Showing papers in "International Journal of Control in 1988"
TL;DR: This paper describes an approach to the design of ‘interaction controllers’ and contrasts this with an Approach to the Design of Approaches toDynamic interaction with the environment is fundamental to the process of manipulation.
Abstract: Dynamic interaction with the environment is fundamental to the process of manipulation. This paper describes an approach to the design of ‘interaction controllers’ and contrasts this with an approa...
611 citations
TL;DR: In this article, an orthogonal parameter estimation algorithm is proposed which allows each parameter in a linear-in-the-parameters nonlinear difference equation model to be estimated sequentially and quite independently of the other parameters in the model.
Abstract: An orthogonal parameter estimation algorithm is derived which allows each parameter in a linear–in–the–parameters non–linear difference equation model to be estimated sequentially and quite independently of the other parameters in the model. The algorithm can be applied for any persistently exciting input and provides both unbiased estimates in the presence of correlated noise and an indication of which terms to include in the model. Several simulated examples are included to demonstrate the effectiveness of the algorithm.
380 citations
TL;DR: In this article, a globally stable tracking controller for robot manipulators is described, which is an extension of Takegaki and Arimoto's position controller to the tracking case where a theorem of Matrosov is used to prove its stability.
Abstract: We describe a globally stable tracking controller for robot manipulators. The controller is an extension of Takegaki and Arimoto's position controller to the tracking case where a theorem of Matrosov is used to prove its stability. An attractive feature of this controller is its resemblance to the computed torque controller with the inertia matrix outside the position and velocity feedback loops. Thus, our controller is decomposed into an inner PD loop and an outer dynamic compensation loop. This structure allows the simple PD computations to be run at a higher speed than the dynamic compensation loop in digital implementations.
377 citations
TL;DR: In this paper, a new class of exponentially stabilizing control laws for joint level control of robot arms is introduced, based on the non-linear dynamics associated with robotic manipulations.
Abstract: A new class of exponentially stabilizing control laws for joint level control of robot arms is introduced. It has recently been recognized that the non-linear dynamics associated with robotic manip...
275 citations
TL;DR: In this article, a differential geometric approach for the design of sliding modes in non-linear variable-structure feedback systems is presented, which uses basic notions from differential geometry involving vector fields, distributions and 1-forms.
Abstract: This article presents a differential geometric approach for the design of sliding modes in non-linear variable-structure feedback systems. Coordinate-free characterizations of local existence conditions for sliding regimes, and a geometric reformulation of some of its most salient features are presented. The approach uses basic notions from differential geometry involving vector fields, distributions and 1-forms. Both single- and multiple-input cases are treated with some illustrative examples.
224 citations
TL;DR: A new algorithm is proposed which incorporates exponential forgetting and resetting to an unprejudiced treatment of data when excitation is poor and is particularly suitable for tracking time-varying parameters.
Abstract: In this paper we present the general analysis of a class of least squares algorithms with emphasis on their dynamic performance particularly in the presence of poor excitation. The analysis is carried out in a deterministic framework and stresses geometrical interpretations. The core of this paper is the proposal and analysis of a new algorithm which incorporates exponential forgetting and resetting to an unprejudiced treatment of data when excitation is poor. The algorithm is particularly suitable for tracking time-varying parameters and is similar in computational complexity to the standard recursive least squares algorithm. The superior performance of the algorithm is verified via simulation studies.
224 citations
TL;DR: A general approach for designing and the theory for analysing robust direct and indirect adaptive control schemes for continuous-time plants is presented in this paper, which involves the development of a general robust adaptive law and the use of the certainty equivalence principle to combine it with robust model reference and pole placement control structures.
Abstract: A general approach for designing and the theory for analysing robust direct and indirect adaptive-control schemes for continuous-time plants is presented. The design approach involves the development of a general robust adaptive law and the use of the certainty equivalence principle to combine it with robust model reference and pole placement control structures. The global stability properties and robustness of the developed adaptive control schemes are established by using a general theory which relates the properties of signals in the mean sense over intervals of time. The developed theory and design approach are used to analyse and compare the robustness properties and performance of a wide class of robust adaptive laws which employ a dead-zone, fixed-σ, e1, and a switching-σ modification as well as their variations.
199 citations
TL;DR: In this article, the problem of stabilizing linear discrete-time systems under state and control linear constraints is studied, and existence conditions of linear state feedback control laws respecting both the constraints are established.
Abstract: In this paper the problem of stabilizing linear discrete-time systems under state and control linear constraints is studied. Based on the concept of positive invariance, existence conditions of linear state feedback control laws respecting both the constraints are established. These conditions are then translated into an algorithm of linear programming.
