Showing papers in "International Journal of Control in 1993"
TL;DR: It turns out that the deviation of the system from its prescribed constraints (sliding accuracy) is proportional to the switching time delay and a new class of sliding modes and algorithms is presented and the concept of sliding mode order is introduced.
Abstract: The synthesis of a control algorithm that stirs a nonlinear system to a given manifold and keeps it within this constraint is considered. Usually, what is called sliding mode is employed in such synthesis. This sliding mode is characterized, in practice, by a high-frequency switching of the control. It turns out that the deviation of the system from its prescribed constraints (sliding accuracy) is proportional to the switching time delay. A new class of sliding modes and algorithms is presented and the concept of sliding mode order is introduced. These algorithms feature a bounded control continuously depending on time, with discontinuities only in the control derivative. It is also shown that the sliding accuracy is proportional to the square of the switching time delay.
2,714 citations
TL;DR: In this paper, a state observer is proposed for nonlinear continuous time systems which extends the well known Luenberger observer, and on the basis of simple assumptions on the regularity of the system equations, which are generally satisfied for physically meaningful dynamic systems, the global asymptotic convergence of the estimated state towards the true state is shown.
Abstract: A state observer is proposed for nonlinear continuous time systems which extends the well known Luenberger observer. In particular, on the basis of simple assumptions on the regularity of the system equations (observability and the global Holder condition for suitable functions), which are generally satisfied for physically meaningful dynamic systems, the global asymptotic convergence of the estimated state towards the true state is shown. Finally, some examples of applications are also reported showing the effectiveness of the proposed observer.
525 citations
TL;DR: It is shown that a large class of non-linear systems can be modelled in this way, and indicated how to decompose the systems range of operation into operating regimes.
Abstract: This paper outlines how it is possible to decompose a complex non-linear modelling problem into a set of simpler linear modelling problems. Local ARMAX models valid within certain operating regimes are interpolated to construct a global NARMAX (non-linear NARMAX) model. Knowledge of the system behaviour in terms of operating regimes is the primary basis for building such models, hence it should not be considered as a pure black-box approach, but as an approach that utilizes a limited amount of a priori system knowledge. It is shown that a large class of non-linear systems can be modelled in this way, and indicated how to decompose the systems range of operation into operating regimes. Standard system identification algorithms can be used to identify the NARMAX model, and several aspects of the system identification problem are discussed and illustrated by a simulation example.
370 citations
TL;DR: In this article, the consequences of the differential algebraic approach in the sliding mode control of nonlinear single-input single-output systems are reviewed in tutorial fashion, and examples illustrating the obtained results are also included.
Abstract: The consequences of the differential algebraic approach in the sliding mode control of nonlinear single-input single-output systems are reviewed in tutorial fashion. Input-dependent sliding surfaces, possibly including time derivatives of the input signal, are shown to arise naturally from elementary differential algebraic results pertaining to the Fliess's Generalized Controller Canonical Forms of nonlinear systems. This class of switching surfaces generally leads to chattering-free dynamically synthesized sliding regimes, in which the highest time derivative of the input signal undergoes all the bang-bang type discontinuities. Examples illustrating the obtained results are also included.
238 citations
TL;DR: In this article, the authors consider tracking in nonlinear systems with unacceptable zero-dynamics (i.e., non-minimum phase systems) and use sliding control to achieve tracking independent of disturbances in the channels of the input.
Abstract: Nonlinear systems affine in the input, and having a well-defined (vector) relative degree are considered. The invertibility of the input output dynamics can be used to achieve tracking of smooth desired trajectories if the associated ‘zero-dynamics’ are stable. We consider tracking in nonlinear systems with unacceptable zero-dynamics (i.e. non-minimum phase systems). The desired trajectories are assumed to be generated by some exosystem. We use sliding control to achieve tracking independent of disturbances entering in the channels of the input. The main idea is (i) to do an output-redefinition such that the zero-dynamics with respect to this new output are acceptable; (ii) to define a modified desired trajectory for the new output to track such that in the process, the original output tracks the original desired trajectory asymptotically.
