Showing papers in "International Journal of Control in 1996"
TL;DR: In this paper, the authors dealt with H ∞ control problem for systems with parametric uncertainty in all matrices of the system and output equations and derived necessary and sufficient conditions for quadratic stability with disturbance attenuation.
Abstract: This paper deals with H ∞ control problem for systems with parametric uncertainty in all matrices of the system and output equations. The parametric uncertainty under consideration is of a linear fractional form. Both the continuous and the discrete-time cases are considered. Necessary and sufficient conditions for quadratic stability with H ∞ disturbance attenuation are obtained.
1,557 citations
TL;DR: In this article, the authors proposed a new approach to design robust (in the disturbance de-coupling sense) fault detection filters which ensure that the residual vector, generated by this filter, has both robust and directional properties.
Abstract: Fault detection filters are a special class of observers that can generate directional residuals for the purpose of fault isolation. This paper proposes a new approach to design robust (in the disturbance de-coupling sense) fault detection filters which ensure that the residual vector, generated by this filter, has both robust and directional properties. This is done by combining the unknown input observer and fault detection filter principles. The paper proposes a new full-order unknown input observer, and gives necessary and sufficient conditions for its existence. After the disturbance de-coupling conditions are satisfied, the remaining design freedom can be used to make the residual have the directional property, based on the fault detection filter principle. A nonlinear jet engine system is used to illustrate the robust fault isolation approach presented. It is shown that linearization errors can be approximately treated as unknown disturbances and be de-coupled in the design of a robust fault detect...
748 citations
TL;DR: An algorithm for iterative learning control is developed on the basis of an optimization principle which has been used previously to derive gradient-type algorithms and has numerous benefits which include realization in terms of Riccati feedback and feedforward components.
Abstract: An algorithm for iterative learning control is developed on the basis of an optimization principle which has been used previously to derive gradient-type algorithms. The new algorithm has numerous benefits which include realization in terms of Riccati feedback and feedforward components. This realization also has the advantage of implicitly ensuring automatic step size selection and hence guaranteeing convergence without the need for empirical choice of parameters. The algorithm is expressed as a very general norm optimization problem in a Hilbert space setting and hence, in principle, can be used for both continuous and discrete time systems. A basic relationship with almost singular optimal control is outlined. The theoretical results are illustrated by simulation studies which highlight the dependence of the speed of convergence on parameters chosen to represent the norm of the signals appearing in the optimization problem.
308 citations
TL;DR: In this paper, a regularized orthogonal least squares learning algorithm for radial basis function networks was proposed, combining the advantages of both the orthogonality forward regression and regularization methods to provide an efficient and powerful procedure for constructing parsimonious network models that generalize well.
Abstract: The paper presents a regularized orthogonal least squares learning algorithm for radial basis function networks. The proposed algorithm combines the advantages of both the orthogonal forward regression and regularization methods to provide an efficient and powerful procedure for constructing parsimonious network models that generalize well. Examples of nonlinear modelling and prediction are used to demonstrate better generalization performance of this regularized orthogonal least squares algorithm over the unregularized one.
237 citations
TL;DR: In this paper, Zhou et al. extended the strong tracking filter (STF) for nonlinear systems with white noise to a class of nonlinear time-varying stochastic systems with coloured noise.
Abstract: The strong tracking filter (STF) proposed by Zhou et al. in 1992, which was developed for nonlinear systems with white noise, is extended to a class of nonlinear time-varying stochastic systems with coloured noise. A new concept of‘softening factor’is introduced to make the state estimator much smoother; its value can be preselected by computer simulations via a heuristic searching scheme. The STF is then used to estimate the parameters of a class of nonlinear time-varying stochastic systems in the presence of coloured noise. The robustness against model uncertainty of the STF is thoroughly studied via Monte Carlo simulations. The results show that the STF has strong robustness against model-plant parameter mismatches in the statistics of the initial conditions, the statistics of the process noise and the measurement noise, the system parameters, and the parameters in the measurement noise model. To a great extent the STF can give bias-free parameter estimations, where the parameters may be randomly time ...
217 citations
TL;DR: In this article, the design of a model reference adaptive controller with terminal sliding modes, while only input and output measurements are available, is discussed, and the equilibrium point is reached in a finite time.
Abstract: The design of a model reference adaptive controller with terminal sliding modes, while only input and output measurements are available, is discussed in this paper. In terminal sliding modes, the equilibrium point is reached in a finite time. By employing terminal sliding modes, the model reference adaptive controller enables the error dynamics to reach zero in a finite time. State variable filters are used to obtain differentiator-free controllers. Simulation results are presented to confirm the discussion.
