Showing papers in "IEEE Transactions on Automatic Control in 1988"
TL;DR: In this paper, a novel approach to hypotheses merging is presented for linear systems with Markovian switching coefficients (dynamic multiple model systems) which is necessary to limit the computational requirements.
Abstract: An important problem in filtering for linear systems with Markovian switching coefficients (dynamic multiple model systems) is the management of hypotheses, which is necessary to limit the computational requirements. A novel approach to hypotheses merging is presented for this problem. The novelty lies in the timing of hypotheses merging. When applied to the problem of filtering for a linear system with Markovian coefficients, the method is an elegant way to derive the interacting-multiple-model (IMM) algorithm. Evaluation of the IMM algorithm shows that it performs well at a relatively low computational load. These results imply a significant change in the state of the art of approximate Bayesian filtering for systems with Markovian coefficients. >
2,342 citations
TL;DR: In this article, a control scheme called repetitive control is proposed, in which the controlled variables follow periodic reference commands, and a high-accuracy asymptotic tracking property is achieved by implementing a model that generates the periodic signals of period L into the closed-loop system.
Abstract: A control scheme called repetitive control is proposed, in which the controlled variables follow periodic reference commands. A high-accuracy asymptotic tracking property is achieved by implementing a model that generates the periodic signals of period L into the closed-loop system. Sufficient conditions for the stability of repetitive control systems and modified repetitive control systems are derived by applying the small-gain theorem and the stability theorem for time-lag systems. Synthesis algorithms are presented by both the state-space approach and the factorization approach. In the former approach, the technique of the Kalman filter and perfect regulation is utilized, while coprime factorization over the matrix ring of proper stable rational functions and the solution of the Hankel norm approximation are used in the latter one. >
1,352 citations
TL;DR: In this article, a simple adaptive controller for manipulator trajectory control problems is proposed, which is shown to have the same level of robustness to unmodeled dynamics as a PD (proportional and differential) controller yet achieves much better tracking accuracy than either PD or computed-torque schemes.
Abstract: The author's previous work (1986, 1987) utilized the particular structure of manipulator dynamics to develop a simple, globally convergent adaptive controller for manipulator trajectory control problems. After summarizing the basic algorithm, they demonstrate the approach on a high-speed two-degree-of-freedom semi-direct-drive robot. They show that the dynamic parameters of the manipulator, assumed to be initially unknown, can be estimated within the first half second of a typical run, and that accordingly, the manipulator trajectory can be precisely controlled. These experimental results demonstrate that the adaptive controller enjoys essentially the same level of robustness to unmodeled dynamics as a PD (proportional and differential) controller, yet achieves much better tracking accuracy than either PD or computed-torque schemes. Its superior performance for high-speed operations, in the presence of parametric and nonparametric uncertainties, and its relative computational simplicity, make it an attractive option both for addressing complex industrial tasks, and for simplifying high-level programming of more standard operations. >
1,013 citations
TL;DR: In this paper, the effects of constraint force required to maintain satisfaction of the constraints are considered, and conditions for stabilization and tracking using feedback are developed using mathematical models for constrained robot dynamics.
Abstract: Mathematical models for constrained robot dynamics, incorporating the effects of constraint force required to maintain satisfaction of the constraints, are used to develop explicit conditions for stabilization and tracking using feedback. The control structure allows feedback of generalized robot displacements, velocities, and the constraint forces. Global conditions for tracking, based on a modified computed-torque controller and local conditions for feedback stabilization, using a linear controller, are presented. The framework is also used to investigate the closed-loop properties if there are force disturbances, dynamics in the force feedback loops, or uncertainty in the constraint functions. >
700 citations
TL;DR: In this article, an integrated approach to the design of practical adaptive control algorithms is presented, where many existing ideas are brought together, and the effect of various design parameters available to a user is explored.
Abstract: An integrated approach to the design of practical adaptive control algorithms is presented. Many existing ideas are brought together, and the effect of various design parameters available to a user is explored. The theory is extended by showing how the problem of stabilizability of the estimated model can be overcome by running parallel estimators. It is shown how asymptotic tracking of deterministic set points can be achieved in the presence of unmodeled dynamics. >
590 citations
TL;DR: Extends certain aspects of the work of P.J. Ramadge and W.M. Wonham on the control of a class of discrete-event processes to the case of decentralized control.
