Showing papers in "IEEE Transactions on Automatic Control in 1985"
TL;DR: In this paper, the problem of moving a manipulator in minimum time along a specified geometric path subject to input torque/force constraints is considered, and the minimum-time solution is deduced in an algorithm form using phase-plane techniques.
Abstract: Conventionally, robot control algorithms are divided into two stages, namely, path or trajectory planning and path tracking (or path control). This division has been adopted mainly as a means of alleviating difficulties in dealing with complex, coupled manipulator dynamics. Trajectory planning usually determines the timing of manipulator position and velocity without considering its dynamics. Consequently, the simplicity obtained from the division comes at the expense of efficiency in utilizing robot's capabilities. To remove at least partially this inefficiency, this paper considers a solution to the problem of moving a manipulator in minimum time along a specified geometric path subject to input torque/force constraints. We first describe the manipulator dynamics using parametric functions which represent geometric path constraints to be honored for collision avoidance as well as task requirements. Second, constraints on input torques/ forces are converted to those on the parameters. Third, the minimum-time solution is deduced in an algorithm form using phase-plane techniques. Finally, numerical examples are presented to demonstrate utility of the trajectory planning method developed.
1,016 citations
940 citations
TL;DR: In this article, the use and design of linear periodic time-varying controllers for the feedback control of linear time-invariant discrete-time plants is considered. And the authors show that for a large class of robustness problems, periodic compensators are superior to time-inariant ones.
Abstract: This paper considers the use and design of linear periodic time-varying controllers for the feedback control of linear time-invariant discrete-time plants. We will show that for a large class of robustness problems, periodic compensators are superior to time-invariant ones. We will give explicit design techniques which can be easily implemented. In the context of periodic controllers, we also consider the strong and simultaneous stabilization problems. Finally, we show that for the problem of weighted sensitivity minimization for linear time-invariant plants, time-varying controllers offer no advantage over the time-invariant ones.
672 citations
TL;DR: In this article, the authors express limitations imposed by right half plane poles and zeros of the open-loop system directly in terms of the sensitivity and complementary sensitivity functions of the closed-loop systems.
Abstract: This paper expresses limitations imposed by right half plane poles and zeros of the open-loop system directly in terms of the sensitivity and complementary sensitivity functions of the closed-loop system. The limitations are determined by integral relationships which must be satisfied by these functions. The integral relationships are interpreted in the context of feedback design.
666 citations
TL;DR: It is concluded that existing adaptive control algorithms, as presented in the literature referenced in this paper, cannot be used with confidence in practical designs where the plant contains unmodeled dynamics because instability is likely to result.
Abstract: This paper examines the robustness properties of existing adaptive control algorithms to unmodeled plant high-frequency dynamics and unmeasurable output disturbances. It is demonstrated thai there exist two infinite-gain operators in the nonlinear dynamic system which determines the time-evolution of output and parameter errors. The pragmatic implication of the existence of such infinite-gain operators is that 1) sinusoidal reference inputs at specific frequencies and/or 2) sinusoidal output disturbances at any frequency (including dc), can cause the loop gain to increase without bound, thereby exciting the unmodeled high-frequency dynamics, and yielding an unstable control system. Hence, it is concluded that existing adaptive control algorithms as they are presented in the literature referenced in this paper, cannot be used with confidence in practical designs where the plant contains unmodeled dynamics because instability is likely to result. Further understanding is required to ascertain how the currently implemented adaptive systems differ from the theoretical systems studied here and how further theoretical development can improve the robustness of adaptive controllers.
657 citations
TL;DR: An analogy between linear systems and a class of discrete-event systems is developed that can be viewed as linear, in the sense of an appropriate algebra, and the potentiality of this approach for the performance evaluation of repetitive production processes is illustrated.
Abstract: A discrete-event system is a system whose behavior can be described by means of a set of time-consuming activities, performed according to a prescribed ordering. Events correspond to starting or ending some activity. An analogy between linear systems and a class of discrete-event systems is developed. Following this analogy, such discrete-event systems can be viewed as linear, in the sense of an appropriate algebra. The periodical behavior of closed discrete-event systems, i.e., involving a set of repeatedly performed activities, can be totally characterized by solving an eigenvalue and eigenvector equation in this algebra. This problem is numerically solved by an efficient algorithm which basically consists of finding the shortest paths from one node to all other nodes in a graph. The potentiality of this approach for the performance evaluation of flexible manufacturing systems is emphasized; the case of a flowshop-like production process is analyzed in detail.