196 citations
TL;DR: The problem of the existence of positively invariant polyhedral sets for linear discrete-time dynamical systems is studied in this paper, where necessary and sufficient conditions for a polyhedral polyhedral set are given.
Abstract: The problem of the existence of positively invariant polyhedral sets for linear discrete-time dynamical systems is studied. In the first part of the paper, necessary and sufficient conditions for a...
193 citations
TL;DR: In this article, the regulator problem for linear discrete-time systems with non-symmetrical constrained control is studied, i.e. systems described by the state equation x k+1/1/ε = Ax k+Bu k, where u k ∊/Ω, and u k = Fx k. Necessary and sufficient conditions allowing to obtain the largest nonsymmetric polyhedral domain of positive invariance and contractivity with respect to motions of the system in the closed loop are established.
Abstract: The regulator problem is studied for linear discrete-time systems with non-symmetrical constrained control, i.e. systems described by the state equation x k+1 = Ax k + Bu k, where u k ∊ Ω, and u k = Fx k. Necessary and sufficient conditions allowing us to obtain the largest non-symmetrical polyhedral domain of positive invariance and contractivity with respect to motions of the system in the closed loop are established. The case of symmetrically constrained control is obtained as a particular case.
183 citations
TL;DR: For non-linear MIMO systems, the extended Luenberger observer as discussed by the authors is a nonlinear observer design for all sufficiently smooth and locally observable systems that can be simplified using the degrees of freedom available in the case of multiple outputs.
Abstract: For non-linear multiple-input multiple-output systems [xdot] = f(x, u), y = h(x, u), nonlinear observers are designed using a transformation into the non-linear observer canonical form and an extended linearization The differential equation of observer error in canonical coordinates is linearized about the reconstructed trajectory, and dimensioned by eigenvalue assignment With reference to the extended Kalman filter algorithm, this non-linear observer design is called the extended Luenberger observer This observer design is possible for all sufficiently smooth and locally observable systems In comparison with single-output systems, the non-linear observer design can be essentially simplified using the degrees of freedom available in the case of multiple outputs
TL;DR: In this paper, an orthonormal Laguerre network is used to model a plant in state-space form and a simple predictive control law is proposed to handle non-minimum phase plants.
Abstract: The behaviour of adaptive controllers in the presence of unmodelled dynamics, and the need for reduced a priori information have led us to abandon the usual ARMA transfer function representation for a representation by an orthonormal series. The appeal of our new approach is that it eliminates the need for assumptions about the plant order and the time delay. The plant is modelled by an orthonormal Laguerre network put in state-space form. A simple predictive control law is proposed. An explicit deterministic adaptive controller is then designed. Simulations show that it is easy to use, able to handle non-minimum phase plants, and more robust than the conventional model-based approach. Although we chose Laguerre functions, other orthonormal functions may be used. We have already tested some with success.
TL;DR: An algorithm is developed and computer coded for failure-diagnosis-system design using a robust observation approach that can locate system failures to first-order components without a priori information on possible failure types.
Abstract: A new concept of faulty component detection via robust observation is proposed. An algorithm is developed and computer coded for failure-diagnosis-system design using a robust observation approach. Such diagnosis systems can locate system failures to first-order components without a priori information on possible failure types.
TL;DR: In this article, the controllability and observability of discrete-time linear systems that possess randomly jumping parameters described by finite-stale Markov processes are investigated. And the relationship between these properties and the solution of the infinite time jump linear quadratic (JLQ) optimal control problem is discussed.
Abstract: This paper is concerned with the controllability and observability of discrete-time linear systems that possess randomly jumping parameters described by finite-stale Markov processes, and the relationship between these properties and the solution of the infinite time jump linear quadratic (JLQ) optimal control problem. The solution of the markovian JLQ problem with finite or infinite time horizons is known. Necessary and sufficient conditions for the existence of optimal constant control laws that lead to finite optimal expected costs as the time horizon becomes infinite are also known. Sufficient conditions for these steady-state control laws to stabilize the controlled system are also available (Chizeck et al. 1986). These conditions are not easy to test, however. Various definitions of controllability and observability for stochastic systems exist in the literature. These definitions are unfortunately not related to the steady-state JLQ control problem in a manner that is analogous to the role of deter...
TL;DR: In this article, the concept of coprime fractional representations has been generalized to discrete-time non-linear systems by viewing the Bezout identity as the basis of the definition of coprimeness.
