Showing papers in "IEEE Transactions on Automatic Control in 1989"
TL;DR: In this article, simple state-space formulas are derived for all controllers solving the following standard H/sub infinity / problem: for a given number gamma > 0, find all controllers such that the H/ sub infinity / norm of the closed-loop transfer function is (strictly) less than gamma.
Abstract: Simple state-space formulas are derived for all controllers solving the following standard H/sub infinity / problem: For a given number gamma >0, find all controllers such that the H/sub infinity / norm of the closed-loop transfer function is (strictly) less than gamma . It is known that a controller exists if and only if the unique stabilizing solutions to two algebraic Riccati equations are positive definite and the spectral radius of their product is less than gamma /sup 2/. Under these conditions, a parameterization of all controllers solving the problem is given as a linear fractional transformation (LFT) on a contractive, stable, free parameter. The state dimension of the coefficient matrix for the LFT, constructed using the two Riccati solutions, equals that of the plant and has a separation structure reminiscent of classical LQG (i.e. H/sub 2/) theory. This paper is intended to be of tutorial value, so a standard H/sub 2/ solution is developed in parallel. >
5,272 citations
TL;DR: In this paper, it was shown that coprime right factorizations exist for the input-to-state mapping of a continuous-time nonlinear system provided that the smooth feedback stabilization problem is solvable for this system.
Abstract: It is shown that coprime right factorizations exist for the input-to-state mapping of a continuous-time nonlinear system provided that the smooth feedback stabilization problem is solvable for this system. It follows that feedback linearizable systems admit such fabrications. In order to establish the result, a Lyapunov-theoretic definition is proposed for bounded-input-bounded-output stability. The notion of stability studied in the state-space nonlinear control literature is related to a notion of stability under bounded control perturbations analogous to those studied in operator-theoretic approaches to systems; in particular it is proved that smooth stabilization implies smooth input-to-state stabilization. >
2,504 citations
TL;DR: In this paper, a control law for teleoperators is presented which overcomes the instability caused by time delay by using passivity and scattering theory, a criterion is developed which shows why existing bilateral control systems are unstable for certain environments, and why the proposed bilateral control law is stable for any environment and any time delay.
Abstract: A control law for teleoperators is presented which overcomes the instability caused by time delay. By using passivity and scattering theory, a criterion is developed which shows why existing bilateral control systems are unstable for certain environments, and why the proposed bilateral control law is stable for any environment and any time delay. The control law has been implemented on a single-axis force-reflecting hand controller, and preliminary results are shown. To keep the presentation clear, a single-degree-of-freedom (DOF) linear time-invariant (LTI) teleoperator system is discussed. Nevertheless, results can be extended, without loss of generality, to an n-DOF nonlinear teleoperation system. >
2,131 citations
TL;DR: In this paper, the adaptive control of minimum-phase nonlinear systems which are exactly input-output linearizable by state feedback is discussed. But the application of the adaptive technique to control of robot manipulators is discussed only in the continuous-time case.
Abstract: The authors give some initial results on the adaptive control of minimum-phase nonlinear systems which are exactly input-output linearizable by state feedback. Parameter adaptation is used as a technique to make robust the exact cancellation of nonlinear terms, which is called for in the linearization technique. The application of the adaptive technique to control of robot manipulators is discussed. Only the continuous-time case is considered; extensions to the discrete-time and sampled-data cases are not obvious. >
1,182 citations
TL;DR: In this article, an LQG (linear quadratic Gaussian) control-design problem involving a constraint on H/sup infinity / disturbance attenuation is considered, and an algorithm is developed for the full-order design problem and illustrative numerical results are given.
Abstract: An LQG (linear quadratic Gaussian) control-design problem involving a constraint on H/sup infinity / disturbance attenuation is considered. The H/sup infinity / performance constraint is embedded within the optimization process by replacing the covariance Lyapunov equation by a Riccati equation whose solution leads to an upper bound on L/sub 2/ performance. In contrast to the pair of separated Riccati equations of standard LQG theory, the H/sup infinity /-constrained gains are given by a coupled system of three modified Riccati equations. The coupling illustrates the breakdown of the separation principle for the H/sup infinity /-constrained problem. Both full- and reduced-order design problems are considered with an H/sup infinity / attenuation constraint involving both state and control variables. An algorithm is developed for the full-order design problem and illustrative numerical results are given. >
865 citations
TL;DR: In this article, the problem of robustly stabilizing a family of linear systems is explicitly solved in the case where the family is characterized by H/sub infinity / bounded perturbations to the numerator and denominator of the normalized left coprime factorization of a nominal system.