533 citations
TL;DR: In this article, the authors provide a comprehensive survey of the existing methods and their applications in engineering fields, and present several examples of application of the proposed technique for low-order (second and third) systems.
Abstract: This paper deals with the problem of the estimation of regions of asymptotic stability for continuous, autonomous, nonlinear systems. The first part of the work provides a comprehensive survey of the existing methods and of their applications in engineering fields. In the second part certain topological considerations are first developed and the "trajectory reversing method" is then presented together with a theorem on which it is based. In the final part, several examples of application are reported, showing the efficiency of the proposed technique for low-order (second and third) systems.
470 citations
TL;DR: The results point to the inherent difficulty of decentralized decision making and suggest that optimality may be an elusive goal.
Abstract: We study the computational complexity of the discrete versions of some simple but basic decentralized decision problems. These problems are variations of the classical "team decision problem" and include the problem of decentralized detection whereby a central processor is to select one of two hypotheses, based on l-bit messages from two noncommunicating sensors. Our results point to the inherent difficulty of decentralized decision making and suggest that optimality may be an elusive goal.
420 citations
TL;DR: The main emphases are on the difference between socially optimal and individually optimal (equilibrium) controls and on the use of dynamic-programming inductive analysis to show that an optimal control is monotonic or characterized by one or more "critical numbers".
Abstract: Congestion in a queueing system can sometimes be controlled by restricting arrivals, either by "closing a gate" or by charging an entrance fee or toll. We review both static (open-loop) and dynamic (closed-loop) models for control of admission to a queueing system. The main emphases are on the difference between socially optimal and individually optimal (equilibrium) controls and on the use of dynamic-programming inductive analysis to show that an optimal control is monotonic or characterized by one or more "critical numbers." We discuss the potential for use of these models in the analysis of computer/ communication systems and compare the results to certain others in the literature.
411 citations
TL;DR: A new method is presented to find stabilizing saturated linear state feedback controllers for linear continuous-time and discrete-time systems.
Abstract: A new method is presented to find stabilizing saturated linear state feedback controllers for linear continuous-time and discrete-time systems. A controller of this type was satisfactorily tested on board a submarine as a depth regulator.
344 citations
TL;DR: In this article, a statistical approach is used to model the dynamics of the electric demand of large aggregates of electric space heaters or air conditioners, and the homogeneons group aggregrate load model is a system of coupled ordinary, and partial differential equations (Fokker-Planck equations).
Abstract: A statistical approach is used to model the dynamics of the electric demand of large aggregates of electric space heaters or air conditioners. The importance of such loads is twofold. First, they account for a significant portion of power system dynamics following a power outage. Second, because they are associated with energy storage, they are often selected for load shedding within a load management program. The derivation of the aggregate electrical dynamics is considered first for a homogeneous group of devices. Subsequently, a perturbation analysis yields the dynamics for a nonhomogeneous group. The homogeneons group aggregrate load model is a system of coupled ordinary, and partial differential equations (Fokker-Planck equations). It is obtained by writing evolution equations for the probability density of a hybrid-state Markov system used to model the switching dynamics of individual devices. This result is new and could give a clue to the analysis of a broad class of hybrid-state stochastic systems. In turn, this could provide a new impetus not only in the area of electric load modeling but other areas such as power system reliability and the design of relay control systems, where stochastic hybrid-state models occur frequently. Simulation results which illustrate the dynamical properties of the model are presented.
TL;DR: In this article, the authors introduce the gap metric to study the robustness of the stability of feedback systems which may employ not necessarily stable open-loop systems, and provide upper bounds to the gap in cases where the exact formulas do not apply.
Abstract: In this paper we introduce the gap metric to study the robustness of the stability of feedback systems which may employ not necessarily stable open-loop systems. We elaborate on the computational aspects of the gap metric and provide upper bounds to the gap in cases where the exact formulas do not apply, By admissible uncertainties we mean those which preserve closed-loop stability and a specified small tolerance on the I/O behavior of a feedback system. We show that admissible uncertainties are precisely those which are constrained in the gap. Finally, we conclude that any metric which preserves a continuous relationship between open-loop systems and the corresponding stable feedback interconnections must have the topology of the gap metric.
