Showing papers in "International Journal of Control in 1992"
TL;DR: In this article, an observer-based controller is designed to stabilize a fully linearizable nonlinear system, where the system is assumed to be left-invertible and minimum-phase.
Abstract: An observer-based controller is designed to stabilize a fully linearizable nonlinear system. The system is assumed to be left-invertible and minimum-phase. The controller is robust to uncertainties in modelling the nonlinearities of the system. The design of the controller and the stability analysis employs the techniques of singular perturbations. A new ‘Tikhonov-like’ theorem is presented and used to analyse the system when the control is globally bounded.
784 citations
TL;DR: In this paper, the authors present two algorithms to realize a finite dimensional, linear time-invariant state-space model from input-output data, which are classified as one of the subspace model identification schemes.
Abstract: In this paper, we present two novel algorithms to realize a finite dimensional, linear time-invariant state-space model from input-output data. The algorithms have a number of common features. They are classified as one of the subspace model identification schemes, in that a major part of the identification problem consists of calculating specially structured subspaces of spaces defined by the input-output data. This structure is then exploited in the calculation of a realization. Another common feature is their algorithmic organization: an RQ factorization followed by a singular value decomposition and the solution of an overdetermined set (or sets) of equations. The schemes assume that the underlying system has an output-error structure and that a measurable input sequence is available. The latter characteristic indicates that both schemes are versions of the MIMO Output-Error State Space model identification (MOESP) approach. The first algorithm is denoted in particular as the (elementary MOESP scheme)...
624 citations
TL;DR: This paper addresses the issues related to the identification of nonlinear discrete-time dynamic systems using neural networks with particular attention to the connections between existing techniques for nonlinear systems identification and some aspects of neural network methodology.
Abstract: Many real-world systems exhibit complex nonlinear characteristics and cannot be treated satisfactorily using linear systems theory. A neural network which has the ability to learn sophisticated nonlinear relationships provides an ideal means of modelling complicated nonlinear systems. This paper addresses the issues related to the identification of nonlinear discrete-time dynamic systems using neural networks. Three network architectures, namely the multi-layer perceptron, the radial basis function network and the functional-link network, are presented and several learning or identification algorithms are derived. Advantages and disadvantages of these structures are discussed and illustrated using simulated and real data. Particular attention is given to the connections between existing techniques for nonlinear systems identification and some aspects of neural network methodology, and this demonstrates that certain techniques employed in the neural network context have long been developed by the control e...
618 citations
TL;DR: In this article, a linearizing feedback control is derived in terms of some unknown nonlinear functions, which can be modelled by layered neural networks and the weights of the networks are updated and used to generate the control.
Abstract: Layered networks are used in a nonlinear adaptive control problem. The plant is an unknown feedback-linearizable discrete-time system, represented by an input-output model. A state space model of the plant is obtained to define the zero dynamics, which are assumed to be stable. A linearizing feedback control is derived in terms of some unknown nonlinear functions. To identify these functions, it is assumed that they can be modelled by layered neural networks. The weights of the networks are updated and used to generate the control. A local convergence result is given. Computer simulations verify the theoretical result.
400 citations
TL;DR: In this article, the concept of sliding modes in abstract dynamic systems described by a semigroup of state space transformations is introduced, and the sliding mode design procedure is used for designing finite observers, sliding mode control for systems with delays and differential-difference systems, which is illustrated by sliding mode controller of longitudinal oscillations.
Abstract: The concept of sliding modes in abstract dynamic systems described by a semigroup of state space transformations is introduced. The sliding mode design procedure is used for designing finite observers, sliding mode control for systems with delays and differential-difference systems, which is illustrated by sliding mode control of longitudinal oscillations
376 citations
TL;DR: A novel approach is adopted which employs a hybrid clustering and least squares algorithm which significantly enhances the real-time or adaptive capability of radial basis function models.
Abstract: Recursive identification of non-linear systems is investigated using radial basis function networks. A novel approach is adopted which employs a hybrid clustering and least squares algorithm. The recursive clustering algorithm adjusts the centres of the radial basis function network while the recursive least squares algorithm estimates the connection weights of the network. Because these two recursive learning rules are both linear, rapid convergence is guaranteed and this hybrid algorithm significantly enhances the real-time or adaptive capability of radial basis function models. The application to simulated real data are included to demonstrate the effectiveness of this hybrid approach.
