Showing papers in "IEEE Transactions on Automatic Control in 1977"
TL;DR: Design and analysis forVariable structure systems are surveyed in this paper and it is shown that advantageous properties result from changing structures according to this switching logic.
Abstract: Variable structure systems consist of a set of continuous subsystems together with suitable switching logic. Advantageous properties result from changing structures according to this switching logic. Design and analysis for this class of systems are surveyed in this paper.
5,076 citations
TL;DR: The properties of controllability, observability, and the theory of minimal realization for linear systems are well-understood and have been very useful in analyzing such systems as discussed by the authors.
Abstract: The properties of controllability, observability, and the theory of minimal realization for linear systems are well-understood and have been very useful in analyzing such systems. This paper deals with analogous questions for nonlinear systems.
2,306 citations
TL;DR: It is shown how a deterministic differential equation can be associated with the algorithm and examples of applications of the results to problems in identification and adaptive control.
Abstract: Recursive algorithms where random observations enter are studied in a fairly general framework. An important feature is that the observations my depend on previous "outputs" of the algorithm. The considered class of algorithms contains, e.g., stochastic approximation algorithm, recursive identification algorithm, and algorithms for adaptive control of linear systems. It is shown how a deterministic differential equation can be associated with the algorithm. Problems like convergence with probability one, possible convergence points and asymptotic behavior of the algorithm can all be studied in terms of this differential equation. Theorems stating the precise relationships between the differential equation and the algorithm are given as well as examples of applications of the results to problems in identification and adaptive control.
1,370 citations
TL;DR: By providing a basis for a systematic approach to approximate reasoning, the theory of fuzzy sets may well have a substantial impact on scientific methodology in the years ahead, particularly in the realms of psychology, economics, law, medicine, decision analysis, information retrieval, and artificial intelligence.
Abstract: The papers presented in this volume were contributed by participants in
the U.S.-Japan Seminar on Fuzzy Sets and Their Applications, held at the
University of California, Berkeley, in July 1974. These papers cover a broad
spectrum of topics related to the theory of fuzzy sets, ranging from its mathematical aspects to applications in human cognition, communication, decisionmaking, and engineering systems analysis. Basically, a fuzzy set is a class in which there may be a continuum of grades of membership as, say, in the class of long objects. Such sets underlie much of our ability to summarize, communicate, and make decisions under uncertainty or partial information. Indeed, fuzzy sets appear to play an essential role in human cognition, especially in relation to concept formation, pattern classification, and logical reasoning.
Since its inception about a decade ago, the theory of fuzzy sets has evolved in many directions, and is finding pplications in a wide variety of fields in which the phenomena under study are too complex or too ill defined to be analyzed by conventional techniques. Thus, by providing a basis for a systematic approach to approximate reasoning, the theory of fuzzy sets may well have a substantial impact on scientific methodology in the years ahead, particularly in the realms of psychology, economics, law, medicine, decision analysis, information retrieval, and artificial intelligence.
The U.S.-Japan Seminar on Fuzzy Sets was sponsored by the U.S.-Japan Cooperative Science Program, with the joint support of the National Science Foundation and the Japan Society for the Promotion of Science. In organizing the seminar, the co-chairmen received considerable help from J.E. O’Connell and L. Trent of the National Science Foundation; the staff of the Japan Society for the Promotion of Science; and D. J. Angelakos and his staff at the University of California, Berkeley. As co-editors of this volume, we wish also to express our heartfelt appreciation to Terry Brown for her invaluable assistance in the preparation of the manuscript, and to Academic Press for undertaking its publication.
For the convenience of the reader, a brief introduction to the theory of fuzzy sets is provided in the Appendix of the first paper in this volume. An up-to-date bibliography on fuzzy sets and their applications is included at the
end of the volume.
903 citations
TL;DR: In this article, the authors studied a general form of sets of equations that is often the product of problem formulation in large-scale systems, especially when the equations are expressed in terms of the natural describing variables of the system.
Abstract: This paper studies a general form of sets of equations that is often the product of problem formulation in large-scale systems, especially when the equations are expressed in terms of the natural describing variables of the system. Such equations represent a broad class of time-evolutionary phenomena, and include as special cases ordinary static equations of arbitrary dimension, ordinary state-space equations, combinations of static and dynamic equations, and noncausal systems. The main thrust of the paper is to show (for sets of linear equations) that familiar concepts of dynamic system theory can be extended to this more general class, although sometimes with significant modification. Two new (and essentially dual) concepts, that of solvable and conditionable sets of equations, are found to be fundamental to the study of equations of this form. The notion of initial conditions, although not directly related to a state, is used as a general solution method for equations of this type. In addition a set of necessary and sufficient conditions for a set of dynamic equations to contain an embedded state-space representation is derived.
