Showing papers in "IEEE Transactions on Automatic Control in 1982"
TL;DR: In this paper, a linear system with delayed control action is transformed into a system without delays under an absolute continuity condition, and the new system is a measure-differential control system.
Abstract: Linear systems with delayed control action are transformed into systems without delays. Under an absolute continuity condition, the new system is an ordinary differential control equation. In the general case, the new system is a measure-differential control system. It is shown how the controllability, stabilization, and various optimization problems can be analyzed via the reduced systems.
994 citations
TL;DR: In this article, a model reduction procedure based on balanced state space representations is studied, and the reduced order model is examined from the point of view of stability, controllability, and observability.
Abstract: A model reduction procedure, based on balanced state space representations, is studied in this paper. The reduced order model is examined from the point of view of stability, controllability, and observability. Both continuous time and discrete time systems are considered.
903 citations
TL;DR: This paper presents a mathematical framework for discussion of large space structure (LSS) control theory, and current trends in LSS control theory and related topics in general control science are surveyed.
Abstract: This paper presents a mathematical framework for discussion of large space structure (LSS) control theory. Within this framework, current trends in LSS control theory and related topics in general control science are surveyed.
672 citations
TL;DR: In this paper, the problem of simultaneously stabilizing l + 1 plants using a stable compensator is reduced to a purely algebraic problem, which can be expressed as follows: given a plant G, we would like to know whether or not there exists a single compensator C that stabilizes G ; if not, what is the smallest number of right half-place poles (counted according to their McMillan degree) that any stabilizing compensator must have?
Abstract: In this paper we study two problems in feedback stabilization. The first is the simultaneous stabilization problem, which can be stated as follows. Given plants G_{0}, G_{1},..., G_{l} , does there exist a single compensator C that stabilizes all of them? The second is that of stabilization by a stable compensator, or more generally, a "least unstable" compensator. Given a plant G , we would like to know whether or not there exists a stable compensator C that stabilizes G ; if not, what is the smallest number of right half-place poles (counted according to their McMillan degree) that any stabilizing compensator must have? We show that the two problems are equivalent in the following sense. The problem of simultaneously stabilizing l + 1 plants can be reduced to the problem of simultaneously stabilizing l plants using a stable compensator, which in turn can be stated as the following purely algebraic problem. Given 2l matrices A_{1}, ..., A_{l}, B_{1}, ..., B_{l} , where A_{i}, B_{i} are right-coprime for all i , does there exist a matrix M such that A_{i} + MB_{i} , is unimodular for all i? Conversely, the problem of simultaneously stabilizing l plants using a stable compensator can be formulated as one of simultaneously stabilizing l + 1 plants. The problem of determining whether or not there exists an M such that A + BM is unimodular, given a right-coprime pair ( A, B ), turns out to be a special case of a question concerning a matrix division algorithm in a proper Euclidean domain. We give an answer to this question, and we believe this result might be of some independent interest. We show that, given two n \times m plants G_{0} and G_{1} we can generically stabilize them simultaneously provided either n or m is greater than one. In contrast, simultaneous stabilizability, of two single-input-single-output plants, g 0 and g 1 , is not generic.
403 citations
TL;DR: In this article, the authors describe an approach to ultimate boundedness control under hypotheses less stringent than heretofore required, instead of imposing the so-called matching conditions of previous authors, a certain "decomposition" of the dynamics is performed.
Abstract: This paper describes an approach to ultimate boundedness control under hypotheses less stringent than heretofore required. Instead of imposing the so-called matching conditions of previous authors, a certain "decomposition" of the dynamics is performed. The resulting "decomposed system" has two parts-a matched portion and a mismatched portion. A certain measure of mismatch M is defined and it is shown that effective control is possible as long as M does not exceed some critical mismatch threshold M*. It is seen that this threshold depends on the choice of feedback. Hence, it becomes possible to investigate the tradeoffs between the size of the mismatch threshold and the sizes of the feedback gains which achieve the desired ultimate boundedness of solutions.