359 citations
TL;DR: The elementary MOESP algorithm presented in the first part of this series of papers is analysed and the asymptotic properties of the estimated state-space model when only considering zero-mean white noise perturbations on the output sequence are studied.
Abstract: The elementary MOESP algorithm presented in the first part of this series of papers is analysed in this paper. This is done in three different ways. First, we study the asymptotic properties of the estimated state-space model when only considering zero-mean white noise perturbations on the output sequence. It is shown that, in this case, the MOESPl implementation yields asymptotically unbiased estimates. An important constraint to this result is that the underlying system must have a finite impulse response and subsequently the size of the Hankel matrices, constructed from the input and output data at the beginning of the computations, depends on the number of non-zero Markov parameters. This analysis, however, leads to a second implementation of the elementary MOESP scheme, namely MOESP2. The latter implementation has the same asymptotic properties without the finite impulse response constraint. Secondly, we compare the MOESP2 algorithm with a classical state space model identification scheme. The latter...
300 citations
TL;DR: It is shown that systems identification can indeed be achieved in the presence of noise and that optimal control can be formulated in a learning mode, by neural nets.
Abstract: In this article, we are concerned with neural-nets which can learn to control systems in accordance with a guiding intent, and can also learn how to formulate that control strategy or intent. The overall task of systems control is viewed as being carried out by four components, these being the predictive monitoring net, the control action generator net, the objective function net and the optimization net. This approach and perspective are described and illustrated in this article. In our examples, we show that systems identification can indeed be achieved in the presence of noise and that optimal control can be formulated in a learning mode, by neural nets.
268 citations
TL;DR: Properties of neural network performance are investigated by studying the modelling of non-linear dynamical systems, including node selection, prediction, prediction and the effects of noise.
Abstract: Properties of neural network performance are investigated by studying the modelling of non-linear dynamical systems Network complexity, node selection, prediction and the effects of noise are studied and some new metrics of performance are introduced The results are illustrated with both simulated and industrial examples
266 citations
TL;DR: In this article, the design of variable structure control schemes for uncertain discrete-time systems is considered and theoretical results indicate that such a parallel approach is not necessarily desirable, and a novel design methodology for discrete time variable-time structure control systems is then formulated.
Abstract: The design of variable structure control schemes for uncertain discrete-time systems is considered. Previous work in this area which parallels the discrete-time sliding mode philosophy with that for the continuous-time case is reviewed. Theoretical results are presented which indicate that such a parallel approach is not necessarily desirable. A novel design methodology for discrete-time variable structure control systems is then formulated. A numerical example is given to illustrate the results described.
174 citations
TL;DR: In this paper, an estimation process for dynamic perturbations is employed jointly with the sliding mode control (SMC) technique, which offers a robust feedback control with much lower gains than its conventional counterparts against slowly varying perturbation.
Abstract: Sliding mode control (SMC) of a general class of nonlinear control systems is considered in this work. The conventional SMC technique requires knowledge of the upperbounds of disturbances and modelling uncertainties to assure robustness. However, this may not be easy to obtain. As a remedy, an estimation process for these dynamic perturbations is employed jointly with the SMC technique. This new methodology, sliding mode control with perturbation estimation (SMCPE), offers a robust feedback control with much lower gains than its conventional counterparts against slowly varying perturbations. This resolves one of the problematic issues which has caused concern over the years of development of SMC applications. An interesting perspective of selecting the cut-off frequency for s dynamics is presented with a novel upperbound argument. Much desirable tracking fidelity is arrived through SMCPE in the computer simulation studies for a two-link manipulator. A companion approach to SMCPE, the discrete equ...
TL;DR: In this article, a tracking controller for rigid-link electrically-driven (RLED) robot manipulators is proposed, which is robust with regard to parametric uncertainties and additive bounded disturbances while correcting for the typically ignored electrical actuator dynamics.
Abstract: This paper illustrates a simple, hand-crafted approach which can be used to design tracking controllers for rigid-link electrically-driven (RLED) robot manipulators. The control methodology is intuitively simple since it is based on concepts readily identified by most control engineers. To illustrate the approach, we develop a corrective tracking controller for the RLED robot dynamics which yields global exponential stability for the link tracking error under the assumption of exact model knowledge. To compensate for the uncertainties in the rigid-link electrically-driven robot model, we then design a corrective robust tracking controller which yields global uniform ultimate bounded stability of the link tracking error. The proposed controller is robust with regard to parametric uncertainties and additive bounded disturbances while correcting for the typically ignored electrical actuator dynamics.