232 citations
188 citations
TL;DR: In this article, two main results for uncertain time-delay systems are derived, namely, the robustness and stability degree of perturbed systems in the sliding mode, and the successful application of variable structure control to the stabilization problem of uncertain time delay systems.
Abstract: In this paper, two main results for uncertain time-delay systems are derived. The first result is the presentation of a new robust stability criterion for uncertain time-delay systems. The second result is the successful application of the concept of variable structure control to the stabilization problem of uncertain time-delay systems. The robustness and stability degree of perturbed systems in the sliding mode are also discussed. Last, some examples are included to illustrate our results.
181 citations
TL;DR: In this article, the stability analysis of active fault tolerant control systems is addressed using stochastic Lyapunov functions and supermartingale theorems, and necessary and sufficient conditions for exponential stability in the mean square and almost-sure asymptotic stability in probability are developed.
Abstract: Active fault tolerant control systems are feedback control systems that reconfigure the control law in real time based on the response from an automatic failure detection and identification (FDI) scheme. The dynamic behaviour of such systems is characterized by stochastic differential equations because of the random nature of the failure events and the FDI decisions. The stability analysis of these systems is addressed in this paper using stochastic Lyapunov functions and supermartingale theorems. Both exponential stability in the mean square and almost-sure asymptotic stability in probability are addressed. In particular, for linear systems where the coefficients of the closed loop system dynamics are functions of two random processes with markovian transition characteristics (one representing the random failures and the other representing the FDI decision behaviour), necessary and sufficient conditions for exponential stability in the mean square are developed.
153 citations
TL;DR: This paper applies known principles of rational behaviour in such situations to propose a plausible and well justified solution to the problem of under-determined parameter estimation which is close to classical exponential forgetting, but regularized by available prior information.
Abstract: Practice leads us to seek a simple method which would make parameter estimation (and subsequent control or signal processing) reliably adaptive. Unfortunately, in most applications we lack sufficient information to specify a complete model of parameter variations. In other words, the problem is ‘under-determined’ which prevents us from employing standard equations of probability calculus. In this paper we apply known principles of rational behaviour in such situations to propose a plausible and well justified solution. The result we get is close to classical exponential forgetting, but regularized by available prior information. We demonstrate the practical implications of this feature.
147 citations
TL;DR: In this paper, the authors studied the stability properties of the zeros of sampled-data systems resulting from continuous-time systems preceded by a hold and followed by a sampler.
Abstract: This paper is concerned with the zeros of sampled-data systems resulting from continuous-time systems preceded by a hold and followed by a sampler. The holds we shall consider are a zero-order hold and a first-order hold. For sufficiently small or large sampling periods, such zeros are called limiting zeros. For sufficiently small sampling periods, they are known to consist of two different types of zeros: the zeros of the first type correspond to the zeros of the original continuous-time system, while those of the second type have no continuous-time counterparts. We first show basic properties of the zeros of sample-data systems for sufficiently small sampling periods. Next, we clarify, in more detail, the correspondence between the former-type zeros of the sampled-data systems and the zeros of the original continuous-time system, including the stability property of these zeros. We also study stability properties of the latter-type zeros. In addition, we study limiting zeros for sufficiently large sampli...
143 citations
TL;DR: ASMOD, a new learning paradigm for higher dimensional data (> > 3) based on B-spline interpolation, is described, giving a model of small size and high accuracy.
Abstract: Nonlinear system identification by modelling the underlying relationships in observation data is an important application area for artificial neural networks and other learning paradigms. Splines have been used for scattered data interpolation, but the applications have mainly been restricted to low dimensional input spaces. This paper describes ASMOD, a new learning paradigm for higher dimensional data (> > 3) based on B-spline interpolation. The models can be trained online, and a method for step-wise model refinement is applied during model training for gradually increasing the modelling capability until the desired or best possible accuracy is obtained. For every refinement step a number of possible refinement actions are evaluated, and the one that gives the highest improvement of the model accuracy is chosen. The model structure is hence adapted to the modelling problem, giving a model of small size and high accuracy. ASMOD has very efficient implementations on serial computers. The scheme has been ...