Abstract: Extends certain aspects of the work of P.J. Ramadge and W.M. Wonham (see SIAM J. Control Optimiz., vol.25, Jan. 1987) on the control of a class of discrete-event processes. The controlled process is described by a language L having strings that specify the sequences of events sigma /sub 1/ . . . sigma /sub n/ that the process can execute. The controller makes partial observations on the process events. Based on these observations the controller must enable or disable certain process events so that the resulting language generated by the closed-loop process is the specified sublanguage K contained in/implied by L. The case of decentralized control in which there are several controllers each of which makes partial observations and controls a subset of the process events is also studied. The results are illustrated for an example of communication protocols. >
587 citations
TL;DR: The stability of the Aloha random-access algorithm in an infinite-user slotted channel with multipacket-reception capability is considered and it is shown that the channel backlog Markov chain is ergodic if the packet-arrival rate is less than the expected number of packets successfully received in a collision of n as n goes to infinity.
Abstract: The stability of the Aloha random-access algorithm in an infinite-user slotted channel with multipacket-reception capability is considered. This channel is a generalization of the usual collision channel, in that it allows the correct reception of one or more packets involved in a collision. The number of successfully received packets in each slot is modeled as a random variable which depends exclusively on the number of simultaneously attempted transmissions. This general model includes as special cases channels with capture, noise, and code-division multiplexing. It is shown by drift analysis that the channel backlog Markov chain is ergodic if the packet-arrival rate is less than the expected number of packets successfully received in a collision of n as n goes to infinity. The properties of the backlog in the nonergodicity region are examined. >
547 citations
TL;DR: In this article, an adaptive observer/identifier for single input/single output observable nonlinear systems that can be transformed to a certain observable canonical form is described, and sufficient conditions for stability of this observer are provided.
Abstract: An adaptive observer/identifier for single input/single output observable nonlinear systems that can be transformed to a certain observable canonical form is described. Sufficient conditions for stability of this observer are provided. These conditions are in terms of the structure of the system and canonical form, the boundedness of the parameter variations, and the sufficient richness of some signals. The scope of the canonical form and the use of the observer/identifier is motivated by the presentation of applications to time-invariant bilinear systems, nonlinear systems in phase-variable form a biotechnological process, and a robot manipulator. In each case, the specific stability conditions are presented. >
501 citations
TL;DR: H hierarchical network structures are developed that have the property that the optimal global estimate based on all the available information can be reconstructed from estimates computed by local processor nodes solely on the basis of their own local information and transmitted to a central processor.
Abstract: Various multisensor network scenarios with signal processing tasks that are amenable to multiprocessor implementation are described The natural origins of such multitasking are emphasized, and novel parallel structures for state estimation using the Kalman filter are proposed that extend existing results in several directions In particular, hierarchical network structures are developed that have the property that the optimal global estimate based on all the available information can be reconstructed from estimates computed by local processor nodes solely on the basis of their own local information and transmitted to a central processor The algorithms potentially yield an approximately linear speedup rate, are reasonably failure-resistant, and are optimized with respect to communication bandwidth and memory requirements at the various processors >
482 citations
TL;DR: In this article, the stability boundary of a stable equilibrium point is shown to consist of the stable manifolds of all the equilibrium points (and/or closed orbits) on the stable boundary.
Abstract: A topological and dynamical characterization of the stability boundaries for a fairly large class of nonlinear autonomous dynamic systems is presented. The stability boundary of a stable equilibrium point is shown to consist of the stable manifolds of all the equilibrium points (and/or closed orbits) on the stability boundary. Several necessary and sufficient conditions are derived to determine whether a given equilibrium point (or closed orbit) is on the stability boundary. A method for finding the stability region on the basis of these results is proposed. The method, when feasible, will find the exact stability region, rather than a subset of it as in the Lyapunov theory approach. Several examples are given to illustrate the theoretical prediction. >
457 citations
TL;DR: In this article, a direct design procedure of a full-order observer for a linear system with unknown inputs is presented, using straightforward matrix calculations; in these examples, a reduced order observer is also derived.
Abstract: A direct design procedure of a full-order observer for a linear system with unknown inputs is presented, using straightforward matrix calculations. Some examples are given; in these examples a reduced-order observer is also derived. It is shown that this may restrict the rate of convergence of some state estimates. >
TL;DR: In this paper, the authors present a framework to incorporate a knowledge of modeling error in the analysis and design of failure detection systems, called the threshold selector, which is a nonlinear inequality whose solution defines the set of detectable sensor failure signals and identifies the optimal threshold to be used in innovations-based DIA algorithms.