TL;DR: A general forgetting algorithm that contains most existing forgetting schemes as special cases and is applied to a specific algorithm with selective forgetting, which is non-uniform in time and space.
Abstract: Fn the first part of this paper, a general forgetting algorithm is formulated and analysed. It contains most existing forgetting schemes as special cases. Conditions are given ensuring that the basic convergence properties will hold. In the second part of the paper, the results are applied to a specific algorithm with selective forgetting. Here, the forgetting is non-uniform in time and space. The theoretical analysis is supported by a simulation example demonstrating the practical performance of this algorithm.
TL;DR: In this paper, a robust adaptive control term is proposed to improve the control performance of simple adaptive control (SAC) techniques, and a practical procedure is described for designing the parallel feed forward compensator, which is necessary for the actual realization of the SAC system.
Abstract: This paper deals with two problems for the improvement of the control performance of simple adaptive control (SAC) techniques. First, it is discussed that the introduction of a robust adaptive control term much robustifies the SAC system concerning plant uncertainties such as state dependent disturbance. Second, a practical procedure is described for designing the parallel feedforward compensator, which is necessary for the actual realization of the SAC system, given prior information concerning the plant such that: (1) the plant is minimum phase; (2) an upper bound on the relative degree exists; and (3) approximate values of high and low frequency gains are known. The effectiveness of the proposed methods is confirmed through the simulation of typical examples of adaptive control systems.
TL;DR: In this paper, the authors consider the design of H ∞ optimal discrete-time controllers in continuous-time systems, where the continuous and discrete inputs and outputs are essentially identical.
Abstract: We consider the design of H ∞ optimal discrete-time (digital) controllers in continuous-time systems. An apparent difficulty, especially in utilizing modern transform-domain analysis in this context, stems from the absence of an appropriate (transfer function) model for the hybrid-time (discrete and continuous) closed-loop system. This difficulty is overcome through the introduction of an equivalent difference-equation model for the continuous-time system, with distributed inputs and outputs; equivalence being in the sense that the continuous-and discrete-time inputs and outputs are essentially identical. Using the interplay between the discrete and the continuous time models, solutions of the well-known purely continuous-time and purely discrete-time standard problems extend to solutions of the problem at hand. They comprise Riccati equation characterizations of feasible combinations of sampling rates and bounds on the closed-loop induced input-output norm, and parameterization of compensators. We consid...
TL;DR: In this article, the continuous sliding mode control (CSMC) approach is proposed to satisfy the sliding condition using a continuous control law. But the control chattering due to the discontinuity in the control law is undesirable in most processes applications.
Abstract: Classical sliding mode control (SMC) uses a discontinuous control action to drive the state from an arbitrary initial state to the origin along a user-specified path and exhibits excellent robustness to disturbances and parameter uncertainty. However, the control chattering due to the discontinuity in the control law is undesirable in most processes applications. The continuous sliding mode control (CSMC) approach developed in this paper satisfies the sliding condition using a continuous control law. It therefore retains the positive properties of SMC but without the disadvantage of control chattering. The concept of boundary layer equivalence is used to show that in the presence of unknown disturbances and/or parameter uncertainty, CSMC keeps the state trajectories within a boundary layer of user-specified width. It is also shown that CSMC is equivalent to a cubic feedback control law and can be reduced to a linear form (LSMC) which provides a useful link between sliding mode control and traditional line...
TL;DR: In this paper, a model predictive control (MPC) technique is developed for systems with measurements available at different sampling rates, and a simple suboptimal cascade filter is also proposed for dual-rate (DR) systems where the primary measurements are available at a'slow' rate and the secondary measurements at a ''fast'' rate.
Abstract: A model predictive control (MPC) technique is developed for systems with measurements available at different sampling rates. The method uses general state-space system representations that incorporate secondary measurements as well as primary measurements. The optimal multi-rate (MR) filtering method is used to develop prediction equations for MPC. A simple suboptimal cascade filter is also proposed for dual-rate (DR) systems where the primary measurements are available at a 'slow’ rate and the secondary measurements are available at a 'fast’ rate. In addition to significant reduction in filter-gain computation requirements, the suboptimal filtering strategy offers superior primary-measurement-failure tolerance. The applicability of the proposed methods to realistic systems is demonstrated through an example application to a high-purity distillation column.
