# Showing papers in "IEEE Transactions on Automatic Control in 1992"

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TL;DR: The stability of a queueing network with interdependent servers is considered and a policy is obtained which is optimal in the sense that its Stability Region is a superset of the stability region of every other scheduling policy, and this stability region is characterized.

Abstract: The stability of a queueing network with interdependent servers is considered. The dependency among the servers is described by the definition of their subsets that can be activated simultaneously. Multihop radio networks provide a motivation for the consideration of this system. The problem of scheduling the server activation under the constraints imposed by the dependency among servers is studied. The performance criterion of a scheduling policy is its throughput that is characterized by its stability region, that is, the set of vectors of arrival and service rates for which the system is stable. A policy is obtained which is optimal in the sense that its stability region is a superset of the stability region of every other scheduling policy, and this stability region is characterized. The behavior of the network is studied for arrival rates that lie outside the stability region. Implications of the results in certain types of concurrent database and parallel processing systems are discussed. >

2,892 citations

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TL;DR: The paper presents an SA algorithm that is based on a simultaneous perturbation gradient approximation instead of the standard finite-difference approximation of Keifer-Wolfowitz type procedures that can be significantly more efficient than the standard algorithms in large-dimensional problems.

Abstract: The problem of finding a root of the multivariate gradient equation that arises in function minimization is considered. When only noisy measurements of the function are available, a stochastic approximation (SA) algorithm for the general Kiefer-Wolfowitz type is appropriate for estimating the root. The paper presents an SA algorithm that is based on a simultaneous perturbation gradient approximation instead of the standard finite-difference approximation of Keifer-Wolfowitz type procedures. Theory and numerical experience indicate that the algorithm can be significantly more efficient than the standard algorithms in large-dimensional problems. >

1,912 citations

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TL;DR: In this paper, an observer for nonlinear systems is constructed under rather general technical assumptions (the fact that some functions are globally Lipschitz) and a tentative application to biological systems is described.

Abstract: An observer for nonlinear systems is constructed under rather general technical assumptions (the fact that some functions are globally Lipschitz). This observer works either for autonomous systems or for nonlinear systems that are observable for any input. A tentative application to biological systems is described. >

1,701 citations

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TL;DR: In this article, the results on L2-gain analysis of smooth nonlinear systems are unified and extended using an approach based on Hamilton-Jacobi equations and inequalities, and their relation to invariant manifolds of an associated Hamiltonian vector field.

Abstract: Previously obtained results on L2-gain analysis of smooth nonlinear systems are unified and extended using an approach based on Hamilton-Jacobi equations and inequalities, and their relation to invariant manifolds of an associated Hamiltonian vector field. On the basis of these results a nonlinear analog is obtained of the simplest part of a state-space approach to linear H/sub infinity / control, namely the state feedback H/sub infinity / optimal control problem. Furthermore, the relation with H/sub infinity / control of the linearized system is dealt with. >

1,415 citations

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TL;DR: In this article, a design procedure is introduced which incorporates loop shaping methods to obtain performance/robust stability tradeoffs, and a particular H/sub infinity / optimization problem to guarantee closed-loop stability and a level of robust stability at all frequencies.

Abstract: A design procedure is introduced which incorporates loop shaping methods to obtain performance/robust stability tradeoffs, and a particular H/sub infinity / optimization problem to guarantee closed-loop stability and a level of robust stability at all frequencies. Theoretical justification of this technique is given, and the effect of loop shaping on closed-loop behavior is examined. The procedure is illustrated in a controller design for a flexible space platform. >

990 citations

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TL;DR: In this paper, a stabilizing adaptive controller for a nonlinear system depending affinely on some unknown parameters is presented, where the adaptive law is designed using the Lyapunov equation.

Abstract: A stabilizing adaptive controller for a nonlinear system depending affinely on some unknown parameters is presented. It is assumed that this system is feedback stabilizable. A key feature of the method is the use of the Lyapunov equation to design the adaptive law. A result on local stability, two different conditions for global stability, and a local result where the initial conditions of the state of the system only are restricted are given. >

934 citations

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TL;DR: In this article, a solution to the problem of disturbance attenuation via measurement feedback with internal stability is presented for an affine nonlinear system, in which the concept of truncated L/sub 2/ norms can be given an interpretation in terms of the response to periodic inputs in the sense of RMS amplitude, even in the nonlinear setup.