373 citations
TL;DR: In this paper, the problem of parameter estimation and of the evaluation of related uncertainty intervals is considered in the case that a probabilistic description of noise and errors is not available (of suitable), but only a bound on them is known.
Abstract: The problem of parameter estimation and of the evaluation of related uncertainty intervals is considered in the case that a probabilistic description of noise and errors is not available (of suitable), but only a bound on them is known. In the present paper only linear parametrizations and estimators are considered. Very simple and computationally feasible algorithms are derived for evaluating two different types of uncertainty intervals (Estimates Uncertainty Intervals, Parameter Uncertainty Intervals). The relationships between the EUI's and the PUI's are established, and the solution to the problem of the minimum uncertainty intervals estimator is given: the latter can be obtained by means of a simple linear programming algorithm.
351 citations
TL;DR: A subset of agents forms a communicating ring if for every pair of ring members, there is a sequence of ring ring members such that each ring member knows that he is a ring member, and the estimates of all the ring members asymptotically agree as mentioned in this paper.
Abstract: Each of several agents updates his estimate of the same random variable whenever he makes a new observation or receives the estimate made by another agent. In turn, each agent transmits his estimate to a randomly chosen subset of the other agents. A subset of agents forms a communicating ring if for every pair \underline{m}, \underline{p} of ring members, there is a sequence of ring members \underline{m} = \underline{m}_{1}, \underline{m}_{2}, ... , \underline{m}_{n+1} = \underline{p} such that \underline{m}_{i} sends his estimate to \underline{m}_{i+1} infinitely often. If each ring member knows that he is a ring member, then the estimates of all the ring members asymptotically agree. However, this common limit can depend upon the order in which estimates are transmitted.
336 citations
TL;DR: In this paper, the adaptive control of a linear time-invariant plant in the presence of bounded disturbances is considered, and the adaptive controller suggested assures the boundedness of all signals in the overall system.
Abstract: The adaptive control of a linear time-invariant plant in the presence of bounded disturbances is considered. In addition to the usual assumptions made regarding the plant transfer function, it is also assumed that the high-frequency gain k p of the plant and an upper bound on the magnitude of the controller parameters are known. Under these conditions the adaptive controller suggested assures the boundedness of all signals in the overall system.
285 citations
TL;DR: In this paper, an explicit relationship between the fractional representation approach feedback system design and the algebro-geometric approach to system theory is formulated and used to derive a global solution to the feedback system problem.
Abstract: An explicit relationship between the fractional representation approach feedback system design and the algebro-geometric approach to system theory, is formulated and used to derive a global solution to the feedback system problem. These techniques are then applied to the simultaneous stabilization problem, yielding a natural geometric criterion for a set of plants to be simultaneously stabilized by a single compensator.
277 citations
TL;DR: It is proposed that the goal of retransmission policies should be to maintain the traffic intensity at a nearly constant, optimum level, and introduced policies to achieve this goal by nearly decoupling the dynamics of the trafficintensity from the backlog fluctuations.
Abstract: Retransmission policies are presented for the decentralized control of a multiaccess packet-switched broadcast channel. The policies have a simple recursive form yielding a Markov description of the system. Finite average delay is achieved for an infinite-population Poisson arrival model for any rate \lambda . It is proposed that the goal of retransmission policies should be to maintain the traffic intensity at a nearly constant, optimum level. The policies we introduce achieve this goal by nearly decoupling the dynamics of the traffic intensity from the backlog fluctuations. Analysis and simulations show that the policies perform well, even when the channel feedback information is unreliable or incomplete.
269 citations
TL;DR: In this article, the problem of combining and updating estimates that may have been generated in a distributed fashion or may represent estimates, generated at different times, of the same process sample path is considered.
Abstract: In this paper we consider the problem of combining and updating estimates that may have been generated in a distributed fashion or may represent estimates, generated at different times, of the same process sample path. The first of these cases has applications in decentralized estimation, while the second has applications in updating maps of spatially-distributed random quantities given measurements along several tracks. The method of solution for the second problem uses the result of the first, and the similarity in the formulation and solution of these problems emphasizes the conceptual similarity between many problems in decentralized control and in the analysis of random fields.