TL;DR: In this article, a model-following approach is developed to design reconfigurable control systems, which yields fewer constraints on the reference model than before, and provides much greater flexibility in specifying the state trajectories of the impaired system.
Abstract: A novel model-following approach is developed to design reconfigurable control systems. The conventional state-space linear model-following approach to control is first re-examined with emphasis on the conditions for perfect model following and its application to reconfigurable control system design. New frequency domain necessary and sufficient conditions for perfect model following are then obtained and they are used to gain insight into the selection of the reference model and to develop a new design approach. This novel design approach yields fewer constraints on the reference model than before, and provides much greater flexibility in specifying the state trajectories of the impaired system.
TL;DR: Simplex type dynamic output feedback variable structure control for stabilizing multivariable linear time-invariant plants is analyzed in this article, where two types of controllers are considered; a compensator type and an observer type.
Abstract: Simplex type dynamic output feedback variable structure control for stabilizing multivariable linear time-invariant plants is analysed. Two types of controllers are considered; a compensator type and an observer type. It is shown that while the compensator-type controller stabilizes the plant only if the plant is minimum-phase, the observer-type controller does not face the same restriction. The design of low-order (less than the order of the plant) observer-type controllers is also considered.
TL;DR: In this article, the problem of output stabilization for uncertain S1SO systems is considered using structural transformations, which can change to the form convenient for output feedback design, and the synthesis of observer-based variable structure control for asymptotical stabilization or uniform ultimate boundedness of the closed-loop system is provided.
Abstract: The problem of output stabilization for uncertain S1SO systems is considered. Using structural transformations uncertain systems can change to the form convenient for output feedback design. Synthesis of observer-based variable structure control for asymptotical stabilization or uniform ultimate boundedness of the closed-loop system is provided. Examples are considered and simulation results are given.
TL;DR: This paper proposes a new class of discrete-time models that originates from the z transfer function but which is close to continuous- time models in structure and parameters, thereby retaining its advantageous features.
Abstract: Digital computing in estimation, control or signal processing for continuous-time systems requires the use of discrete-time models. While conventional difference equation or z-transfer function models are widely popular, a class of methods exists that uses discrete approximations of continuous signals and operators, retaining the continuous-time parameters. Some important advantages of this class have been demonstrated in the contexts of parameter estimation, adaptive control and controller design. This paper proposes a new class of discrete-time models that originates from the z transfer function but which is close to continuous-time models in structure and parameters, thereby retaining its advantageous features. The recently proposed ‘delta’ model is seen to be a member of this class. The interrelations among various digital model types are brought out. Better sensitivity properties over z transfer function models are established. Finite word length properties of these models vis-a-vis the z-transfer fu...
TL;DR: An indirect adaptive fuzzy controller is proposed where an intermediate process model, identified for observed data, is used to peform on-line controller design and the resulting separation of the adaptation system from controller design enables learning convergence to be investigated.
Abstract: Fuzzy controllers may be either static systems, which have fixed rule base, or adaptive systems, which have the ability to alter their rules. A discussion of adaptive fuzzy controllers and a comparison with corresponding algebraic techniques concludes that all previous adaptive fuzzy controllers have been of the direct adaptive type. Such controllers use observations of closed loop control performance to manipulate the controller rule base directly without any intermediate process model being produced. In this paper, an indirect adaptive fuzzy controller is proposed where an intermediate process model, identified for observed data, is used to peform on-line controller design. The resulting separation of the adaptation system from controller design enables learning convergence to be investigated. Examples are given of both fuzzy model identification and controller design for linear and nonlinear processes.
TL;DR: Most processes of realistic complexity cannot be described by simple linear relationships, so an alternative to creating high order/non-linear models is to develop 'composite models’, i.e. a collectio ...
Abstract: Most processes of realistic complexity cannot be described by simple linear relationships. An alternative to creating high order/non-linear models is to develop 'composite models’, i.e. a collectio ...
TL;DR: In this paper, a linear, time-invariant, multi-input multi-output unity-feedback system with possible failures in the sensor or actuator-connections is analyzed.
Abstract: This paper studies the linear, time-invariant, multi-input multi-output unity-feedback system with possible failures in the sensor or actuator-connections. The purpose of this paper is to analyse the system with failures in k of the sensor-connections or with failures in m of the actuator-connections and develop conditions for stability, It is shown that if the system is stable for all possible failures of k of the sensor-connections or of m of the actuator-connections, then the plant and the controller must have certain properties explained in terms of denominator-matrices of their coprime-factorizations. These conditions imposed on the coprime-factorizations are important for design of fault-tolerant systems.