Abstract: The performance of all failure detection, isolation, and accommodation (DIA) algorithms is influenced by the presence of model uncertainty. The authors present a unique framework to incorporate a knowledge of modeling error in the analysis and design of failure detection systems. A concept is introduced called the threshold selector, which is a nonlinear inequality whose solution defines the set of detectable sensor failure signals. It identifies the optimal threshold to be used in innovations-based DIA algorithms. The optimal threshold is shown to be a function of the bound on modeling errors, the noise properties, the speed of DIA filters and the classes of reference and failure signals. The size of the smallest detectable failure is also determined. The results are applied to a multivariable turbofan jet engine example, which demonstrates improvements compared to previous studies. >
TL;DR: In this article, a high-purity distillation column is used to explain the physical reason for poor conditioning and its implications on control system design and performance, and it is shown that an acceptable performance/robustness tradeoff cannot be obtained by simple loop-shaping techniques (using singular values) and that a good understanding of the model uncertainty is essential for robust control systems design.
Abstract: Using a high-purity distillation column as an example, the physical reason for the poor conditioning and its implications on control system design and performance are explained. It is shown that an acceptable performance/robustness tradeoff cannot be obtained by simple loop-shaping techniques (using singular values) and that a good understanding of the model uncertainty is essential for robust control system design. Physically motivated uncertainty descriptions (actuator uncertainties) are translated into the H/sup infinity //structured singular value framework, which is demonstrated to be a powerful tool to analyze and understand the complex phenomena. >
TL;DR: In this article, a mapping theorem by L.A. Zadeh et al. is used to compute the stability margin k/sub m/ of diagonally perturbed multivariable feedback systems without conservatism.
Abstract: A mapping theorem by L.A. Zadeh and C.A. Desoer (1963) serves as the basis for an algorithm that computes the stability margin k/sub m/ of diagonally perturbed multivariable feedback systems without conservatism. The stability margin determination not only verifies system stability but also quantifies how much further the plan uncertainties can be extended before instability occurs. The essence of the computational approach is the realization that the true image of a given domain can be approximated with arbitrary accuracy by first subdividing the domain into the requisite number of subdomains and then forming the union of the convex hulls of their images. The technique is illustrated in an example with a plant model having three uncertainties. In general, the method is applicable to either SISO or MIMO LTI systems whose uncertainties can be modeled with noninteracting coefficients in the open-loop transfer function representations. >
TL;DR: In this article, a numerical technique for solving nonlinear optimal control problems is introduced, where the state and control variables are expanded in the Chebyshev series, and an algorithm is provided for approximating the system dynamics, boundary conditions, and performance index.
Abstract: A numerical technique for solving nonlinear optimal control problems is introduced. The state and control variables are expanded in the Chebyshev series, and an algorithm is provided for approximating the system dynamics, boundary conditions, and performance index. Application of this method results in the transformation of differential and integral expressions into systems of algebraic or transcendental expressions in the Chebyshev coefficients. The optimum condition is obtained by applying the method of constrained extremum. For linear-quadratic optimal control problems, the state and control variables are determined by solving a set of linear equations in the Chebyshev coefficients. Applicability is illustrated with the minimum-time and maximum-radius orbit transfer problems. >
TL;DR: In this paper, a global bounded-input-bounded-state stability theory for a class of continuously adapting controllers applied to time-varying linear systems is presented. But no persistence of excitation requirement is needed.
Abstract: The authors present a global bounded-input-bounded-state stability theory for a class of continuously adapting controllers applied to time-varying linear systems. This gives theoretical support to the application of many of the algorithms used in practice. A key feature of the analysis is that no persistence of excitation requirement is needed. >
TL;DR: In this article, a new type of controller is proposed which detects the ith plant output N/sub i/ times during a period of T/sub 0/ and changes the plant inputs once during T /sub 0/.
Abstract: A new type of controller is proposed which detects the ith plant output N/sub i/ times during a period of T/sub 0/ and changes the plant inputs once during T/sub 0/. It is shown that an arbitrary state feedback can be realized by such controllers if the plant is observable. This implies, for instance, that arbitrary symmetric pole assignment is possible if the plant is controllable. It is also shown that, if the plant has no zeros at the origin, the state transition matrix of the controller itself can be set arbitrarily without changing the state feedback to be realized. That is to say, inversely expressed, any state feedback can be equivalently realized by a controller with any prescribed degree of stability. >
TL;DR: A computer-aided design (CAD) method and associated architectures are proposed for linear controllers based on recent results that parameterize all controllers that stabilize a given plant.