216 citations
TL;DR: The main contribution of this paper is the development of an equivalent principle; that is, the design of a fuzzy control system is equivalent to thedesign of a set of linear time-invariant ‘extreme’ systems.
Abstract: This paper presents a design method for a class of fuzzy control systems. The class of fuzzy systems considered can be represented by the Takagi-Sugeno fuzzy model which is a type of dynamic fuzzy model. A constructive algorithm is developed to obtain the stabilizing feedback control law for the system. The main contribution of this paper is the development of an equivalent principle; that is, the design of a fuzzy control system is equivalent to the design of a set of linear time-invariant ‘extreme’ systems. Thus any design method in linear control system theory can be used to design a fuzzy control system. An example is given to illustrate the application of the method.
206 citations
TL;DR: In this paper, the authors present recursive algorithms for state bounding, using ellipsoidal sets to describe the state uncertainties and to bound the process and observation noises, and they optimize each stage of updating, according to the minimum volume and minimum trace criteria.
Abstract: The paper presents recursive algorithms for state bounding, using ellipsoidal sets to describe the state uncertainties and to bound the process and observation noises The algorithms optimize each stage of updating, according to the minimum-volume and minimum-trace criteria Simulations compare the performance of the bounding algorithms with that of a Kalman filter, and investigate the influence of noise distribution within the bounds
181 citations
TL;DR: In this paper, some interesting properties of output frequencies of Volterra-type nonlinear systems are particularly investigated, and the results provide a very novel and useful insight into the super-harmonic and inter-modulation phenomena in output frequency response with consideration of the effects incurred by different nonlinear components in the system.
Abstract: Some interesting properties of output frequencies of Volterra-type nonlinear systems are particularly investigated. These results provide a very novel and useful insight into the super-harmonic and inter-modulation phenomena in output frequency response of nonlinear systems, with consideration of the effects incurred by different nonlinear components in the system. The new properties theoretically demonstrate several fundamental output frequency characteristics and unveil clearly the mechanism of the interaction (or coupling effects) between different harmonic behaviors in system output frequency response incurred by different nonlinear components. These results have significance in the analysis and design of nonlinear systems and nonlinear filters in order to achieve a specific output spectrum in a desired frequency band by taking advantage of nonlinearities. They can provide an important guidance to modeling, identification, control and signal processing by using the Volterra series theory in practice.
180 citations
TL;DR: In this article, the authors outline the extension of the MOESP family of subspace model identification schemes to the Hammerstein type of nonlinear system, where only limited a priori information regarding the structure of the nonlinearity is available.
Abstract: In this paper, we outline the extension of the MOESP family of subspace model identification schemes to the Hammerstein-type of nonlinear system. Two types of identification problem are considered. The first type assumes the (polynomial) structure of the static nonlinearity to be given and the task is to identify both the linear system dynamics and the unknown proportional constants in the para-metrization of the static nonlinearity. The second type addresses the identification of both the linear dynamic part and the static nonlinearity, where only limited a priori information regarding the structure of the nonlinearity is available. The improved robustness properties of the algorithms developed for this second type of Hammerstein identification problem over existing correlation-based schemes is illustrated by a numerical example.
176 citations
TL;DR: In this paper, a stable but non-causal inverse is obtained offline that can be incorporated into a stabilizing controller for dead-beat output tracking in non-minimum phase nonlinear systems.
Abstract: Output tracking control of non-minimum phase systems is a highly challenging problem encountered in the control of flexible manipulators, space structures, and elsewhere. Classical inversion provides exact output tracking but leads to internal instability, while recent nonlinear regulation provides stable asymptotic tracking but admits large transient errors. As a first step to solve this problem, this paper addresses the stable inversion of non-minimum phase nonlinear systems. Using the notions of zero dynamics and stable/unstable manifolds, an invertibility condition is established for a class of systems. A stable but non-causal inverse is obtained offline that can be incorporated into a stabilizing controller for dead-beat output tracking. This inverse contrasts with the causal inverse proposed by Hirschorn where unstable zero dynamics result in unbounded inverse solutions. Our results reduce to those of Hirschorn for minimum phase systems, however. In a numerical example, the stable inverse has achiev...
TL;DR: In this paper, two new methods for solution of the eigenvalue assignment problem associated with the second-order control system were proposed, which construct feedback matrices F 1 and F 2 such that the closed-loop quadratic pencil has a desired set of eigenvalues and the associated eigenvectors are well conditioned.