Abstract: A solution to the problem of disturbance attenuation via measurement feedback with internal stability is presented for an affine nonlinear system. It is shown that the concept of disturbance attenuation, in the sense of truncated L/sub 2/ norms, can be given an interpretation in terms of the response to periodic inputs in the sense of RMS amplitude, even in the nonlinear setup. In the case of state feedback, a family of controllers is also provided. The proofs of all these results are simple and provide deeper insight even in the analysis of the corresponding linear control problem. >

846 citations

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TL;DR: In this article, a class of inherently nonlinear control problems arising directly from physical assumptions about constraints on the motion of a mechanical system is identified and a general procedure for constructing a piecewise analytic state feedback which achieves the desired result is suggested.

Abstract: A class of inherently nonlinear control problems has been identified, the nonlinear features arising directly from physical assumptions about constraints on the motion of a mechanical system. Models are presented for mechanical systems with nonholonomic constraints represented both by differential-algebraic equations and by reduced state equations. Control issues for this class of systems are studied and a number of fundamental results are derived. Although a single equilibrium solution cannot be asymptotically stabilized using continuous state feedback, a general procedure for constructing a piecewise analytic state feedback which achieves the desired result is suggested. >

840 citations

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TL;DR: In this paper, the authors studied stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties, and showed that all second moment stability properties are equivalent and are sufficient for almost sure sample path stabilisation.

Abstract: Jump linear systems are defined as a family of linear systems with randomly jumping parameters (usually governed by a Markov jump process) and are used to model systems subject to failures or changes in structure. The authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties. It is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability, and a testable necessary and sufficient condition for second moment stability is derived. The Lyapunov exponent method for the study of almost sure sample stability is discussed, and a theorem which characterizes the Lyapunov exponents of jump linear systems is presented. Finally, for one-dimensional jump linear system, it is proved that the region for delta -moment stability is monotonically converging to the region for almost sure stability at delta down arrow 0/sup +/. >

702 citations

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TL;DR: In this article, a methodology for the design of reliable centralized and decentralized control systems is developed, and the resulting control systems are reliable in that they provide guaranteed stability and H/sub infinity / performance not only when all control components are operational, but also for sensor or actuator outages in the centralized case, or for control-channel outages for the decentralized case.

Abstract: A methodology for the design of reliable centralized and decentralized control systems is developed. The resulting control systems are reliable in that they provide guaranteed stability and H/sub infinity / performance not only when all control components are operational, but also for sensor or actuator outages in the centralized case, or for control-channel outages in the decentralized case. Reliability is guaranteed provided these outages occur only within a prespecified subset of control components. Strongly stabilizing designs are also developed, for both centralized and decentralized systems. >

695 citations

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TL;DR: In this paper, a design of reduced-order observers for linear systems with unknown inputs is presented with a straightforward treatment, and explanations are given within the framework of descriptor system observer design principles.

Abstract: With a straightforward treatment, a design of reduced-order observers is presented for linear systems with unknown inputs. The observers are derived with a physical meaning. Some explanations are given within the framework of descriptor system observer design principles. The conditions for the existence of the observers are presented. Some illustrative examples are included. >

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TL;DR: In this paper, an approximate input-output linearization of nonlinear systems which fail to have a well defined relative degree is studied, and a method for constructing approximate systems that are input output linearizable is provided.

Abstract: Approximate input-output linearization of nonlinear systems which fail to have a well defined relative degree is studied. For such systems, a method for constructing approximate systems that are input-output linearizable is provided. The analysis presented is motivated through its application to a common undergraduate control laboratory experiment-the ball and beam-where it is shown to be more effective for trajectory tracking than the standard Jacobian linearization. >

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TL;DR: A lifting technique is used to describe the continuous-time (i.e., intersample) behavior of sampled-data systems, and to obtain a complete solution to the problem of parameterizing all controllers that constrain the L/sup 2/-induced norm of a sampled- data system to within a certain bound.