TL;DR: In this article, a modified gain extended Kalman observer (MGEKO) was developed for a special class of systems and a sufficient condition for the estimation errors of the MGEKF to be exponentially bounded in the mean square was obtained.
Abstract: A new globally convergent nonlinear observer, called the modified gain extended Kalman observer (MGEKO), is developed for a special class of systems. This observer structure forms the basis of a new stochastic filter mechanization called the modified gain extended Kalman filter (MGEKF). A sufficient condition for the estimation errors of the MGEKF to be exponentially bounded in the mean square is obtained. Finally, the MGEKO and the MGEKF are applied to the three-dimensional bearings-only measurement problem where the extended Kalman filter often shows erratic behavior.
TL;DR: In this paper, it was shown that feedback system design objectives, such as disturbance attenuation and rejection, power and bandwidth limitation, and robustness, may be expressed in terms of required bounds of the sensitivity function and its complement on the imaginary axis.
Abstract: It is shown that feedback system design objectives, such as disturbance attenuation and rejection, power and bandwidth limitation, and robustness, may be expressed in terms of required bounds of the sensitivity function and its complement on the imaginary axis. This leads to a minimax frequency domain optimization problem, whose solution is reduced to the solution of a polynomial equation.
TL;DR: A certain kind of metric on the disk (the "hyperbolic" metric) is used which allows the problem of robust stabilization of systems with many types of real and complex parameter variations to an easily solvable problem in non-Euclidian geometry.
Abstract: This paper considers, from a complex function theoretic point of view, certain kinds of robust synthesis problems. In particular, we use a certain kind of metric on the disk (the "hyperbolic" metric) which allows us to reduce the problem of robust stabilization of systems with many types of real and complex parameter variations to an easily solvable problem in non-Euclidian geometry. It is shown that several apparently different problems can be treated in a unified general framework. A new result on the gain margin problem for multivariable plants is also given. Finally, we apply our methods to systems with real zero or pole variations.
TL;DR: In this article, a smoothness priors time varying AR coefficient model approach for the modeling of nonstationary in the covariance time series is presented, where the unknown white noise variances are hyperparameters of the AR coefficient distribution.
Abstract: A smoothness priors time varying AR coefficient model approach for the modeling of nonstationary in the covariance time series is shown. Smoothness priors in the form of a difference equation constraint excited by an independent white noise are imposed on each AR coefficient. The unknown white noise variances are hyperparameters of the AR coefficient distribution. The critical computation is of the likelihood of the hyperparameters of the Bayesian model. This computation is facilitated by a state-space representation Kalman filter implementation. The best difference equation order-best AR model order-best hyperparameter model locally in time is selected using the minimum AIC method. Also, an instantaneous spectral density is defined in terms of the instantaneous AR model coefficients and a smoothed estimate of the instantaneous time series variance. An earthquake record is analyzed. The changing spectral analysis of the original data and of simulations from a time varying AR coefficient model of that data are shown.
TL;DR: In this paper, a sequential numerical algorithm is described which obtains gains minimizing a broad class of performance indexes, including the standard LQ case, under nonrestrictive assumptions.
Abstract: A sequential numerical algorithm is described which obtains gains minimizing a broad class of performance indexes, including the standard LQ case. The primary contribution is a proof that the algorithm converges to a local minimum under nonrestrictive assumptions. Numerical examples illustrate the theory. The second example demonstrates an important LQ design technique which permits the designer to prespecify the feedback structure, subject to the requirement of output feedback stabilizability.
TL;DR: In this paper, the first-order necessary conditions for quadratically optimal reduced-order modeling of linear time-invariant systems are derived in the form of a pair of modified Lyapunov equations coupled by an oblique projection which determines the optimal reduced order model.