Abstract: A computer-aided design (CAD) method and associated architectures are proposed for linear controllers. The design method and architecture are based on recent results that parameterize all controllers that stabilize a given plant. With this architecture, the design of controllers is a convex programming problem that can be solved numerically. Constraints on the closed-loop system, such as asymptotic tracking, decoupling, limits on peak excursions of variables, step response, settling time, and overshoot, as well as frequency-domain inequalities, are readily incorporated in the design. The minimization objective is quite general, with LQG (linear quadratic Gaussian) H/sub infinity / and new l/sub 1/ types as special cases. The constraints and objective are specified in a control specification language which is natural for the control engineer, referring directly to step responses, noise powers, transfer functions, and so on. >
TL;DR: The main theorem in this article can be considered as the positive realness lemma for strictly positive real systems and is clarified by means of a three-tier diagram; each tier represents a set of equivalent conditions successively stronger than the lower tier.
Abstract: The author states various time-domain and frequency-domain conditions pertaining to multivariate strict positive real systems and establishes the relationship between these conditions. Their relationship is clarified by means of a three-tier diagram; each tier represents a set of equivalent conditions successively stronger than the lower tier. The main theorem in the present study can be considered as the positive realness lemma for strictly positive real systems. >
TL;DR: In this paper, a controller design for manipulators using the theory of variable-structure systems (VSS) is presented to deal with the set-point regulation problem, and the major obstacle of VSS vector control with strong dynamic coupling is overcome for a class of systems with positive symmetric inertia matrices.
Abstract: A controller design for manipulators using the theory of variable-structure systems (VSS) is presented to deal with the set-point regulation problem. The major obstacle of VSS vector control with strong dynamic coupling is overcome for a class of systems with positive symmetric inertia matrices. Parameter variations can easily be considered in the design methodology, which is readily extendable to a higher number of links. The problem of chattering is solved by the introduction of sliding sectors. >
TL;DR: In this paper, the production control of a single-product manufacturing system with arbitrary number of machine states (failure modes) is discussed, where the objective is to find a production policy that would meet the demand for the product with minimum average inventory or backlog cost.
Abstract: The production control of a single-product manufacturing system with arbitrary number of machine states (failure modes) is discussed. The objective is to find a production policy that would meet the demand for the product with minimum average inventory or backlog cost. The optimal production policy has a special structure and is called a hedging-point policy. If the hedging points are known, the optimal production rate is readily specified. Assuming a set of tentative hedging points, the simple structure of the optimal policy is utilized to find the steady-state probability distribution of the surplus (inventory or backlog). Once this function is determined, the average surplus cost is easily calculated in terms of the values of the hedging points. The average cost is then minimized to find the optimum hedging points. >
TL;DR: In this paper, the authors considered a H/sub infinity /-optimal control problem in which the measured outputs are the states of the plant and showed that the infimum of the norm of the closed-loop transfer function using linear static state-feedback equals the √ √ n −1/n −1 √ 2/n √ 1/n/n−2 √ 0.
Abstract: A H/sub infinity /-optimal control problem in which the measured outputs are the states of the plant is considered. The main result shows that the infimum of the norm of the closed-loop transfer function using linear static state-feedback equals the infimum of the norm of the closed-loop transfer function over all stabilizing dynamic (even, nonlinear time-varying) state-feedback controllers. >
TL;DR: In this paper, a model reference adaptive control (MRAC) scheme for nonlinear systems in a pure-feedback canonical form with unknown parameters is presented, where the present of parameter uncertainty in the system causes imperfect linearization, i.e. it introduces nonlinear additive terms in the transformed coordinates.
Abstract: A model reference adaptive control (MRAC) scheme is presented for nonlinear systems in a pure-feedback canonical form with unknown parameters. The present of parameter uncertainty in the system causes imperfect linearization, i.e. it introduces nonlinear additive terms in the transformed coordinates. Under some mild technical assumptions, global convergence of the output error is established for all initial estimates of the parameter vector lying in an open neighborhood of the true parameters in the parameter space. >
TL;DR: Methods for multirate digital control system design, sampling rate selection, discretization, and synthesis methods are applied to two example design problems andMultirate and single-rate compensators synthesized by the different methods are compared based on closed-loop responses with compensators having the same real-time computation load.
Abstract: Methods for multirate digital control system design are discussed. A simple method for sampling rate selection based on control bandwidths is proposed. Methods for generating a discrete-time state model of a sampled-data plant and a discrete-time equivalent to an analog cost function for a sampled-data plant are described. The successive loop closures and linear quadratic Gaussian synthesis methods are reviewed, and a constrained optimization synthesis method is introduced. The proposed sampling rate selection, discretization, and synthesis methods are applied to two example design problems. Multirate and single-rate compensators synthesized by the different methods are compared based on closed-loop responses with compensators having the same real-time computation load. >
TL;DR: In this paper, the problem of making a given stabilizing controller robust so that the closed-loop system remains stable for prescribed ranges of variations of a set of physical parameters in the plant is treated in the state-space and transfer-function domains.