TL;DR: In this article, the authors propose a new approach to robust control of nonlinear systems that is indirect in the sense that they will translate a robust control problem into an optimal control problem and apply optimal control methods to solve the robust control problems.
Abstract: We propose a new approach to robust control of nonlinear systems. The approach is indirect in the sense that we will translate a robust control problem into an optimal control problem and apply optimal control methods to solve the robust control problem. We show that the method can be applied to nonlinear systems that satisfy the matching condition.
TL;DR: In this paper, the authors describe the application of nonlinear quadratic regulator (NLQR) theory to the design of control laws for a typical high-performance aircraft.
Abstract: This paper describes the application of nonlinear quadratic regulator (NLQR) theory to the design of control laws for a typical high-performance aircraft. The NLQR controller design is performed using truncated solutions of the Hamilton-Jacobi-Bellman equation of optimal control theory. The performance of the NLQR controller is compared with the performance of a conventional P + I gain scheduled controller designed by applying standard frequency response techniques to the equations of motion of the aircraft linearized at various angles of attack. Both techniques result in control laws which are very similar in structure to one another and which yield similar performance. The results of applying both control laws to a high-g vertical turn are illustrated by nonlinear simulation.
TL;DR: A fuzzy associative memory system called FAMOUS (Fuzzy Associative Memory Organizing Units System) simulates the knowledge representation and inference process by using fuzzy notation and by association in neural networks.
Abstract: To achieve self-organizing control based on fuzzy rules, we propose a fuzzy associative memory system called FAMOUS (Fuzzy Associative Memory Organizing Units System). FAMOUS simulates the knowledge representation and inference process by using fuzzy notation and by association in neural networks. FAMOUS's learning algorithm uses training steps to generate operation skills by modifying the expert knowledge that is initially built-in. A set of fuzzy if-then rules is used for controlling variable parameter processes. The control knowledge is represented as pairs consisting of a ‘condition’ in the if-part and an ‘operation (controller)’ in the then-part. The controllers are designed for optimization and stabilization in specific conditions. The fuzzy controller described in FAMOUS recalls well-trained controllers associated with the input condition and makes the final control output by synthesizing the intermediate outputs of their controllers. FAMOUS can highly refine knowledge by using neural network learn...
TL;DR: This paper is the first part of a two-part investigation into the extension of the ICD framework, and the performance issues thereof, to general m-input m-output systems.
Abstract: A new applications-oriented approach—individual channel design (ICD)—to multivariable feedback control for 2-input 2-output systems was presented and justified in a series of papers (O'Reilly and Leithead 1991, Leithead and O'Reilly 1991 a, b, 1992 a). This paper is the first part of a two-part investigation into the extension of the ICD framework, and the performance issues thereof, to general m-input m-output systems. The main results of this first part are fourfold. First, the ICD framework for general m-input m-output systems is justified for all multivariable system structures (RHP poles and zeros). In particular, it is shown that ICD on the original m-input m-output cross-coupled multivariable system is valid irrespective of the degree of cross-coupling. Second, the influence of (individual transfer function, channel, transmission) right half-plane zeros on controller design and closed-loop channel performance is elucidated. Third, the existence of fixed stabilizing controllers for uncertain m-input...
TL;DR: It is shown that a class of three layer (two hidden layer) neural networks is equivalent to a canonical form approximation of nonlinearity and this theoretical framework leads to insights about the architecture of multilayer feedforward neural networks.
Abstract: The ability of a neural network to represent an input-output mapping is usually only measured in terms of the data fit according to some error criteria. This ‘black box’ approach provides little understanding of the network representation or how it should be structured. This paper investigates the topological structure of multilayer feedforward neural networks (MFNN) and explores the relationship between the numbers of neurons in the hidden layers and finite dimensional topological spaces. It is shown that a class of three layer (two hidden layer) neural networks is equivalent to a canonical form approximation of nonlinearity. This theoretical framework leads to insights about the architecture of multilayer feedforward neural networks, confirms the common belief that three layer (two hidden layer) feedforward networks are sufficient for general application and yields an approach for determining the appropriate numbers of neurons in each hidden layer.