TL;DR: In this paper, compensators are designed to attenuate the frequency contents of the sliding mode dynamics such that unmodelled dynamics are minimally excited, and the design method using frequency shaping is applied to the control of a flexible link robot arm.
Abstract: In this paper, compensator dynamics are introduced in sliding mode through a new class of switching surfaces which has the interpretation of linear operators. Two design methods are presented, the first is based on pole placement, whereas the second is based on frequency-shaped quadratic optimal control formulation. The compensators are designed to attenuate the frequency contents of the sliding mode dynamics such that unmodelled dynamics are minimally excited. The design method using frequency shaping is applied to the control of a flexible link robot arm. Simulation results show that the excitation of the link deformations are minimized while preserving the insensitivity of the sliding mode.
TL;DR: Multilayer neural networks are used in a non-linear adaptive control problem to control square multi-input/multi-output systems and the control law is defined in terms of the outputs of the neural networks.
Abstract: Multilayer neural networks are used in a non-linear adaptive control problem. The plant is an unknown feedback linearizable continuous-time system with relative degree 1. The single-input:/single-output system is studied first and then the methodology is extended to control square multi-input/multi-output systems. The control objective is for the plant to track a reference trajectory, and the control law is defined in terms of the outputs of the neural networks. The parameters of the networks are updated on-line according to an augmented tracking error and the network derivatives. A local convergence theorem is given on the convergence of the tracking error. This control algorithm is applied to control a two-input/two-output relative-degree-two system.
TL;DR: In this paper, the authors present a preliminary study of a systematic methodology to account robustly for parametric uncertainties in the original system model, which is based on combining sliding control ideas with the recursive construction of a closed-loop Lyapunov function.
Abstract: To make input-output feedback linearization a practical and systematic design methodology for single-input nonlinear systems, two problems need to be addressed One is to handle systematically the difficulties associated with the internal dynamics or zero-dynamics when the relative degree is less than the system order The other is to account for the effect of model uncertainties in the successive differentiations of the output of interest While the first problem has recently received considerable attention, the second has been largely unexplored This paper represents a preliminary study of a systematic methodology to account robustly for parametric uncertainties in the original system model The approach is based on combining sliding control ideas with the recursive construction of a closed-loop Lyapunov function, and is illustrated with a simple example
TL;DR: In this paper, a moving horizon feedback system based on constrained optimal control algorithms is proposed for nonlinear plants with input saturation, disturbances and plant uncertainty, which is robustly stable and is capable of attenuating L ∞ bounded disturbances.
Abstract: We present a moving horizon feedback system, based on constrained optimal control algorithms, for nonlinear plants with input saturation, disturbances and plant uncertainty. The system is a non-conventional sampled-data system: its sampling periods vary from sampling instant to sampling instant, and the control during the sampling time is not constant, but determined by the solution of an open loop optimal control problem. We show that the proposed moving horizon control system is robustly stable and is capable of attenuating L ∞ bounded disturbances
TL;DR: In this article, a sliding mode control strategy was developed to minimize the effects of the unmatched uncertainty on the dynamic performance of the switching surfaces of a light aircraft under a variety of flight conditions.
Abstract: It is well known that sliding mode control schemes provide robustness to the class of uncertainty acting within channels implicit in the control inputs: the so-called matched uncertainty. However, the unmatched uncertainty will affect the ideal dynamics prescribed by the chosen switching surfaces. This paper develops a control strategy to minimize the effects of the unmatched uncertainty upon the dynamic performance prescribed by the switching surfaces. This is achieved for a subclass of the uncertainty class considered by previous authors. The practical application of the control strategy to the design of a stability augmentation system for a light aircraft is presented. For this problem an ideal performance is well known and it is desirable that these ideal dynamics are exhibited across a wide range of flight conditions without degradation.