Abstract: The problem of making a given stabilizing controller robust so that the closed-loop system remains stable for prescribed ranges of variations of a set of physical parameters in the plant. The problem is treated in the state-space and transfer-function domains. In the state-space domain a stability hypersphere is determined in the parameter space using Lyapunov theory. The radius of this hypersphere is iteratively increased by adjusting the controller parameters until the prescribed perturbation ranges are contained in the stability hypersphere. In the transfer-function domain a corresponding stability margin is defined and optimized on the basis of the recently introduced concept of the largest stability hypersphere in the space of coefficients of the closed-loop characteristic polynomial. The design algorithms are illustrated by examples. >
TL;DR: In this paper, the problem of optimal disturbance rejection of bounded persistent disturbances is solved in the general nonsquare case, and the minimum value of the objective function can be obtained by solving a semi-infinite linear programming problem, and an iterative procedure for obtaining approximate solutions is introduced.
Abstract: The problem of optimal disturbance rejection of bounded persistent disturbances is solved in the general nonsquare case. The minimum value of the objective function can be obtained by solving a semi-infinite linear programming problem, and an iterative procedure for obtaining approximate solutions is introduced. Application of the l/sup 1/-optimal problem to robustness is discussed. A mixed sensitivity problem is formulated and shown to guarantee good disturbance rejection in the presence of plant perturbations. >
TL;DR: In this paper, the authors consider a redundant manipulator whose hand is to trace a path in its workspace and determine a priori whether a given local control strategy guarantees repeatability or not.
Abstract: Consider a redundant manipulator whose hand is to trace a path in its workspace. A local control strategy that governs the manipulator is a law that assigns an infinitesimal change in the joint angles so that the hand will move infinitesimally in the direction designated by the path. Because of the redundancy, there can be many such control strategies. For some strategies it turns out that when the hand returns to its initial position, the joint angles do not always return to their initial values. To determine a priori whether a given local control strategy guarantees repeatability or not, it is necessary to deduce its global properties as well as its local properties. This is achieved by considering integral surfaces for a distribution in the joint space. This yields a necessary and sufficient condition, in terms of Lie brackets, for a control to be repeatable. >
TL;DR: In this paper, the Riccati-equation approach is extended to include problems with time-varying uncertainty in the input connection matrix and several examples are included to demonstrate the efficacy of this result.
Abstract: A useful technique for determining a linear feedback control law stabilizes an uncertain system is the Riccati-equation approach of I.R. Petersen and C.V. Hollot (1986). They consider systems with time-varying uncertainty in the system matrix and obtain the constant feedback gains for the linear stabilizing controller in terms of the solutions of a Riccati equation. The technique is extended to include problems with time-varying uncertainty in the input connection matrix. Several examples are included to demonstrate the efficacy of this result. >
TL;DR: The connection between the constant energy surface and the stability boundary of the power system is explored and gives valuable insight into classical stability tests, which are based on the constantEnergy surface.
Abstract: Complete results are presented on the phase portrait of a class of large nonlinear dynamic systems that includes the power system The connection between the constant energy surface and the stability boundary of the power system is explored This gives valuable insight into classical stability tests, which are based on the constant energy surface An approach to stability monitoring of the power system derived from these results is outlined >
TL;DR: In this article, the authors analyzed the symmetric periodic positive semidefinite (SPPS) solution of the DPRE under appropriate assumptions of stabilizability and detectability of the periodic system.
Abstract: Gives a comprehensive treatment of several important aspects of the discrete-time periodic Riccati equation (DPRE) arising from the prediction problem for linear discrete-time periodic systems. The authors analyze the symmetric periodic positive semidefinite (SPPS) solution of the DPRE under appropriate assumptions of stabilizability and detectability of the periodic system. Among the results obtained are necessary and sufficient conditions for the existence and uniqueness of the SPPS solution and the stability of the resulting closed-loop system. Some of these results can be seen as extensions of the corresponding results for the time-invariant case; however, a number of them contain contributions to the time-invariant case as well. The paper also gives a numerical algorithm based on an iterative linearization procedure for computing the SPPS solution. The algorithm is a periodic version of Kleinman's algorithm for the time-invariant case. >