752 citations
TL;DR: In this article, the problem of observing the state of an unknown, time invariant linear system from measurements of its input and output is considered, and the approach taken here proceeds from a parametrized observer, which is only an alternative, equivalent representation of the Luenberger observer.
Abstract: The problem of observing the state of an unknown, time invariant linear system from measurements of its input and output is considered. Instead of adapting the parameters in a Luenberger observer to solve the problem, as was done by earlier authors, the approach taken here proceeds from a so-called parametrized observer, which is only an alternative, equivalent representation of the Luenberger observer. However, the parametrized observer has a different structure where the state estimate is a linear function (and not a functional) of its parameters. Therefore, adapting the parameters in the parametrized observer results in a complete separation of the observer dynamics from the adaptive loop which substantially simplifies the design of suitable parameter adaptation schemes. Three such schemes are presented and proven to be globally exponentially rather than asymptotically convergent. In particular, the second and the third adaptation schemes allow the construction of adaptive observers with arbitrarily high (exponential) rates of convergence.
701 citations
523 citations
TL;DR: In this article, robust Bayesian estimates of the vector x are constructed for the following two distinct situations: (1) the state x is Gaussian and the observation error v is (heavy-tailed) non-Gaussian and (2) the states x and v are Gaussian.
Abstract: Starting with the vector observation model y = Hx + v , robust Bayesian estimates \hat{x} of the vector x are constructed for the following two distinct situations: 1) the state x is Gaussian and the observation error v is (heavy-tailed) non-Gaussian and 2) the state is heavy-tailed non-Gaussian and the observation error is Gaussian. Bounds with respect to broad symmetric non-Gaussian families are derived for the error covariance matrix of these estimates. These "one-step" robust estimates are then used to obtain robust estimates for the Kalman filter setup y_{k}= H_{k}x_{k}+ v_{k}, x_{k+1}=\Phi_{k}x_{k}+w_{k} . Monte Carlo results demonstrate the robustness of the proposed estimation procedure, which might be termed a robustified Kalman filter.
422 citations
TL;DR: The convergence with probability one of a recently suggested recursive identification method by Landau is investigated and the positive realness of a certain transfer function is shown to play a crucial role, both for the proof of convergence and for convergence itself.
Abstract: The convergence with probability one of a recently suggested recursive identification method by Landau is investigated. The positive realness of a certain transfer function is shown to play a crucial role, both for the proof of convergence and for convergence itself. A completely analogous analysis can be performed also for the extended least squares method and for the self-tuning regulator of Astrom and Wittenmark. Explicit conditions for convergence of all these schemes are given. A more general structure is also discussed, as well as relations to other recursive algorithms.
413 citations
TL;DR: In this article, a feedback control law for linear systems based on a minimum energy regulator problem with fixed terminal constraints on the state was considered and a modification of this control law was shown to be asymptotically stable.
Abstract: This paper considers a feedback control law for linear systems based on a minimum energy regulator problem with fixed terminal constraints on the state. A modification of this control law based on a receding horizon notion is shown to be asymptotically stable and to result in a new method for stabilizing linear time-varying systems, as well as extending some well-known methods for stabilizing time-invariant systems by state variable feedback.
383 citations
TL;DR: In this article, the stability properties of various time-varying linear differential equations arising in model reference adaptive identification schemes are examined and necessary and sufficient conditions for exponential stability are presented.
Abstract: The stability, properties are examined of various time-varying linear differential equations which arise in model reference adaptive identification schemes. Necessary and sufficient conditions for exponential stability are presented.
TL;DR: In this article, a singular perturbation approach is used to unify a class of classical and recent results on high-gain systems and to show their relationships with multivariable transmission zero analysis, cheap control problems, and sliding mode in variable structure systems.
Abstract: In this paper a singular perturbation approach is used to unify a class of classical and recent results on high-gain systems and to show their relationships with multivariable transmission zero analysis, cheap control problems, and sliding mode in variable structure systems. A new pole placement method and a decomposition of near optimal high-gain regulator problems are presented.
TL;DR: In this article, the authors summarize some results obtained for the adaptive control of the F-8C aircraft using the so-called MMAC method, including the selection of the performance criteria for both the lateral and the longitudinal dynamics, the design of the Kalman filters for different flight conditions, the identification aspects of the design using hypothesis testing ideas, and the performance of the closed-loop adaptive system.