Abstract: Fractional representation methods for finite-dimensional linear time-invariant (FDLTI) systems have been developed in an algebraic framework of principal ideal domains. The concept of coprime fractional representations has been generalized to discrete-time non-linear systems by Hammer (1985, 1987), by viewing the Bezout identity as the basis of the definition of coprimeness. In this paper, we view the role of (right) coprime fractional representation in representing the set of all stable input-output pairs of a (possibly unstable) non-linear system. This notion of coprimeness is shown to be equivalent to that of FDLTI systems. Using coprime fractional representations of non-linear systems, we obtain a characterization of the stability of non-linear feedback systems. This characterization is similar to that obtained in the case of FDLTI systems. We also obtain a parameterization of all non-linear and time-varying stabilizing controllers for linear (possibly time-varying) plants which has the same form as t...
TL;DR: In this paper, a globally stable finite spectrum assignment adaptive controller for systems with delay is proposed, assuming that the process is minimum phase, though not necessarily stable, and the delay is known.
Abstract: We propose a globally stable finite spectrum assignment adaptive controller for systems with delay. It is assumed that the process is minimum phase, though not necessarily stable, and the delay is known. It is shown that the plant output asymptotically tracks a reference model output with all signals remaining bounded.
TL;DR: In this paper, the relation between the sampling period and the properties of complementary sensitivity functions in digital control systems was investigated. And the lower bounds of the H ∞-norm were derived, which showed that the feedback performance for the unstable plant with the stable digital compensator can be improved as the sample period goes to zero.
Abstract: Sensitivity and complementary sensitivity functions play a key role in feedback control system design. This paper is concerned with the relation between the sampling period and the properties of these functions in digital control systems. Some integral constraints and the lower bounds of the H ∞-norm are derived, which show that the feedback performance for the unstable plant with the stable digital compensator can be improved as the sampling period goes to zero.
TL;DR: In this article, the stabilization of time-delay systems containing saturating actuators is considered and two kinds of feedback stabilizing laws are treated: state feedback and sampled-state feedback.
Abstract: The problem of the stabilization of time-delay systems containing saturating actuators is considered. Two kinds of feedback stabilizing laws are treated: state feedback and sampled-state feedback. Several sufficient conditions are derived to guarantee the stability of the saturating time-delay system under control. Each of these results, expressed by a scalar inequality, permits us to assess the transient behaviour of the controlled system. The results presented enable a practical consideration of the unavoidable saturation of the actuators and give an insight into the stabilization analysis of saturating time-delay systems.
TL;DR: In this paper, a direct method for solving variational problems using Fourier series is presented, where an operational matrix of integration is first introduced and is utilized to reduce a variational problem to the solution of algebraic equations.
Abstract: A direct method for solving variational problems using Fourier series is presented. An operational matrix of integration is first introduced and is utilized to reduce a variational problem to the solution of algebraic equations. Illustrative examples are also given.
TL;DR: In this paper, the authors present necessary and sufficient conditions in terms of the ranks of matrices for the existence of a non-linear state coordinate change under which a time-variable system is transformed into an observer canonical form.
Abstract: This paper studies the non-linear observer design problem by observer canonical forms. We present necessary and sufficient conditions in terms of the ranks of matrices for the existence of a non-linear state coordinate change under which a time-variable system is transformed into an observer canonical form. These conditions give the multiple versions of Li and Tao (1986) for the single-output case. Then a comparison is made with the Lie algebraic conditions obtained by Krener and Respondek (1985), and modified by the authors in a recent paper (Xia and Gao 1987).
TL;DR: In this paper, a closed-loop observer that can identify states and inputs simultaneously is developed for linear time-invariant systems with unknown inputs, and necessary and sufficient conditions for the existence of the observer are derived and proved.
Abstract: A closed-loop observer that can identify states and inputs simultaneously is developed for linear time-invariant systems with unknown inputs. The necessary and sufficient conditions for the existence of the observer are derived and proved. Parameter identification of a system with a few unknown or time-varying parameters is investigated by applying the observer technique developed in this paper. Potential usage in machine monitoring (machine diagnostics) appears promising.
TL;DR: A modified version of the original differential dynamic programming (DDP) algorithm for unconstrained discrete optimal control problems is described, which differs from the original by a significant amount.
Abstract: A modified version of the original differential dynamic programming (DDP) algorithm for unconstrained discrete optimal control problems is described. This version, which differs from the original b...
TL;DR: In this paper, the authors show how to choose a Liapunov function to obtain the best and sometimes exact estimates of the degree of exponential stability for linear time-invariant discrete systems.