Abstract: The problem of robustly stabilizing a family of linear systems is explicitly solved in the case where the family is characterized by H/sub infinity / bounded perturbations to the numerator and denominator of the normalized left coprime factorization of a nominal system. This problem can be reduced to a Nehari extension problem directly and gives an optimal stability margin. All controllers satisfying a suboptimal stability margin are characterized, and explicit state-space formulas are given. >
707 citations
TL;DR: In this article, a solution to the problem of detecting and identifying control system component failures in linear, time-invariant systems is given using the geometric concept of an unobservability subspace.
Abstract: Using the geometric concept of an unobservability subspace, a solution is given to the problem of detecting and identifying control system component failures in linear, time-invariant systems. Conditions are developed for the existence of a causal, linear, time-invariant processor that can detect and uniquely identify a component failure, first for the case where components can fail simultaneously, and then for the case where they fail only one at a time. Explicit design algorithms are provided when these conditions are satisfied. In addition to time-domain solvability conditions, frequency-domain interpretations of the results are given, and connections are drawn with results already available in the literature. >
605 citations
TL;DR: It is shown that a not-necessarily-balanced state-space realization of the Moore reduced model can be computed directly without balancing via projections defined in terms of arbitrary bases for the left and right eigenspaces associated with the large eigenvalues of the product PQ of the reachability and controllability Grammians.
Abstract: It is shown that a not-necessarily-balanced state-space realization of the Moore reduced model can be computed directly without balancing via projections defined in terms of arbitrary bases for the left and right eigenspaces associated with the large eigenvalues of the product PQ of the reachability and controllability Grammians Two specific methods for computing these bases are proposed, one based on the ordered Schur decomposition of PQ and the other based on the Cholesky factors of P and Q The algorithms perform reliably even for nonminimal models >
593 citations
TL;DR: This paper considers the problem of passing from a linear time-invariant high order controller designed for a linearTimeInvariant plant (of presumably high order) to a low order approximation of the controller.
Abstract: The problem of passing from a linear time-invariant high-order controller designed for a linear time-invariant plant (of presumably high order) to a low-order approximation of the controller is discussed. The approximation problem is often best posed as a frequency-weighted L/sub infinity / approximation problem. Many different controller representations are possible, giving different performances of the various reduction algorithms. >
502 citations
TL;DR: In this article, a decentralized adaptive control scheme for a class of large-scale interconnected systems is presented, which has the advantage that in addition to the standard assumption about the uncertainty of the subsystems, the strength of interconnection is assumed unknown.
Abstract: Decentralized adaptive control schemes are presented for a class of large-scale interconnected systems. These schemes have the advantage that in addition to the standard assumption about the uncertainty of the subsystems, the strength of interconnection is assumed unknown. Provided certain structural constraints are satisfied, the adaptation gains automatically adjust to levels that assure stability of the overall system. Simulations of a spring-coupled dual pendulum showed that for high interconnection strengths, the proposed algorithm exhibits better tracking performance than existing algorithms. >
420 citations
TL;DR: In this paper, an adaptive update law which counteracts the effects of unknown parameters is shown to be robust to the unmodeled dynamics, and conditions are given for global stability of an adaptive control law designed for the reduced-order model of a class of nonlinear plants.
Abstract: A feedback linearization design is presented which includes unknown parameters and unmodeled dynamics. An adaptive update law which counteracts the effects of unknown parameters is shown to be robust to the unmodeled dynamics. The proposed design methodology is based on a conceptually simple stability analysis. Conditions are given for global stability of an adaptive control law designed for the reduced-order model of a class of nonlinear plants. In the presence of unmodeled dynamics, the regulation property is preserved in a stability region. The size of the region is estimated using bounds that not only prove robustness, but also allow a comparison between adaptive and nonadaptive nonlinear controls. >
TL;DR: In this paper, the authors consider general flexible manufacturing/assembly/disassembly systems with the following features: (i) there are several types, each with given processing time requirements at a specified sequence of machines; (ii) each part type needs to be produced at a prespecified rate; parts may incur variable transportation delays when moving from one machine to another; set-up times are required whenever a machine changes from a production run of parts of one type to a run of another type; some part types may also need assembly or disassembly; and (iii) a proportion of
Abstract: The authors consider general flexible manufacturing/assembly/disassembly systems with the following features: (i) there are several types, each with given processing time requirements at a specified sequence of machines; (ii) each part type needs to be produced at a prespecified rate; (iii) parts may incur variable transportation delays when moving from one machine to another; (iv) set-up times are required whenever a machine changes from a production run of parts of one type to a run of another type; (v) some part types may also need assembly or disassembly; and (vi) a proportion of parts of a part type may require separate routing on exiting from a machine, for reasons including, but not limited to, poor quality. The authors exhibit a class of scheduling policies implementable in real time in a distributed way at the various machines, which ensure that the cumulative production of each part type trails the desired production by no more than a specific constant. The buffers of all the machines are guaranteed to be bounded, and the system can thus operate with finite buffer capacities. >
TL;DR: In this article, the kinematics of rolling contact are derived for two surfaces of arbitrary shape rolling on each other, and a scheme is presented for the control of such a hand which is a generalization of the computed torque method of control of robot manipulators.