Abstract: The purpose of this paper is to summarize some results obtained for the adaptive control of the F-8C aircraft using the so-called MMAC method. The discussion includes the selection of the performance criteria for both the lateral and the longitudinal dynamics, the design of the Kalman filters for different flight conditions, the "identification" aspects of the design using hypothesis testing ideas, and the performance of the closed-loop adaptive system.
TL;DR: This paper presents a new approach to the solution of multi-target tracking problems that is approached as an unsupervised pattern recognition problem and has the computational structure of the set packing and set partitioning problems of 0-1 integer programming.
Abstract: This paper presents a new approach to the solution of multi-target tracking problems. 0-1 integer programming methods are used to alleviate the combinatorial computing difficulties that accompany any but the smallest of such problems. Multitarget tracking is approached as an unsupervised pattern recognition problem. A multiple-hypothesis test is performed to determine which particular combination of the many feasible tracks is most likely to represent actual targets. This multiple hypothesis test is shown to have the computational structure of the set packing and set partitioning problems of 0-1 integer programming. Multitarget tracking problems that are translated into this form can be rapidly solved, using well-known discrete optimization techniques such as implicit enumeration.
TL;DR: The structure of a sensor failure detection and identification system designed for the NASA F-8 DFBW aircraft is outlined, and preliminary simulation results indicate good behavior of the analytic decision statistic, based on the sequential probability ratio test.
Abstract: In this paper, we outline the structure of a sensor failure detection and identification system designed for the NASA F-8 DFBW aircraft The system is for use in a dual-redundant environment, and it takes maximal advantage of all functional relationships among the sensed variables The identification logic uses the quality sequential probability ratio, which provides a useful on-line measure of confidence in the various forms of analytic redundancy Preliminary simulation results indicate good behavior of the analytic decision statistic, based on the sequential probability ratio test
TL;DR: In this paper, a new and computationally efficient algorithm for inversion of linear time-invariant systems is presented and existence conditions for either left or right-inverse systems are also presented together with stability criteria.
Abstract: A new and computationally efficient algorithm for inversion of linear time-invariant systems is presented. Existence conditions for either left- or right-inverse systems are also presented together with stability criteria. These criteria indicate that the algorithm will find a stable inverse whenever one exists. The results apply to both left and right inversion of a linear system and include the special case of linear finite automata or convolutional encoders.
TL;DR: In this article, a Kalman filtering approach is proposed to obtain optimal smoothed estimates of the so-called reflection coefficient sequence, which contains important information about subsurface geometry.
Abstract: This paper is motivated by a problem from seismic data processing in oil exploration. We develop a Kalman filtering approach to obtaining optimal smoothed estimates of the so-called reflection coefficient sequence. This sequence contains important information about subsurface geometry. Our problem is shown to be equivalent to that of estimating white-plant noise for a linear dynamic system. By means of the equations which are derived herein, it is possible to compute fixed-interval, fixed-point, or fixed-lag optimal smoothed estimates of the reflection coefficient sequence, as well as respective error covariance-matrix information. Our optimal estimators are compared with an ad hoc "prediction error filter," (PEF) which has recently been reported on in the geophysics literature. We show that one of our estimators performs at least as well as, and in most cases, better than the prediction error filter. Simulation results are given which support and illustrate the theoretical developments.
TL;DR: In this paper, the stabilizing property of linear quadratic state feedback (LQSF) design is used to obtain a quantitative measure of the robustness of LQSF designs in the presence of perturbations.
Abstract: The well-known stabilizing property of linear quadratic state feedback (LQSF) design is used to obtain a quantitative measure of the robustness of LQSF designs in the presence of perturbations. Bounds are obtained for allowable nonlinear, time-varying perturbations such that the resulting closed-loop system remains stable. The special case of linear, time-invariant perturbations is also treated. The bounds are expressed in terms of the weighting matrices in a quadratic performance index and the corresponding positive definite solution of the algebraic matrix Riccati equation, and are easy to compute for any given LQSF design. A relationship is established between the perturbation bounds and the dominant eigenvalues of the closed-loop optimal system model. Some interesting asymptotic properties of the bounds are also discussed. An autopilot for the flare control of the Augmentor Wing Jet STOL Research Aircraft (AWJSRA) is designed, based on LQSF theory, and the results presented in this paper. The variation of the perturbation bounds to changes in the weighting matrices in the LQSF design is studied by computer simulations, and appropriate weighting matrices are chosen to obtain a reasonable bound for perturbations in the system matrix and at the same time meet the practical constraints for the flare maneuver of the AWJSRA. Results from the computer simulation of a satisfactory autopilot design for the flare control of the AWJSRA are presented.