Abstract: The objective of this paper is to show how to choose a Liapunov function to obtain the best and sometimes exact estimates of the degree of exponential stability for linear time-invariant discrete systems. The choice is interesting because it is also shown that it provides the largest robustness bounds on non-linear time-varying perturbations which can be established by either norm-like or quadratic Liapunov functions. By applying the results obtained to large-scale systems, where the role of perturbations is played by the interconnections among the subsystems, the least conservative stability conditions are derived for the overall system which are available in the context of vector Liapunov functions and M-matrices.
TL;DR: In this paper, the convergence of poles and zeros of transfer functions and noise filters as the sampling interval tends to zero is studied. But the convergence results are generalizations of the results of Astrom, Hagander and Sternby (1984) on convergence of pole and zero for zero-order hold sampled transfer functions.
Abstract: Properties of discrete time systems obtained by sampling continuous time systems are described. By introducing prefilters, we can treat different ways of sampling within one framework. Results on the convergence of poles and zeros of transfer functions and noise filters as the sampling interval tends to zero are given. These results are generalizations of the results of Astrom, Hagander and Sternby (1984) on the convergence of poles and zeros for zero-order hold sampled transfer functions. Sampled noise models are also analysed. Knowledge of these properties is very important in, for example, discrete time simulations of continuous time systems, and identification of continuous time models based on discrete time measurements.
TL;DR: In this paper, a deterministic design approach for decentralized robust control of a class of large-scale uncertain dynamical systems is proposed, where no a priori statistical information is assumed or utilized.
Abstract: A deterministic design approach for decentralized robust controls of a class of large-scale uncertain dynamical systems is proposed. The uncertainty under consideration can be fast time-varying; no a priori statistical information is assumed or utilized. Only the possible bound of this uncertainty is known. Two important types of robust control algorithms are proposed. The local control utilizes the local state of each subsystem as the feedback information. The global control utilizes the local state as well as the states of the neighbouring subsystems as the feedback information. Both types of control algorithms are continuous functions of the state.
TL;DR: In this paper, the authors consider analytical control-affine non-linear continuous systems and use the matrix calculus to solve the problems of model identification, by orthogonal functions, and the construction of a nonlinear state-feedback for the optimal control problem.
Abstract: We consider analytical control-affine non-linear continuous systems. By the introduction of a notation based on the tensor product, we can use the matrix calculus to solve the problems of model identification, by orthogonal functions, and the construction of a non-linear state-feedback for the optimal control problem.
TL;DR: In this paper, the problem of designing a stable sliding mode giving robust performance of a variable structure control system is studied, where a set of specified eigenvalues are assigned to the closed-loop feedback system during the sliding mode.
Abstract: The problem of designing a stable sliding mode giving robust performance of a variable structure control system is studied. A set of specified eigenvalues is assigned to the closed-loop feedback system during the sliding mode. The design philosophy seeks to build on the known robustness and invariance properties associated with the use of discontinuous (or continuous) non-linear controls, by assigning the eigenvectors associated with the sliding-mode eigenvalues in a manner that leads to a robust control scheme. A previously developed canonical form for the hyperplane design problem is again employed. The design technique centres on a recently published eigenvalue assignment algorithm, and is illustrated by the inclusion of an example.
TL;DR: It is proved that an observer pole selection method can be formulated to minimize the observer gain to the system input and is a deterministic approach to the recovery of the loop transfer function and robustness of direct state feedback systems.
Abstract: This paper shows that based on the recent development of observer design solution, an observer pole selection method can be formulated to minimize the observer gain to the system input. It is proved that this method is a deterministic approach to the recovery of the loop transfer function and robustness of direct state feedback systems.
TL;DR: In this article, it was shown that the fractional-order hold and the pulse amplitude modulation signal reconstruction methods produce an inverse stable sampled transfer function H(z) in some cases when zero-order holds fails to do so.
Abstract: It is shown that for low-pass systems the fractional-order hold and the pulse amplitude modulation signal reconstruction methods produce an inverse stable sampled transfer function H(z) in some cases when zero-order hold fails to do so. Therefore they may be desirable alternatives to the zero-order hold reconstruction in certain control problems. The problem of how well H(z) models the continuous G(s) is also discussed.
TL;DR: In this paper, necessary and sufficient conditions are presented which guarantee that linear state-space models will not exhibit overshoot, and several examples illustrate the utility and simplicity of the new results.
Abstract: In practical control problems it is often desirable to make setpoint changes without overshoot. In this paper necessary and sufficient conditions are presented which guarantee that linear state-space models will not exhibit overshoot. Several examples illustrate the utility and simplicity of the new results