Abstract: The authors present a framework for dealing with continuous-time periodic systems. The main tool is a lifting technique which provides a strong correspondence between continuous-time periodic systems and certain types of discrete-time time-invariant systems with infinite-dimensional input and output spaces. Despite the infinite dimensionality of the input and output spaces, a lifted system has a finite-dimensional state space if the original system does. This fact permits rather constructive methods for analyzing these systems. As a demonstration of the utility of this framework, the authors use it to describe the continuous-time (i.e., intersample) behavior of sampled-data systems, and to obtain a complete solution to the problem of parameterizing all controllers that constrain the L/sup 2/-induced norm of a sampled-data system to within a certain bound. >

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TL;DR: In this paper, an exponentially stable controller for a two-degree-of-freedom robot with nonholonomic constraints is presented, which is shown to be nonstabilizable via pure smooth feedback.

Abstract: An exponentially stable controller for a two-degree-of-freedom robot with nonholonomic constraints is presented. Although this type of system is open-loop controllable, this system has been shown to be nonstabilizable via pure smooth feedback. A particular class of piecewise continuous controllers is shown to exponentially stabilize the mobile robot about the origin. This controller has the characteristic of not requiring infinite switching like other approaches, such as the sliding controller. Simulation results are presented. >

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TL;DR: In this article, a singularity function method is presented which consists of cascaded branches of a number of pole-zero (negative real) pairs or simple RC section, which can be simulated by a combination of singularity functions, each representing a single-fractal system.

Abstract: A fractional slope on the log log Bode plot has been observed in characterizing a certain type of physical phenomenon and has been called the fractal system or the fractional power pole. In order to represent and study its dynamical behavior, a singularity function method is presented which consists of cascaded branches of a number of pole-zero (negative real) pairs or simple RC section. The distribution spectrum of the system can also be easily calculated, and its accuracy depends on a prescribed error specified in the beginning. The method is then extended to a multiple-fractal system which consists of a number of fractional power poles. The result can be simulated by a combination of singularity functions, each representing a single-fractal system. >

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TL;DR: In this article, a robust H/sub infinity / control design for linear systems with uncertainty in both the state and input matrices is treated, and a state feedback control design which stabilizes the plant and guarantees an H/ sub infinity /-norm bound constraint on disturbance attenuation for all admissible uncertainties is presented.

Abstract: Robust H/sub infinity / control design for linear systems with uncertainty in both the state and input matrices is treated. A state feedback control design which stabilizes the plant and guarantees an H/sub infinity /-norm bound constraint on disturbance attenuation for all admissible uncertainties is presented. The robust H/sub infinity / control problem is solved via the notion of quadratic stabilization with an H/sub infinity /-norm bound. Necessary and sufficient conditions for quadratic stabilization with an H/sub infinity /-norm bound are derived. The results can be regarded as extensions of existing results on H/sub infinity / control and robust stabilization of uncertain linear systems. >

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TL;DR: In this paper, the robust H/sub infinity / control problem of designing a linear dynamic output feedback controller such that the closed-loop system is quadratically stable and achieves a prescribed level of disturbance attenuation for all admissible parameter uncertainties is considered.

Abstract: The article concerns linear systems which are subject to both time-varying norm-bounded parameter uncertainty and exogenous disturbance It addresses the robust H/sub infinity / control problem of designing a linear dynamic output feedback controller such that the closed-loop system is quadratically stable and achieves a prescribed level of disturbance attenuation for all admissible parameter uncertainties It is shown that such a problem is equivalent to a scaled H/sub infinity / control problem >

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TL;DR: In this article, a necessary and sufficient condition is given for the existence of a solution to the problem of finding decentralized supervisors that ensure that the behavior of the closed-loop system lies in a given range.

Abstract: Decentralized supervisory control is investigated by considering problem formulations that model systems whose specifications are given as global constraints, but whose solution is described by local controllers. A necessary and sufficient condition is given for the existence of a solution to the problem of finding decentralized supervisors that ensure that the behavior of the closed-loop system lies in a given range. Where the range of behavior can be described by regular languages, it can be effectively tested whether the decentralized control problem is solvable; in this case, a procedure is given to compute the associated supervisors. >

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TL;DR: The model validation problem addressed is: given experimental data and a model with both additive noise and norm-bounded perturbations, is it possible that the model could produce the observed input-output data?