Abstract: The kinematics of rolling contact are derived for two surfaces of arbitrary shape rolling on each other. The kinematic equations are applied to a multifingered hand manipulating some object of arbitrary shape in three dimensions, and a scheme is presented for the control of such a hand which is a generalization of the computed torque method of control of robot manipulators. In implementing the control, it is required that all applied forces lie within the friction cone of the object so that sliding does not occur. The theory has been validated by dynamic graphical simulations of the resulting closed-loop system for several examples. >
TL;DR: It is shown in particular that, given any desired product mix, it is possible to start the system with enough jobs in process so that some machines will be fully utilized in steady-state and the productivity is optimal.
Abstract: Timed event-graphs, a special class of timed Petri nets, are used for modelling and analyzing job-shop systems. The modelling allows the steady-state performance of the system to be evaluated under a deterministic and cyclic production process. Given any fixed processing times, the productivity (i.e., production rate) of the system can be determined from the initial state. It is shown in particular that, given any desired product mix, it is possible to start the system with enough jobs in process so that some machines will be fully utilized in steady-state. These machines are called bottleneck machines, since they limit the throughput of the system. In that case, the system works at the maximal rate and the productivity is optimal. The minimal number of jobs in process allowing optimal functioning of the system is further specified as an integer linear programming problem. An efficient heuristic algorithm is developed to obtain a near-optimal solution. >
TL;DR: The results obtained in studies of robust stability and stabilizability of control systems with parametric (structured) uncertainties are reviewed in this paper, where both the algebraic methods based upon characteristic equations and the methods using Lyapunov functions and Riccati equations are discussed and compared.
Abstract: The results obtained in studies of robust stability and stabilizability of control systems with parametric (structured) uncertainties are reviewed. Both the algebraic methods based upon characteristic equations and the methods using Lyapunov functions and Riccati equations are discussed and compared. In the context of algebraic methods, most promising are the Kharitonov-type approach and the optimization procedure of embedding a geometric figure of some kind inside the stability regions of the parameter space, maximizing its size using minimax or some other mathematical programming technique. In the framework of Lyapunov's direct method, the dominant approach has been a quadratic function estimation of stability regions in the parameter space. In large-sale systems, the concept of vector Lyapunov functions has been used with the possibility of choosing quadratic forms, norm-like functions, and their combinations. >
TL;DR: In this article, the authors generalized the four-polynomial concept to the case of linearly dependent coefficient perturbations and more general zero location regions and proposed a specially constructed scalar function of a scalar variable for robustness analysis.
Abstract: Kharitonov's four-polynomial concept is generalized to the case of linearly dependent coefficient perturbations and more general zero location regions. To this end, a specially constructed scalar function of a scalar variable is instrumental to the robustness analysis. The present work is motivated by two fundamental limitations of Kharitonov's theorem, namely: (1) the theorem only applies to polynomials with independent coefficient perturbations and (2) it only applies to zeros in the left-hand plane. >
TL;DR: A method is discussed for changing the network to speed up the simulation of a rare event, using a heuristic method, which can be several orders of magnitude faster than direct simulations.
Abstract: Excessive backlogs in stable open Jackson networks are studied. Although these events occur rarely, they can be critical, since they can impair the functioning of the network. The use of simulation to estimate their probability is attempted. Since a direct simulation of a rare event takes a very long time, a method is discussed for changing the network to speed up the simulation, using a heuristic method. It is shown by examples that the method can be several orders of magnitude faster than direct simulations. >
TL;DR: In this article, a necessary and sufficient condition for the robust stabilization of interval plants is developed, using a generalization of V. L. Kharitonov's theorem (1978).