Abstract: We propose two new methods for solution of the eigenvalue assignment problem associated with the second-order control system \global\hsize=30pc Specifically, the methods construct feedback matrices F 1 and F 2 such that the closed-loop quadratic pencil has a desired set of eigenvalues and the associated eigenvectors are well conditioned. Method 1 is a modification of the singular value decomposition-based method proposed by Juang and Maghami which is a second-order adaptation of the well-known robust eigenvalue assignment method by Kautsky et al. for first-order systems. Method 2 is an extension of the recent non-modal approach of Datta and Rincon for feedback stabilization of second-order systems. Robustness to numerical round-off errors is achieved by minimizing the condition numbers of the eigenvectors of the closed-loop second-order pencil. Control robustness to large plant uncertainty will not be explicitly considered in this paper. Numerical results for both the two methods are favourable. A compara...
TL;DR: In this article, the concept of swinging control is introduced, meaning achievement of arbitrary large level of the objective function by arbitrary small control level, and the existence of swing control for hamiltonian systems is established.
Abstract: The speed-gradient method of control design used previously for problems of regulation and tracking is extended to oscillating systems with energy-based objective functions. The concept of swinging control is introduced, meaning achievement of arbitrary large level of the objective function by arbitrary small control level. The existence of swinging control for hamiltonian systems is established. Simulation results for pendulum swinging problem are demonstrated.
TL;DR: In this article, a nonlinear control strategy is devised which, in some sense, optimizes performance across the operating envelope, and realizations which satisfy the extended local linear equivalence condition are derived for SISO systems scheduled upon an internal plant or controller variable.
Abstract: Power regulation of horizontal-axis grid-connected up-wind constant-speed pitch-regulated wind turbines presents a demanding control problem with the plant, actuation system and control objectives all strongly nonlinear. In this paper, a novel nonlinear control strategy is devised which, in some sense, optimizes performance across the operating envelope. In comparison with linear control, the nonlinear strategy achieves a substantial improvement in performance. The realization adopted is crucial in attaining the required performance. An extended local linear equivalence condition is introduced which provides a basis for the selection of an appropriate realization. This is an important, and general, issue in the design of gain-scheduled systems and generic realizations, which satisfy the extended local linear equivalence condition, are derived for SISO systems scheduled upon an internal plant or controller variable. For the wind turbine nonlinear controller, realizations which satisfy the extended local li...
TL;DR: In this paper, the properties of controllability and reachability of discrete time positive systems are analyzed based on a graph-theoretic approach, together with canonical forms for describing reachable/controllable pairs.
Abstract: Discrete time positive systems have been the object of widespread interest in the literature. In the last decade particular attention has been devoted to the analysis and characterization of the different notions of reachability and controllability which, in this context, make their appearance. In this paper, the properties of (ordinary and essential) controllability and reachability are analysed. Based on a graph-theoretic approach, we provide practical criteria to verify whether a given positive system (F, G) is endowed with these properties, together with canonical forms for describing reachable/controllable pairs.
TL;DR: It is shown that the pure error term in the learning control law can be positively utilized to improve the system performance, making it robust against varying initial conditions.
Abstract: In this paper, we investigate some effects of errors in the initial conditions as a learning control algorithm is iteratively applied. We show that the pure error term in the learning control law can be positively utilized to improve the system performance, making it robust against varying initial conditions. For better performance in the face of variable initial conditions, we propose a method of ‘iterative learning control with multi-modal input’. In this proposed control method, an input is synthesized based on the state of initial condition. Numerical examples are given to show the effectiveness of the proposed learning control algorithm.
TL;DR: In this article, a multiple-surface sliding control for a class of single-input single-output nonlinear systems whose uncertainties do not satisfy the standard matching condition is developed, where a coordinate dependence condition on the uncertainty bound is assumed.
Abstract: We develop a ‘multiple-surface’ sliding control for a class of single-input single-output nonlinear systems whose uncertainties do not satisfy the standard matching condition. A coordinate dependence condition on the uncertainty bound is assumed. A ‘computed normal form’ is defined to handle such uncertainties instead of the normal form used in conventional input-output linearization. A control algorithm which can be applied to global tracking problems has been developed and evaluated for a benchmark example.
TL;DR: A controller/observer pair is presented, on the basis of sliding mode ideas, which provides robust output tracking of a reference signal using only measured output information.
Abstract: A controller/observer pair is presented, on the basis of sliding mode ideas, which provides robust output tracking of a reference signal using only measured output information. Closed-loop analysis indicates that asymptotic tracking of a constant reference signal will be achieved despite the presence of a class of matched uncertainty. Furthermore, a form of ‘separation principle’ is shown to hold for this class of controller and observer, in the sense that they can be designed independently apart from a scalar function of the uncertainty bounds.