Abstract: The gap between the models used in control synthesis and those obtained from identification experiments is considered by investigating the connection between uncertain models and data. The model validation problem addressed is: given experimental data and a model with both additive noise and norm-bounded perturbations, is it possible that the model could produce the observed input-output data? This problem is studied for the standard H/sub infinity // mu framework models. A necessary condition for such a model to describe an experimental datum is obtained. For a large class of models in the robust control framework, this condition is computable as the solution of a quadratic optimization problem. >

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TL;DR: In this article, a robust nonlinear control law for n-link robot manipulators is derived using the Lyapunov-based theory of guaranteed stability of uncertain systems, where the uncertainty bounds needed to derive the control law and to prove uniform ultimate boundedness of the tracking error depend only on the inertial parameters of the robot.

Abstract: A simple robust nonlinear control law for n-link robot manipulators is derived using the Lyapunov-based theory of guaranteed stability of uncertain systems. The novelty of this result lies in the fact that the uncertainty bounds needed to derive the control law and to prove uniform ultimate boundedness of the tracking error depend only on the inertial parameters of the robot. In previous results of this type, the uncertainty bounds have depended not only on the inertia parameters but also on the reference trajectory and on the manipulator state vector. The presented result also removes previous assumptions regarding closeness in norm of the computed inertia matrix to the actual inertial matrix. The design used thus provides the simplest such robust design available to date. >

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TL;DR: The paper concludes by showing how the obtained error bounds can be used for intelligent model order selection that takes into account both measurement noise and under-model- ing.

Abstract: Previous results on estimating errors or error bounds on identified transfer functions have relied on prior assumptions about the noise and the unmodeled dynamics. This prior information took the form of parameterized bounding functions or parameterized probability density functions, in the time or frequency domain with known parameters. It is shown that the parameters that quantify this prior information can themselves be estimated from the data using a maximum likelihood technique. This significantly reduces the prior information required to estimate transfer function error bounds. The authors illustrate the usefulness of the method with a number of simulation examples. How the obtained error bounds can be used for intelligent model-order selection that takes into account both measurement noise and under-modeling is shown. Another simulation study compares the method to Akaike's well-known FPE and AIC criteria. >

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TL;DR: The hysteresis switching algorithm of R.H. Middleton et al. as discussed by the authors is applied to various families of identifier-based parameterized controllers of both the direct and indirect control types.

Abstract: The hysteresis switching algorithm of R.H. Middleton et al. (ibid., vol.33, no.1, p.50-8, Jan. 1988) is reexamined in a broader context. To demonstrate its utility, the algorithm is applied to various families of identifier-based parameterized controllers of both the direct and indirect control types. Application to the direct control type results in a model reference adaptive controller capable of stabilizing, without excitation, any SISO process which can be modeled by a minimum phase linear system whose transfer function has relative and McMillan degrees not exceeding prescribing integers m and n, respectively. It is shown that such processes can also be adaptively stabilized with indirect adaptive controllers and hysteresis switching. A simple numerical example involving a non-minimum-phase process model is used to illustrate how hysteresis switching might be applied to implicitly tuned parameterized controllers to realize an adaptive controller with capabilities which might prove very difficult, if not impossible, to achieve without hysteresis switching or some other form of discontinuous control. >

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TL;DR: In this paper, a method of compensating for friction in control systems is presented, which involves the use of an observer to estimate the friction which is modeled as a constant times the sign of the velocity.

Abstract: A method of compensating for friction in control systems is presented. The method entails the use of an observer to estimate the friction which is modeled as a constant times the sign of the velocity. The purpose of the observer is to estimate this constant. The observer model is selected to ensure that the error in estimation of the friction constant converges asymptotically to zero. Simulation results verify the theory and show that the method can significantly improve the performance of a control system in which it is used. Although based on the assumption of a constant friction magnitude, the observer displays the ability to 'track' friction whose magnitude depends on velocity. >

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TL;DR: In this article, the problem of determining global adaptive observers for a class of single-output nonlinear systems which are linear with respect to an unknown constant parameter vector is addressed, and sufficient conditions are given to observe asymptotically an equivalent state without persistency of excitation.

Abstract: The problem of determining global adaptive observers for a class of single-output nonlinear systems which are linear with respect to an unknown constant parameter vector is addressed. Sufficient conditions are given to observe asymptotically an equivalent state without persistency of excitation. Under additional geometric conditions the original state can be observed as well. The results obtained are based on a nonlinear change of coordinates driven by auxiliary filters (filtered transformations). >

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TL;DR: In this article, the effects of state disturbances, output noise, and errors in initial conditions on a class of learning control algorithms are investigated, and bounds on the asymptotic trajectory errors for the learned input and the corresponding state and output trajectories are obtained.