TL;DR: In this article, the authors consider the class of delay differential systems of the retarded type with commensurate time delays and give sufficient conditions and a necessary condition based on local stabilizability.
Abstract: Notions of exponential stability independent of delay and stabilizability independent of delay are developed for the class of delay differential systems of the retarded type with commensurate time delays. Various criteria for exponential stability independent of delay with a given order are specified in terms of matrices whose entries are functions of a single real parameter and polynomials in one variable whose coefficients are functions of a single real parameter. Sufficient conditions and a necessary condition based on local stabilizability are given for stabilizability independent of delay using state feedback with commensurate time delays. Constructive methods for determining a stabilizing feedback are also presented. The last part of the paper deals with a standard type of observer and regulator with the requirement that the closed-loop system be stable independent of delay.
TL;DR: Characterizations and algorithmic approaches for a class of two-level problems are discussed and a formulation to help model this type of decision making hierarchy is offered.
Abstract: Decentralized planning has long been recognized as an important decision making problem. Many approaches based on the concepts of large scale system decomposition have generally lacked the ability to model the type of truly independent subsystems which have often existed in practice. Similarly, tractable game-theoretic approaches have not allowed for a continuous solution space in which one player's decision restricts the feasible choices of another. This correspondence offers a formulation to help model this type of decision making hierarchy. Characterizations and algorithmic approaches for a class of two-level problems are discussed.
TL;DR: In this paper, a robust multivariable PI-controller was proposed for a class of distributed parameter systems. But it is not shown that the controller can be tuned on the basis of step responses without exact knowledge of the system's parameters.
Abstract: A robust multivariable controller is introduced for a class of distributed parameter systems. The system to be controlled is given as \dot{x} = Ax + Bu, y = Cx in a Banach space. The purpose of the control, which is based on the measurement y , is to stabilize and regulate the system so that y(t) \rightarrow y_{r}, as t \rightarrow \infty , where y r is a constant reference vector. Under the assumptions that operator A generates a holomorphic stable semigroup, B is linear and bounded, C is linear and A -bounded, and the input and output spaces are of the same dimension; a necessary and sufficient condition is found for the existence of a robust multivariable controller. This controller appears to be a multivariable PI-controller. Also, a simple necessary criterion for the existence of a decentralized controller is derived. The tuning of the controller is discussed and it is shown that the I-part of the controller can be tuned on the basis of step responses, without exact knowledge of the system's parameters. The presented theory is then used as an example to control the temperature profile of a bar, with the Dirichlet boundary conditions.
TL;DR: The optimal policy is of the form u=a or u=0 according as x_{1} and S is a switching function and can be nonergodic, but it is ergodic for the case of average cost.
Abstract: Customers arrive in a Poisson stream into a network consisting of two M/M/1 service stations in tandem. The service rate u \in [0, a] at station 1 is to be selected as a function of the state ( x_{1}, x_{2} ) where x i is the number of customers at station i so as to minimize the expected total discounted or average cost corresponding to the instantaneous cost c_{1}x_{1} + c_{2}x_{2} . The optimal policy is of the form u=a or u=0 according as x_{1} and S is a switching function. For the case of discounted cost, the optimal process can be nonergodic, but it is ergodic for the case of average cost.
TL;DR: In this paper, an adaptive control structure which can be used to assign all poles and zeros of a continuous-time linear multivariable system represented by an (m \times m ) strictly proper transfer matrix T(s) is presented.
Abstract: This paper presents an adaptive control structure which can be used to assign all poles and zeros of a continuous-time linear multivariable system represented by an ( m \times m ) strictly proper transfer matrix T(s) , provided T(s) has no right-half plane zeros. The controller parameters can be directly estimated from input-output data. The paper also serves to point out the type of a priori information necessary for multivariable adaptive controller design. This information is a natural extension of that required in the scalar case.
TL;DR: In this paper, a modal approach utilizing known finite-dimensional algorithms for observer and stabilizer design is proposed for a large class of parabolic distributed systems, where the observer is constructed from observations taken from point or averaging sensors and the compensator is a feedback of this observer and can be a "distributed" or "boundary" implementation.