TL;DR: The optimum decision rule is asymptotically consistent and gives a quantitative explanation for the "principle of parsimony" often used in the construction of models from empirical data.
Abstract: This paper deals with the Bayesian methods of comparing different types of dynamical structures for representing the given set of observations. Specifically, given that a given process y(\cdot) obeys one of r distinct stochastic or deterministic difference equations each involving a vector of unknown parameters, we compute the posterior probability that a set of observations {y(1),...,y(N)} obeys the i th equation, after making suitable assumptions about the prior probability distribution of the parameters in each equation. The difference equations can be nonlinear in the variable y but should be linear in the parameter vector in it. Once the posterior probability is known, we can find a decision rule to choose between the various structures so as to minimize the average value of a loss function. The optimum decision rule is asymptotically consistent and gives a quantitative explanation for the "principle of parsimony" often used in the construction of models from empirical data. The decision rule answers a wide variety of questions such as the advisability of a nonlinear transformation of data, the limitations of a model which yields a perfect fit to the data (i.e., zero residual variance), etc. The method can be used not only to compare different types of structures but also to determine a reliable estimate of spectral density of process. We compare the method in detail with the hypothesis testing method, and other methods and give a number of illustrative examples.
TL;DR: In this article, a characterization of generalized eigenvector chains can be obtained with a given set of nondistinct eigenvalues, and an algorithm for computing a feedback matrix which gives the selected closed-loop eigen values and generalized eigvector chains.
Abstract: In a recent paper [1], a characterization has been given for the class of all closed-loop eigenvector sets which can be obtained with a given set of distinct closed-loop eigenvalues. This note extends these results to characterize the class of generalized eigenvector chains which can be obtained with a given set of nondistinct eigenvalues. Included is an algorithm for computing a feedback matrix which gives the selected closed-loop eigenvalues and generalized eigenvector chains. Although there are limitations on the Jordan structure of the closed-loop system, this algorithm allows one to realize any "allowable" closed-loop Jordan configuration.
TL;DR: In this article, the Burg reflection-coefficient method for maximum entropy (antoregressive) spectral estimation is generalized to apply to multichannel complex signal, and it is shown that all resulting power matrices are positive definite.
Abstract: The Burg reflection-coefficient method for maximum entropy (antoregressive) spectral estimation is generalized to apply to multichannel complex signal. It is shown that all resulting power matrices are positive definite. Preliminary numerical results obtained for a monochromatic signal with noise indicate that the determinants of the power matrices are rapidly reduced as the number of filter coefficients is increased, and that superior spectral resolution can be expected.
TL;DR: This paper discusses Petri nets in the context of the state equation for a linear discrete-time system and shows that the controllability and reachability of a Petri net are related to maximal matchings of its bipartite graph.
Abstract: Petri nets are a versatile modeling device for studying the structure and control of concurrent systems. Petri nets and related graph models have been used for modeling a wide variety of systems from computers to social systems. In order to introduce this interesting modeling device to the researcher in control theory, this paper discusses Petri nets in the context of the state equation for a linear discrete-time system. The controllability concept of dynamic systems is applied to Petri nets for the first time. It is also shown that the controllability and reachability of a Petri net are related to maximal matchings of its bipartite graph.
TL;DR: An approach to analyzing biped locomotion problems is presented which applies the principles of Lagrangian dynamics to derive the equations of motion of locomotion gaits, state-variable techniques to analyze locomotion dynamics, and multivariable feedback to design locomotion controls.
Abstract: An approach to analyzing biped locomotion problems is presented. This approach applies the principles of Lagrangian dynamics to derive the equations of motion of locomotion gaits, state-variable techniques to analyze locomotion dynamics, and multivariable feedback to design locomotion controls. A robot model which has no knee joints or feet and is constrained to motion in the sagittal plane is chosen as a sufficiently simple model of a biped to illustrate the approach. A goal of the analysis is the design of a locomotion control for the robot which produces a walking gait having a velocity and stride length similar to those of a human walking gait. The principle feature of the approach is a much deeper understanding of the dynamics of biped locomotion than previous approaches have provided.
TL;DR: In this paper, the authors examined the properties of probing signals employed in a model reference identification procedure which guarantee identification of the parameters of a linear multivariable system, including persistent excitation.
Abstract: This paper examines certain properties of probing signals employed in a model reference identification procedure which guarantee identification of the parameters of a linear multivariable system. The property of persistent excitation is examined with respect to a new class of (persistently spanning) signals. In particular, this class of signals includes many (periodic or almost periodic) signals which have previously been considered as effective probing signals, The results yield concrete guidelines useful in the practical design of probing signals.