Abstract: The robust stability problem is considered for interval plants, in the case of single input (multioutput) or single output (multi-input) systems. A necessary and sufficient condition for the robust stabilization of such plants is developed, using a generalization of V. L. Kharitonov's theorem (1978). The generalization given provides necessary and sufficient conditions for the stability of a family of polynomials delta (s)=Q/sub 1/(s)P/sub 1/(s)+ . . . +Q/sub m/(s)P/sub m/(s), where the Q/sub i/ are fixed and the P/sub i/ are interval polynomials, the coefficients of which are regarded as a point in parameter space which varies within a prescribed box. This generalization, called the box theorem, reduces the question of the stability of the box, in parameter space to the equivalent problem of the stability of a prescribed set of line segments. It is shown that for special classes of polynomials Q/sub i/(s) the set of line segments collapses to a set of points, and this version of the box theorem in turn reduces to Kharitonov's original theorem. >
TL;DR: In this paper, the tightest possible bound has been obtained for the absolute magnitude of the Euclidean 2 or infinity norm of the time-domain response of a multioutput system to certain classes of input disturbance.
Abstract: Some norms are derived for convolution and Hankel operators associated with linear, time-invariant systems. In certain cases, these norms are shown to be identical. The tightest possible bound has been obtained for the absolute magnitude of the Euclidean 2 or infinity norm of the time-domain response of a multioutput system to certain classes of input disturbance. >
TL;DR: In this article, the authors present an approximate method for the analysis of transfer lines with unreliable machines and finite buffers, which leads to a simple and fast algorithm which provides performance parameters such as production rate and average buffer levels.
Abstract: The authors present an approximate method for the analysis of transfer lines with unreliable machines and finite buffers. In these systems blocking and starvation, which occur as a consequence of machine failures, are important phenomena. They first consider homogeneous lines, i.e., lines for which all machines have the same processing times. The behavior of the line is approximated by a continuous flow model. They then use a decomposition technique which enables one to decompose the analysis of the line into the analysis of a set of two-machine lines. This leads to a simple and fast algorithm which provides performance parameters such as production rate and average buffer levels. Experimental results show that this approximate technique is very accurate. They then consider the case of transfer lines with machines having different processing times. A simple transformation is introduced which replaces the line by a homogeneous line. This approximate transformation provides good results for a large class of systems. >
TL;DR: In this paper, the authors consider a class of time-varying systems with uncertain input and parameters and present sufficient conditions on the open loop to obtain an arbitrary-degree closed-loop stability.
Abstract: The authors consider a class of time-varying systems with time-varying state delay and uncertain input and parameters. They present sufficient conditions on the open loop to obtain an arbitrary-degree closed-loop stability. They construct a min-max controller from knowledge of the upper bound of the delay. >
TL;DR: In this article, a constructive methodology for estimating stability regions of general nonlinear dynamical systems is developed, which starts with a given Lyapunov function and yields a sequence of LyAPunov functions which are then used to estimate the stability region.
Abstract: A constructive methodology for estimating stability regions of general nonlinear dynamical systems is developed. The constructive methodology starts with a given Lyapunov function (either a global or a local Lyapunov function) and yields a sequence of Lyapunov functions which are then used to estimate the stability region. The resulting sequence of estimated stability regions is shown to be a strictly monotonic increasing sequence, and yet each of them remains inside the entire stability region. The significance of this methodology includes: its ability to reduce significantly the conservativeness in estimating the stability regions; its computational efficiency; its adaptability; and its sound theoretical basis. >
TL;DR: In this article, the existence of an ideal equivalence among sliding regimes of variable-structure feedback control and pulsewidth-modulated (PWM) control responses in nonlinear dynamical systems is demonstrated.
Abstract: The author demonstrates, under the assumption of high-frequency control switchings, the existence of an ideal equivalence among sliding regimes of variable-structure feedback control and pulse-width-modulated (PWM) control responses in nonlinear dynamical systems. This equivalence constitutes the basis for a geometric approach approach to PWM control loops design. An illustrate example of energy conversion in a lossless switched-controlled bilinear network is presented. >
TL;DR: In this article, a novel approach to the control of induction motors is presented, based on differential-geometric concepts for control of nonlinear systems, which yields, by means of static state-feedback, exact state linearization and input-output decoupling of the closed-loop system.
Abstract: A novel approach to the control of induction motors is presented. The approach is based on differential-geometric concepts for the control of nonlinear systems. Structural properties of the model are pointed out, and a proper selection of physically meaningful system outputs is indicated which yields, by means of static state-feedback, exact state linearization and input-output decoupling of the closed-loop system. The approach is used to design a controller for motor torque and flux. Simulation results are included. >
TL;DR: In this article, a stability criterion for linear time-delay systems described by a differential difference equation of the form dx(t)=Ax(t)+Bx(t- tau ) is proposed.