TL;DR: In this paper, the relations of a number of bounds for the solutions of the algebraic Riccati and Lyapunov equations that have been reported during the last two decades are investigated.
Abstract: This paper summarizes and investigates the relations of a number of bounds for the solutions of the algebraic Riccati and Lyapunov equations that have been reported during the last two decades. Also presented are bounds for the unified Riccati equation using the delta operator and it is shown that some bounds for the continuous and discrete Riccati equations can be unified by them.
TL;DR: A reusable computing paradigm based on genetic algorithms is developed to transform the ‘unsolvable problem' of optimal designs into a practically solvable ‘non-deterministic polynomial problem’, which results in computer automated designs directly from nonlinear plants.
Abstract: Although various nonlinear control theories, such as sliding mode control, have proved sound and successful, there is a serious lack of effective or tractable design methodologies due to difficulties encountered in the application of traditional analytical and numerical methods. This paper develops a reusable computing paradigm based on genetic algorithms to transform the ‘unsolvable problem’ of optimal designs into a practically solvable ‘non-deterministic polynomial problem’, which results in computer automated designs directly from nonlinear plants. The design methodology takes into account practical system constraints and extends the solution space, allowing new control terms to be included in the controller structure. In addition, the practical implementations using laboratory-scale systems demonstrate that such ‘off-the-computer’ designs offer a superior performance to manual designs in terms of transient and steady-state responses and of robustness. Various contributions to the genetic algorithm te...
TL;DR: An adaptive learning control scheme is presented for uncertain robotic systems that is capable of tracking the entire profile of the reference input and estimates the desired control input and uncertain system parameters.
Abstract: An adaptive learning control scheme is presented for uncertain robotic systems that is capable of tracking the entire profile of the reference input. The control scheme consists of three control blocks: a linear feedback, a feedforward error compensation and a learning strategy. At each iteration, the linear feedback with the feedforward error compensation provides stability of the system and keeps its state errors within uniform bounds. The learning strategy, on the other hand, estimates the desired control input and uncertain system parameters, which are used to track the entire span of a reference input over a sequence of iterations. In contrast with many other learning control techniques, the proposed learning algorithm neither uses derivative terms of feedback errors nor assumes any perturbations on the learning control input as a prerequisite. The parameter estimator neither uses any joint acceleration terms nor uses any inversion of the estimated inertia matrix, which makes its implementation pract...
TL;DR: In this paper, an adaptive model output following control utilizing almost strictly positive real (ASPR) characteristics of the plant is considered, where the ASPR condition imposes severe restrictions on the plant with relation to the practical application.
Abstract: In this paper, an adaptive model output following control utilizing almost strictly positive real (ASPR) characteristics of the plant is considered. The plant is said to be ASPR if there exists a static output feedback such that the resulting closed-loop transfer function is strictly positive real. A design scheme of an adaptive model output following control system having a simple structure is proposed for the ASPR plant. The ASPR condition imposes severe restrictions on the plant with relation to the practical application. However, we can construct an ASPR augmented plant, which is regarded as a virtually new controlled plant, by implementing a parallel feedforward compensator or pre-compensator on the plant. The design scheme of such compensators that make the non-ASPR plant virtually ASPR is proposed by taking plant uncertainties into consideration. As a result, the applicable class of the proposal can be expanded. The effectiveness of the proposed methods is confirmed through numerical simulations.
TL;DR: In this paper, a fast orthogonal estimation algorithm is derived for a wide class of nonlinear stochastic models including training radial basis function neural networks. But the selection of significant regressors and the estimation of unknown parameters are considered, and simulated examples are included to demonstrate the efficiency of the new procedure.
Abstract: A new fast orthogonal estimation algorithm is derived for a wide class of nonlinear stochastic models including training radial basis function neural networks. The selection of significant regressors and the estimation of unknown parameters in the presence of nonlinear noise sources are considered, and simulated examples are included to demonstrate the efficiency of the new procedure.
TL;DR: In this paper, a sufficient condition is derived such that the closed-loop state delayed system is stable and guarantees a prescribed H ∞ norm bound of the transfer matrix from the disturbance to the controlled output.
Abstract: A sufficient condition is derived such that the closed-loop state delayed system is stable and guarantees a prescribed H ∞ norm bound of the closed-loop transfer matrix from the disturbance to the controlled output. Based on this derivation, a full-order observer-based H ∞ controller for the stace delayed linear systems is constructed by solving two modified algebraic Riccati equations. The state feedback H ∞ controller for the state delayed linear systems is also obtained by solving a modified algebraic Riccati equation. An illustrative example is given to show the applicability of the proposed approach.