Abstract: A compensator design is proposed for a large class of parabolic distributed systems. Basically, it is a modal approach utilizing known finite-dimensional algorithms for observer and stabilizer design. The observer is constructed from observations taken from point or averaging sensors and the compensator is a feedback of this observer and can be a "distributed" or "boundary" implementation. Explicit sufficient conditions are given for the convergence of this scheme.
TL;DR: In this article, a new criterion for asymptotic stability of solutions of certain linear differential-difference equations (independent of the delay duration) is given in terms of the solutions of a complex Lyapunov matrix equation.
Abstract: A new criterion for asymptotic stability of solutions of certain linear differential-difference equations (independent of the delay duration) is given in terms of solutions of a complex Lyapunov matrix equation.
TL;DR: In this article, the eigenvalue-assignment approach of Brogan was generalized and extended to the assignment of the entire closed-loop eigenstructure of linear multivariable systems.
Abstract: The eigenvalue-assignment approach of Brogan [1], [2] is generalized and extended to the assignment of the entire closed-loop eigenstructure of linear multivariable systems The set of assignable eigenvectors and generalized eigenvectors emerges naturally in the solution and is given, moreover, in an explicit parametric form Two numerical examples are worked out to demonstrate the application of the procedure
TL;DR: In this article, a new method of model reduction is introduced based on the differentiation of polynomials, which is computationally very simple and is equally applicable to unstable and non-minimum phase systems.
Abstract: A new method of model reduction is introduced based on the differentiation of polynomials. The reciprocals of the numerator and denominator polynomials of the high-order transfer function are differentiated suitably many times to yield the coefficients of the reduced order transfer function. An error analysis shows the accuracy of the method, and an eighth-order example illustrates it. The method is computationally very simple and is equally applicable to unstable and nonminimum phase systems.
TL;DR: In this article, the balanced representations of linear systems due to Moore are shown to be natural and convenient mediums for singular perturbational model reduction, and the balanced representation is used for linear systems in the singular model reduction problem.
Abstract: The balanced representations of linear systems due to Moore are shown to be natural and convenient mediums for singular perturbational model reduction.
TL;DR: In this article, it was shown that all admissible structures will give asymptotically the same value to this criterion, and two heuristic structure estimation methods were analyzed.
Abstract: When identifying a model for a multivariate stationary stochastic process, an important problem is that of determining the structure of the state-variable model. Several "overlapping" parameterizations can usually be fitted to a given process, and the question arises as to which structure leads to the most accurate parameter estimates. The accuracy of parameter estimates is often measured by the determinant of the Fisher information matrix. We show that all admissible structures will give asymptotically the same value to this criterion. For finite data some structures may still be better than others, and two heuristic structure estimation methods are analyzed. Some simulation results are also presented.
IBM1
TL;DR: The conceptual form of an algorithm is presented for finding a feedback solution to the optimal control problem when the inputs are assumed to be constant in time and the algorithm employs a combination of necessary conditions, dynamic programming, and linear programming to construct a set of convex polyhedral cones which cover the admissible state space with optimal controls.
Abstract: This paper explores the application of optimal control theory to the problem of dynamic routing in networks. The approach derives from a continuous state space model for dynamic routing and an associated linear optimal control problem with linear state and control variable inequality constraints. The conceptual form of an algorithm is presented for finding a feedback solution to the optimal control problem when the inputs are assumed to be constant in time. The algorithm employs a combination of necessary conditions, dynamic programming, and linear programming to construct a set of convex polyhedral cones which cover the admissible state space with optimal controls. An implementable form of the algorithm, along with a simple example, is presented for a special class of single destination networks.
TL;DR: It is shown that minimum queuing delay path algorithms tend to exhibit violent oscillatory behavior in the absence of a damping mechanism, and two types of schemes are analyzed in this paper.