Abstract: A stability criterion for linear time-delay systems described by a differential difference equation of the form dx(t)=Ax(t)+Bx(t- tau ) is proposed. The result obtained includes information on the size of the delay and therefore can be a delay-dependent stability condition. Its relation to existing delay-independent stability criteria is also discussed. >
TL;DR: In this paper, the robust stability problem for a class of uncertain delay systems where the characteristic equations involve a polytope P of quasi-polynomials (i.e. polynomials in one complex variable and exponential powers of the variable) is discussed.
Abstract: The robust stability problem is discussed for a class of uncertain delay systems where the characteristic equations involve a polytope P of quasi-polynomials (i.e. polynomials in one complex variable and exponential powers of the variable). Given a set D in the complex plane, the goal is to find a constructive technique to verify whether all roots of every quasi-polynomial in P belong to D (that is, to verify the D-stability of P). First it is demonstrated by counterexample that Kharitonov's theorem does not hold for general delay systems. Next it is shown that under a mild assumption on the set D a polytope of quasi-polynomials is D-stable if and only if the edges of the polytope are D-stable. This extends the edge theorem for the D-stability of a polytope of polynomials. The third result gives a constructive graphical test for checking the D-stability of a polytope of quasi-polynomials which is especially simple when the set D is the open left-half plane. An application is given to demonstrate the power of the results. >
TL;DR: The perfect state information case in which the stations can use the instantaneous value of the backlog to compute the retransmission probability is studied first, and the vest throughput possible for a decentralized control protocol is obtained, as well as an algorithm that achieves it.
Abstract: A decentralized control algorithm is sought that maximizes the stability region of the infinite-user slotted multipacket channel and is easily implementable. To this end, the perfect state information case in which the stations can use the instantaneous value of the backlog to compute the retransmission probability is studied first. The vest throughput possible for a decentralized control protocol is obtained, as well as an algorithm that achieves it. These results are then applied to derive a control scheme when the backlog is unknown, which is the case of practical relevance. This scheme, based on a binary feedback, is shown to be optimal, given some restrictions on the channel multipacket reception capability. >
TL;DR: A class of iterative aggregation algorithms for solving infinite horizon dynamic programming problems is proposed, to interject aggregation iterations in the course of the usual successive approximation method, which allows acceleration of convergence in difficult problems involving multiple-ergodic classes.
Abstract: A class of iterative aggregation algorithms for solving infinite horizon dynamic programming problems is proposed. The idea is to interject aggregation iterations in the course of the usual successive approximation method. An important feature that sets this method apart from earlier ones is that the aggregate groups of states change adaptively from one aggregation iteration to the next, depending on the progress of the computation. This allows acceleration of convergence in difficult problems involving multiple-ergodic classes for which methods using fixed groups of aggregate states are ineffective. No knowledge of special problem structure is utilized by the algorithms. >
TL;DR: In this article, a Fourier series-based method for approximation of stable infinite-dimensional linear time-invariant system models is discussed, where the Fourier coefficients can be replaced by the discrete Fourier transform coefficients while maintaining H/sup infinity / convergence.
Abstract: A Fourier series-based method for approximation of stable infinite-dimensional linear time-invariant system models is discussed. The basic idea is to compute the Fourier series coefficients of the associated transfer function T/sub d/(Z) and then take a high-order partial sum. Two results on H/sup infinity / convergence and associated error bounds of the partial sum approximation are established. It is shown that the Fourier coefficients can be replaced by the discrete Fourier transform coefficients while maintaining H/sup infinity / convergence. Thus, a fast Fourier transform algorithm can be used to compute the high-order approximation. This high-order finite-dimensional approximation can then be reduced using balanced truncation or optimal Hankel approximation leading to the final finite-dimensional approximation to the original infinite-dimensional model. This model has been tested on several transfer functions of the time-delay type with promising results. >
TL;DR: In this article, a method is described which exactly characterizes the set of all the values of the parameter vector of a linear model that are consistent with bounded errors on the measurements, and provides a parameterized expression of this set, which can be used for robust control design or for optimizing any criterion over the set.
Abstract: A method is described which exactly characterizes the set of all the values of the parameter vector of a linear model that are consistent with bounded errors on the measurements. It provides a parameterized expression of this set, which can be used for robust control design or for optimizing any criterion over the set. This approach is based on a new variant of the double description method for determining the edges of a polyhedral cone. It can be used in real time and provides a suitable context for implementation on a computer. Whenever a new measurement modifies the set, the characterization is updated. The technique is illustrated with a simple example. >