TL;DR: In this paper, a new result in the problem of pole assignment by gain output feedback is given, which states that arbitrary pole assignment is possible for almost all systems if n, r and m are the number of states, of inputs and of outputs, respectively, and ν and μ are the controllability index and the observability index of the system, respectively.
Abstract: In this paper a new result in the problem of pole assignment by gain output feedback is given. Roughly speaking, this result says that arbitrary pole assignment is possible for almost all systems if n \mu, m \geq
u . Here n, r and m are the number of states, of inputs and of outputs, respectively, and ν and μ are the so-called controllability index and the observability index of the system, respectively. This result extends the author's previous one in [1]. The basic idea in [1] is developed further and its geometrical meaning is amplified. The proof of the theorem itself gives a method of constructing a desired gain matrix. An example is given to show the feasibility of the algorithm.
TL;DR: In this paper, basic theorems of algebraic geometry are applied to prove some pole-placement theorem, including an improved version of pole placement with output feedback.
Abstract: -Basic theorems of algebraic geometry are applied to prove some pole-placement theorems, including an improved version of pole placement with output feedback. Examples are given which show the limitations of the algebro-geometric theorems and their potential value for systems theory. This paper and those to follow might contribute towards making the powerful theorems of modern algebraic geometry accessible and applicable to problems of engineering.
TL;DR: In this paper, an abstract theory of variational expansions, similar to that of L. M. Graves (1927), is developed, which leads directly to concrete expressions (multilinear integral operators) for the functionals of the expansions and sets conditions on the differential systems which insure that the expansions give reasonable approximations of the response.
Abstract: This paper is concerned with representing the response of nonlinear differential systems by functional expansions. An abstract theory of variational expansions, similar to that of L. M. Graves (1927), is developed. It leads directly to concrete expressions (multilinear integral operators) for the functionals of the expansions and sets conditions on the differential systems which insure that the expansions give reasonable approximations of the response. Similarly, it is shown that the theory of analytic functions in Banach spaces leads directly to conditions which imply uniform convergence of functional series. The main results on differential systems are summarized in a set of theorems, some of which overlap and extend the recent results of Brockett on Volterra series representations for the response of linear analytic differential systems. Other theorems apply to more general nonlinear differential systems. They provide a rigorous foundation for a large body of previous research on Volterra series expansions. The multilinear integral operators are obtained from systems of differential equations which characterize exactly the variations. These equations are of much lower order than those obtained by the technique of Carleman. A nonlinear feedback system serves as an example of an application of the theory.
TL;DR: In this paper, the authors examined several versions of the extended Kalman filter which can be used to estimate the position, velocity, and other key parameters associated with maneuvering reentry vehicles.
Abstract: This paper examines several versions of the extended Kalman filter which can be used to estimate the position, velocity, and other key parameters associated with maneuvering reentry vehicles. These filters are discussed in terms of the fundamental problems of modeling accuracy, filter sophistication, and the real-time computational requirements. Techniques which adaptively increase the process noise to compensate for modeling errors during the maneuvers are examined.
TL;DR: In this article, a planar five-link model of a biped is considered, in which external torques appear explicitly and are derived by d'Alembert's principle.
Abstract: Postural and gait stability of a planar five-link model of a biped is considered. Equations of motion, in which external torques appear explicitly are derived by d'Alembert's principle. Postural stability is achieved at arbitrary equilibrium points by open and closed loop torques in order to create the equilibrium point and to make the equilibrium point stable. Television recording of angles and angle rates of all five segments of a human in normal walk is taken and used as reference input to the system in order to generate the open and closed loop torques needed for locomotion. It is shown that one equilibrium point and one set of constant feedback gains suffice. It is also demonstrated that this method can be utilized to compute the forces at the joints and the components of the applied torques as functions of the state of the system. Simulations results of the nonlinear system with linear feedback and added disturbances are presented. The two main applications of this work are in the design of powered prostheses for the handicapped and, more importantly, in nondestructive testing to estimate feedback gains utilized by human beings in standing and in walking.
TL;DR: In this paper, the controllability of a class of discrete time bilinear systems is discussed and necessary and sufficient conditions for complete control of such systems are derived. And a complete characterization of controllable regions of this class of systems, when not completely controllible, is made.
Abstract: In this paper the controllability of a class of discrete time bilinear systems is discussed. Necessary and sufficient conditions for complete controllability are derived. In addition a complete characterization of the controllable regions of this class of systems, when not completely controllable, is made.