Abstract: Several proposed routing algorithms for store and forward communication networks, including one currently in operation in the ARPANET route messages along shortest paths computed by using some set of link lengths. When these lengths depend on current traffic conditions as they must in an adaptive algorithm, dynamic behavior questions such as stability, convergence, and speed of convergence are of interest. This paper is the first attempt to analyze systematically these issues. It is shown that minimum queuing delay path algorithms tend to exhibit violent oscillatory behavior in the absence of a damping mechanism. The oscillations can be damped by means of several types of schemes two of which are analyzed in this paper. In the first scheme a constant bias is added to the queuing delay thereby providing a preference towards paths with a small number of links. In the second scheme the effects of several past routings are averaged as for example when the link lengths are computed and communicated asynchronously throughout the network.
TL;DR: A criterion is given for measuring the tracking capability of recursive algorithms when applied to slowly time-varying systems; the optimal gain for a given disturbance is also calculated.
Abstract: A criterion is given for measuring the tracking capability of recursive algorithms when applied to slowly time-varying systems; the optimal gain for a given disturbance is also calculated. This criterion is seen to have some connection with the Fisher information matrix, and allows us to select a priori the best algorithm for identifying a given unknown parameter which may be subject to smooth unknown disturbances. Examples of applications are given in the areas of identification theory and data communication theory.
TL;DR: A simplified derivation of the general update formulas for such ladder forms is presented, and is used to develop the growing memory and sliding memory covariance ladder algorithms.
Abstract: Square root normalized ladder algorithms provide an efficient recursive solution to the problem of multichannel autoregressive model fitting. A simplified derivation of the general update formulas for such ladder forms is presented, and is used to develop the growing memory and sliding memory covariance ladder algorithms. New ladder form realizations for the identified models are presented, leading to convenient methods for computing the model parameters from estimated reflection coefficients. A complete solution to the problem of possible singularity in the ladder update equations is also presented.
TL;DR: In this article, a cost function which includes the variance of the innovations process is used to optimize the performance of a stochastic system with unknown parameters, and the relationship among the controller obtained in this paper and the certainty equivalence and cautious controllers is analyzed.
Abstract: The control of a stochastic system with unknown parameters is considered. A novel cost function which includes the variance of the innovations process is used to optimize the performance of the system. The cost function has two parts. One that reflects the goal of regulating the output, and the second one that reflects the need to gather as much information as possible about the parameters of the system, the latter being represented by the variance of the innovation process. The control law derived has an explicit solution that allows for an easy implementation, and has dual properties. The relationships among the controller obtained in this paper and the certainty equivalence and cautious controllers are analyzed. Simulation results show the quasi-optimal performance of the new controller.
TL;DR: In this article, it was shown that a square invertible linear system (C, A, B ) is decouplable by static state feedback if and only if its infinite zero orders are respectively equal to the zero orders of the subsystems (c' i, A, B ), where c' i denotes the i th row of C.
Abstract: The purpose of this note is to demonstrate that a square invertible linear system ( C, A, B ) is decouplable by static state feedback if and only if its infinite zero orders are respectively equal to the infinite zero orders of the subsystems ( c'_{i}, A, B ) where c'_{i} denotes the i th row of C . Until now only the necessity of this condition has been established [1].
TL;DR: In this paper, a theory of regulators is developed for finite-free split linear systems over a commutative ring K, which is achieved by developing a theory, of coefficient-assignment and observers.
Abstract: A theory of regulators is developed for finite-free split linear systems over a commutative ring K . This is achieved by developing a theory, of coefficient-assignment and observers. It is shown that the problem of coefficient-assignment can be solved for reachable systems by using dynamic state feedback. For strongly observable systems, it is shown that observers with arbitrary dynamics can be constructed. Internal stability of observer and state feedback configuration is considered explicitly. Some examples are given to illustrate these techniques.
TL;DR: The basic principle of the stochastic automation has been extended to the dimensionality of the automaton by gradually optimizing the resolution of the input variables.
Abstract: This paper reports on the use of the stochastic automaton theory to configure control algorithms for high precision assembly operations performed with a force-sensing robot. The basic principle of the stochastic automation, i.e., its variable structure, has been extended to the dimensionality of the automaton by gradually optimizing the resolution of the input variables.