Abstract: The authors investigate the effects of state disturbances, output noise, and errors in initial conditions on a class of learning control algorithms. They present a simple learning algorithm and exhibit, via a concise proof, bounds on the asymptotic trajectory errors for the learned input and the corresponding state and output trajectories. Furthermore, these bounds are continuous functions of the bounds on the initial condition errors, state disturbances, and output noise, and the bounds are zero in the absence of these disturbances. >

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TL;DR: In this paper, the measurement-target association problem is formulated as one of maximizing the joint likelihood function of the measurement partition, which leads to a generalization of the 3D assignment (matching) problem, which is known to be NP hard.

Abstract: The static problem of associating measurements at a given time from three angle-only sensors in the presence of clutter, missed detections, and an unknown number of targets is addressed. The measurement-target association problem is formulated as one of maximizing the joint likelihood function of the measurement partition. Mathematically, this formulation leads to a generalization of the 3-D assignment (matching) problem, which is known to be NP hard. The solution to the optimization problem developed is a Lagrangian relaxation technique that successively solves a series of generalized two-dimensional (2-D) assignment problems. The algorithm is illustrated by several application examples. >

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TL;DR: In this article, the authors considered a general representation of interconnections when the strength of the interconnection is bounded by a pth-order polynomial in states, and designed two adaptive controllers with partially centralized compensation and a fully adaptive decentralized controller.

Abstract: Decentralized robust adaptive controller designs for large-scale interconnected systems are investigated. Motivated by real mechanical systems, the authors consider a general representation of interconnections when the strength of the interconnections is bounded by a pth-order polynomial in states. This is in contrast to other studies which have made simpler assumptions about the strength of the interconnections. The authors investigate several scenarios as the control computations become more distributed until the controllers are completely decentralized. The possible bound of the interconnections is assumed to be known for the decentralized semiadaptive controller. Without the knowledge of these bounds, two adaptive controllers are designed: a decentralized adaptive controller with partially centralized compensation and a fully adaptive decentralized controller. >

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TL;DR: In this paper, an adaptive control scheme for flexible joint robot manipulators is presented, and joint position and velocity tracking errors are shown to converge to zero with all the signals in the system remaining bounded.

Abstract: Presents an adaptive control scheme for flexible joint robot manipulators. Asymptotic stability is insured regardless of the joint flexibility value, i.e., the results are not restricted to weak joint elasticity. Moreover, the joint flexibility is not assumed to be known. Joint position and velocity tracking errors are shown to converge to zero with all the signals in the system remaining bounded. >

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TL;DR: In this paper, a design procedure was developed that combines linear-quadratic optimal control with regional pole placement, in which the poles of the closed-loop system are constrained to lie in specified regions of the complex plane.

Abstract: A design procedure is developed that combines linear-quadratic optimal control with regional pole placement. Specifically, a static and dynamic output-feedback control problem is addressed in which the poles of the closed-loop system are constrained to lie in specified regions of the complex plane. These regional pole constraints are embedded within the optimization process by replacing the covariance Lyapunov equation by a modified Lyapunov equation whose solution, in certain cases, leads to an upper bound on the quadratic cost functional. The results include necessary and sufficient conditions for characterizing static output-feedback controllers with bounded performance and regional pole constraints. Sufficient conditions are also presented for the fixed-order (i.e. full- and reduced-order) dynamic output-feedback problem with regional pole constraints. Circular, elliptical, vertical strip, parabolic, and section regions are considered. >

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TL;DR: In this paper, a frequency-response identification technique and a robust control design method are used to set up such an iterative scheme, where each identification step uses the previously designed controller to obtain new data from the plant and the associated identification problem has been solved by means of a coprime factorization of the unknown plant.

Abstract: If approximate identification and model-based control design are used to accomplish a high-performance control system, then the two procedures must be treated as a joint problem. Solving this joint problem by means of separate identification and control design procedures practically entails an iterative scheme. A frequency-response identification technique and a robust control design method are used to set up such an iterative scheme. Each identification step uses the previously designed controller to obtain new data from the plant. The associated identification problem has been solved by means of a coprime factorization of the unknown plant. The technique's utility is illustrated by an example. >