TL;DR: In this article, two general and complementary concepts of system design that have direct relevance to the theory and design of control systems are explained: the principle of matching and the method of inequalities.
Abstract: The paper explains two general and complementary concepts of system design that have direct relevance to the theory and design of control systems: the principle of matching and the method of inequalities. One aim of the paper is to supplement, clarify and unify the ideas and explanations contained in previous publications. To this end, the essential ideas are presented in their simplest forms to make the paper also serve the purposes of an introduction and a review of the field. Another aim is to discuss the effects of the concepts on the foundations of the control theory, without neglecting the practical aspects of design.
TL;DR: In this article, the root-mean-square law of the Hankel singular values is derived for flexible structures in modal and balanced coordinates, and the properties of flexible structures are derived from these properties.
Abstract: Properties of flexible structures in modal and balanced coordinates are derived. From these properties the root-mean-square law of the Hankel singular values is obtained. It says that the squares of the Hankel singular values of a set of sensors and actuators is approximately a root-mean-square sum of the squares of the Hankel singular values for each individual sensor and actuator. This property allows us to evaluate each actuator and sensor in terms of the joint controllability and observability, and to serve as a tool of the actuator and/or sensor placement methodology.
TL;DR: In this paper, the authors developed a procedure to tackle the mixed (real and complex) μ synthesis problem, which involves a "D,G-K iteration" between computing the mixed μ upper bound and solving an H∞ optimal control problem, and has guaranteed convergence to a local minimum of the (nonconvex) problem.
Abstract: A number of techniques have been developed in recent years for the analysis and design of controllers which are robust with respect to structured complex uncertainty. In particular the complex μ synthesis procedure has been successfully applied to a number of engineering problems. However the presence of real parametric uncertainty in the problem description substantially complicates matters, so that standard complex μ synthesis techniques are no longer adequate. In this paper we develop a procedure to tackle the mixed (real and complex) μ synthesis problem. This procedure involves a "D,G-K iteration" between computing the mixed μ upper bound and solving an H∞ optimal control problem, and has guaranteed convergence to a local minimum of the (nonconvex) problem. The procedure has been implemented in software, and several controller designs are compared with the corresponding complex μ synthesis designs.
TL;DR: In this article, a class of two-time-scale single-input single-output nonlinear systems with time-scale multiplicity is considered and a combination of singular perturbation and geometric methods is employed to synthesize well-conditioned static state feedback laws that induce a well-characterized input-output behavior and guarantee stability of the closed-loop system.
Abstract: This article concerns a class of two-time-scale single-input single-output nonlinear systems. For such systems, combination of singular perturbation and geometric methods is employed to synthesize well-conditioned static state feedback laws that induce a well-characterized input-output behaviour and guarantee stability of the closed-loop system. The developed control laws are applied to two nonlinear chemical processes with time-scale multiplicity and their performance is evaluated through simulations.
TL;DR: In this article, the optimal controller under an assumption of a certain type of mode availability is derived for a class of adaptive controllers when the mode is not directly observed, using this optimal feedback gain.
Abstract: Systems, such as those subject to abrupt changes (including failure) or those with uncertain dynamic model (or more than one possible model), can be naturally modelled as jump linear (JL) systems. Because of their applications in fields such as tracking, fault-tolerant control, manufacturing process and robots, JL systems have drawn extensive attention. The optimal control and stabilization problem for JL systems, when the mode (system model) is not assumed to be directly and perfectly observed, a realistic assumption in many applications, is nonlinear and prohibitive both analytically and computationally because of the dual effect. The main contribution of this work is the sufficient condition for stabilization for a class of adaptive controllers when the mode is not directly observed. We first present the optimal controller under an assumption of a certain type of mode availability. Using this optimal feedback gain, we derive a condition that ensures the stabilizing property for a class of adaptive cont...
TL;DR: In this paper, the concept of the integral manifold is utilized to design a dynamical composite control strategy to guarantee a minimum phase closed-loop system restricted to the manifold, resulting in controlling the tip position to an arbitrary degree of accuracy by just measuring the hub angle and the tip positions.
Abstract: The problem of controlling the top position of a flexible-link manipulator is considered. A linear mathematical model of the flexible system is expressed in a standard singularly perturbed form. The concept of the integral manifold is utilized to design a dynamical composite control strategy to guarantee a minimum phase closed-loop system restricted to the manifold, resulting in controlling the tip position to an arbitrary degree of accuracy by just measuring the hub angle and the tip position. Numerical simulations for an approximation to the model of Canadarm (Shuttle arm) are included to demonstrate the advantages of the proposed technique. The proposed control strategy is applied to both the linear and the nonlinear models of the Canadarm with very encouraging results.