Abstract: First-order necessary conditions for quadratically optimal reduced-order modeling of linear time-invariant systems are derived in the form of a pair of modified Lyapunov equations coupled by an oblique projection which determines the optimal reduced-order model. This form of the necessary conditions considerably simplifies previous results of Wilson [1] and clearly demonstrates the quadratic extremality and nonoptimality of the balancing method of Moore [2]. The possible existence of multiple solutions of the optimal projection equations is demonstrated and a relaxation-type algorithm is proposed for computing these local extrema. A component-cost analysis of the model-error criterion similar to the approach of Skelton [3] is utilized at each iteration to direct the algorithm to the global minimum.
TL;DR: In this article, a bound on the structured perturbation of an asymptotically stable linear system is obtained to maintain stability using a Lyapunov matrix equation solution.
Abstract: In this paper, the aspect of "stability robustness" of linear systems is analyzed in the time domain. A bound on the structured perturbation of an asymptotically stable linear system is obtained to maintain stability using a Lyapunov matrix equation solution. The resulting bound is shown to be an improved bound over the ones recently reported in the literature. Also, special cases of the nominal system matrix are considered, for which the bound is given in terms of the nominal matrix, thereby, avoiding the solution of the Lyapunov matrix equation. Examples given include comparison of the proposed approach with the recently reported results.
TL;DR: In this article, the theory of optimal algorithms for problems which cannot be solved exactly is investigated, which allows for the derivation of new and interesting results in parameter estimation and in time series prediction in situations where no reliable statistical hypothesis can be made on the functions and modeling errors involved.
Abstract: This paper deals with the theory of optimal algorithms for problems which cannot be solved exactly. The theory developed allows for the derivation of new and interesting results in parameter estimation and in time series prediction in situations where no reliable statistical hypothesis can be made on the functions and modeling errors involved, but only a bound on them is known, in particular, the derivation of computationally simple optimal algorithms for these two problems is investigated. The practical effectiveness of the algorithms obtained is illustrated by several numerical examples.
TL;DR: In this article, sufficient conditions for linear time-delay systems are derived and expressed by succinct scalar inequalities, which correspond to a certain extent to the tradeoff between simplicity and sharpness.
Abstract: Several sufficient conditions which guarantee stability of linear time-delay systems are derived. Each of these results is expressed by a succinct scalar inequality and corresponds to a certain extent to the tradeoff between simplicity and sharpness.
TL;DR: The result is that the joint covariance matrix of the transfer functions from input to output and from driving white noise source to the additive output disturbance, respectively, is proportional to the inverse of the joint spectrum matrix for the input and driving noise multiplied by the spectrum of the additiveoutput noise.
Abstract: Identification of black-box transfer function models is considered. It is assumed that the transfer function models possess a certain shift-property, which is satisfied for example by all polynomial-type models. Expressions for the variances of the transfer function estimates are derived, that are asymptotic both in the number of observed data and in the model orders. The result is that the joint covariance matrix of the transfer functions from input to output and from driving white noise source to the additive output disturbance, respectively, is proportional to the inverse of the joint spectrum matrix for the input and driving noise multiplied by the spectrum of the additive output noise. The factor of proportionality is the ratio of model order to number of data. This result is independent of the particular model structure used. The result is applied to evaluate the performance degradation due to variance for a number of typical model uses. Some consequences for input design are also drawn.
TL;DR: A reformulation of the bandit problem yields the tax problem, which includes Klimov's waiting time problem, and an index rule is derived for the case where new machines arrive randomly.
Abstract: There are N independent machines. Machine i is described by a sequence {X^{i}(s), F^{i}(s)} where X^{i}(s) is the immediate reward and F^{i}(s) is the information available before i is operated for the sth lime. At each time one operates exacfiy one machine; idle machines remain frozen. The problem is to schedule the operation of the machines so as to maximize the expected total discounted sequence of rewards. An elementary proof shows that to each machine is associated an index, and the optimal policy operates the machine with the largest current index. When the machines are completely observed Markov chains, this coincides with the well-known Gittins index rule, and new algorithms are given for calculating the index. A reformulation of the bandit problem yields the tax problem, which includes, as a special case, Klimov's waiting time problem. Using the concept of superprocess, an index rule is derived for the case where new machines arrive randomly. Finally, continuous time versions of these problems are considered for both preemptive and nonpreemptive disciplines.
TL;DR: In this article, the general state-space model for a 2D linear digital system is presented and a new definition of state-transition matrix is given based on the definition.
