kalman observer (EKO), becomes a useful state estimator when the arbitrary matrices, namely R/sub k/ and Q/sub k/, are adequately chosen. As a first step, we use the linearization technique given by Boutayed et al. (1997), which consists of introducing unknown diagonal matrices to take the approximation errors into account. It is shown that the decreasing Lyapunov function condition leads to a linear matrix inequality (LMI) problem, which points out the connection between a good convergence behavior of the EKO and the instrumental matrices R/sub k/ and Q/sub k/. In order to satisfy the obtained LMI, a particular design of Q/sub k/ is given. High performances of the proposed technique are shown through numerical examples under the worst conditions.

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TL;DR: The adaptive control laws proposed in this paper do not require any dynamic dominating signal to guarantee the robustness property of Lagrange stability and can be regarded as a robustification of the now popular adaptive backstepping algorithm.

Abstract: This paper presents a constructive robust adaptive nonlinear control scheme which can be regarded as a robustification of the now popular adaptive backstepping algorithm. The allowed class of uncertainties includes nonlinearly appearing parametric uncertainty, uncertain nonlinearities, and unmeasured input-to-state stable dynamics. The adaptive control laws proposed in this paper do not require any dynamic dominating signal to guarantee the robustness property of Lagrange stability. The numerical example of a simple pendulum with unknown parameters and without velocity measurement illustrates our theoretical results.

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TL;DR: The asymptotic stability of the impulsive control of a nonlinear system is given and the concept and principles ofImpulsive control are presented.

Abstract: In this paper, the concept and principles of impulsive control are presented. Impulsive control can be applied to a class of systems whose state variables are changeable in a very short time period. In particular, the asymptotic stability of the impulsive control of a nonlinear system is given.

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TL;DR: The authors design a global adaptive output feedback control for a fifth-order model of induction motors, which guarantees asymptotic tracking of smooth speed references on the basis of speed and stator current measurements, for any initial condition and for any unknown constant value of torque load and rotor resistance.

Abstract: The authors design a global adaptive output feedback control for a fifth-order model of induction motors, which guarantees asymptotic tracking of smooth speed references on the basis of speed and stator current measurements, for any initial condition and for any unknown constant value of torque load and rotor resistance. The proposed seventh-order nonlinear compensator generates estimates both for the unknown parameters (torque load and rotor resistance) and for the unmeasured state variables (rotor flux); they converge to the corresponding true values under persistency of excitation which actually holds in typical operating conditions. The control algorithm generates references for the magnetizing flux component and for the torque component of stator current which lead to significant simplification for current-fed motors. Simulations show that the proposed controller is suitable for high dynamic performance applications.

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TL;DR: A dead- time compensator for controlling higher-order processes with integral action and long dead-time is proposed, and the same setpoint response is obtained as in the modified Smith predictor, while the load disturbance rejection is considerably faster.

Abstract: A dead-time compensator for controlling higher-order processes with integral action and long dead-time is proposed. Tuning formulas are derived. If the velocity gain and the dead-time are estimated experimentally, only one parameter, the time constant defining the speed of the closed-loop setpoint response, has to be tuned manually. The same setpoint response is obtained as in the modified Smith predictor, while the load disturbance rejection is considerably faster.

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TL;DR: It is shown that the suggested filter possesses the unbiasedness property and the remarkable deadbeat property irrespective of any horizon initial condition.

Abstract: A receding horizon Kalman FIR filter is presented that combines the Kalman filter and the receding horizon strategy when the horizon initial state is assumed to be unknown. The suggested filter is a FIR filter form which has many good inherent properties. It can always be defined irrespective of singularity problems caused by unknown information about the horizon initial state. The suggested filter can be represented in either an iterative form or a standard FIR form. It is also shown that the suggested filter possesses the unbiasedness property and the remarkable deadbeat property irrespective of any horizon initial condition. The validity of the suggested filter is illustrated by numerical examples.

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TL;DR: The proposed frequency-weighted model reduction method is a generalization of Enns' technique (1984) and yields stable models even when both input and output weightings are included.

Abstract: In this paper, a new frequency-weighted model reduction method with an a priori error bound is proposed. The method is a generalization of Enns' technique (1984) and yields stable models even when both input and output weightings are included. The proposed method is compared with other existing methods using numerical examples.

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TL;DR: The authors propose a method of interpolating linear time-invariant controllers with observer state feedback structure in order to generate a continuously varying family of controllers that stabilizes a family of linear plants.

Abstract: The authors propose a method of interpolating linear time-invariant controllers with observer state feedback structure in order to generate a continuously varying family of controllers that stabilizes a family of linear plants. Gain scheduling is a motivation for this work, and the interpolation method yields guidelines for the design of gain scheduled controllers. The method is illustrated with the design of a missile autopilot using loop-shaping H-infinity controllers.

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TL;DR: A new two-stage Kalman estimator is proposed, i.e., new structure, which is an extension of Friedland's estimator and is optimal in general conditions.

Abstract: The two-stage Kalman estimator was originally proposed to reduce the computational complexity of the augmented state Kalman filter. It was also applied to the tracking of maneuvering targets by treating the target acceleration as a bias term. Except in certain restrictive conditions, the conventional two-stage estimators are suboptimal in the sense that they are not equivalent to the augmented state filter. In this paper, the authors propose a new two-stage Kalman estimator, i.e., new structure, which is an extension of Friedland's estimator and is optimal in general conditions. In addition, we provide some analytic results to demonstrate the computational advantages of two-stage estimators over augmented ones.