Abstract: The general state-space model for a 2-D linear digital system is presented. A new definition of state-transition matrix is given. Based on the definition, it is easy to calculate the state-transition matrix for any linear digital system. The general response formula for a system follows simply from the definition. A new definition of the characteristic function of a system and a theorem parallel to the Cayley-Hamilton theorem are also given. The presented results apply to any linear causal system.
TL;DR: In this article, an algorithm for adaptively controlling a single-input, single-output process admitting an n -dimensional, minimum-phase linear model of relative degree n*, with unknown parameters is presented.
Abstract: This paper presents an algorithm for adaptively controlling a single-input, single-output process admitting an n -dimensional, minimum-phase linear model of relative degree n*, with unknown parameters. A priori knowledge of the sign of the model's high frequency gain is not required, and a sufficiently rich probing signal is not needed for stabilization.
TL;DR: In this paper, the design of linear two-degree-of-freedom stabilizing controllers is treated in a quadratic-cost setting and the class of all such controllers which give finite cost is established and the tradeoff possible between optimum performance, tracking cost sensitivity, and stability margins is discussed.
Abstract: The design of linear two-degree-of-freedom stabilizing controllers is treated in a quadratic-cost setting. The class of all such controllers which give finite cost is established and the tradeoff possible between optimum performance, tracking-cost sensitivity, and stability margins is discussed.
TL;DR: In this article, the authors considered the problem of estimating the transfer function of a linear, stochastic system, where no given order is chosen a priori, and the transfer functions are parametrized as a black box.
Abstract: The problem of estimating the transfer function of a linear, stochastic system is considered. The transfer function is parametrized as a black box and no given order is chosen a priori. This means that the model orders may increase to infinity when the number of observed data tends to infinity. The consistency and convergence properties of the resulting transfer function estimates are investigated. Asymptotic expressions for the variances and distributions of these estimates are also derived for the case that the model orders increase. It is shown that the variance of the transfer function estimate at a certain frequency is asymptotically given by the noise-to-signal ratio at that frequency mulliplied by the model-order-to-number-of-data-points ratio.
TL;DR: In this article, the tracking and disturbance rejection of a class of MIMO nonlinear systems with linear proportional plus integral (PI) compensator was studied. And they showed that a simple PI compensator can be used to yield a stable unity-feedback closed-loop system which asymptotically tracks reference inputs that tend to constant vectors.
Abstract: We study tracking and disturbance rejection of a class of MIMO nonlinear systems with linear proportional plus integral (PI) compensator. Roughly speaking, we show that if the given nonlinear plant is exponentially stable and has a strictly increasing dc steady-state I/O map, then a simple PI compensator can be used to yield a stable unity-feedback closed-loop system which asymptotically tracks reference inputs that tend to constant vectors and asymptotically rejects disturbances that tend to constant vectors.
TL;DR: In this paper, a method is presented for obtaining the largest hypersphere centered at t = [t 1, t n] containing only polynomials which are stable, where t n is the number of vertices that can be perturbed while preserving the stability properties.
Abstract: Given a polynomial P_{c}(S) = S^{n} + t_{1}S^{n-1} + ... t_{n} = 0 which is Hurwitz or P_{d}(Z) = Z^{n} + t_{1}Z^{n-1} + ... t_{n} = 0 which has zeros only within or on the unit circle, it is of interest to know how much the coefficients t j can be perturbed while preserving the stability properties. In this note, a method is presented for obtaining the largest hypersphere centered at t^{T} = [t_{1} ... t_{n}] containing only polynomials which are stable.
TL;DR: In this article, direct and indirect adaptive control schemes for assigning the closed-loop poles of a single-input, single-output system in both the continuous and discrete-time cases are presented.
Abstract: This paper presents direct and indirect adaptive control schemes for assigning the closed-loop poles of a single-input, single-output system in both the continuous- and discrete-time cases. The resulting closed-loop system is shown to be globally stable when driven by an external reference signal consisting of a sum of sinusoids. In particular, persistent excitation of the potentially unbounded closed-loop input-output data, and hence convergence of a sequential least-squares identification algorithm is proved. The results are applicable to standard sequential least squares, and least squares with covariance reset.