TL;DR: In this paper, the authors proposed a new switching surface which is initially designed to pass arbitrary initial conditions, and subsequently move towards a predetermined switching surface by rotating or/and shifting.
Abstract: Most of the switching surfaces proposed so far for a variable structure control system (VSCS) have been determined independently of initial conditions. The VSCS with these typical switching surfaces may be sensitive to parameter variations and extraneous disturbances during the reaching phase. To overcome this drawback, we propose a new switching surface which is initially designed to pass arbitrary initial conditions, and subsequently move towards a predetermined switching surface by rotating or/and shifting. We call it a moving switching surface (MSS). Using the MSS a low sensitivity system is obtained through shortening the reaching phase. Furthermore, the system robustness is guaranteed during whole intervals of control action by eliminating the reaching phase. To illustrate the advantages of the proposed method, a simple second-order linear system subjected to external disturbance is considered as a preliminary example followed by a two-link manipulator.
TL;DR: In this paper, a discrete-time sliding-mode controller based on the theory of variable structure systems is presented, where a predictive corrective scheme is utilized in the calculation of the control inputs and no a priori knowledge of the uncertainty bounds is required.
Abstract: A discrete-time sliding-mode controller is presented in this paper, based on the theory of variable structure systems. It is assumed that the parameters of the system are uncertain and external disturbances are present. A measure of these effects is obtained through the deviations from the desired sliding surface, and this information is incorporated in the control law. A predictive corrective scheme is utilized in the calculation of the control inputs and, as a result, no a priori knowledge of the uncertainty bounds is required. This approach leads to a non-switching type of control, thereby eliminating the fundamental cause of chatter. The convergence and disturbance rejection properties of the approach are verified, and its performance is tested for the tracking control of an industrial robot.
TL;DR: In this article, the rational approximation of a certain class of delay systems in the frequency domain using Pad£ approximants of exp(−sT) is described. And the exact error bounds for L∞ and L L2 error bounds are provided.
Abstract: This paper describes the rational approximation of a certain class of delay systems in the frequency domain using Pad£ approximants of exp(−sT). Three classes of approximants characterized by their relative degrees are considered. Easily computable a priori L∞ and L L2error bounds are provided.
TL;DR: In this paper, a moving horizon feedback system, based on constrained optimal control algorithms, for linear plants with input saturation, is presented, which is a non-conventional sampled data system: its sampling periods vary from sampling instant to sampling instant, and the control during the sampling time is not constant but determined by the solution of an open-loop optimal control problem.
Abstract: We present a moving horizon feedback system, based on constrained optimal control algorithms, for linear plants with input saturation. The system is a non-conventional sampled-data system: its sampling periods vary from sampling instant to sampling instant, and the control during the sampling time is not constant but determined by the solution of an open-loop optimal control problem. This is a two-part paper. In this part, we show that the proposed moving horizon control system is robustly stable, whether the state of the plant is measurable or not. In the second part, we show that the proposed moving horizon control system is capable of following a class of reference inputs and suppressing a class of disturbances. Experimental results show that the behaviour of the moving horizon control system is superior to that resulting from some alternative control laws.
TL;DR: In this paper, the authors derived the set of all quadratic Liapunov functions for output feedback control problems, and in this way parametrized all stabilizing controllers of fixed order.
Abstract: The early work of Liapunov produced some of the most powerful tools for stability analysis that remain to this day. To capture the class of all stabilizing controllers one would be well served by posing the problem in terms of the existence of a Liapunov function, since a Liapunov function is known to exist for stable systems. For linear systems, this paper derives the set of all quadratic Liapunov functions for output feedback control problems, and in this way parametrizes the set of all stabilizing controllers of fixed order. This is a unifying framework from which all other controllers can be produced by special choices of the free parameters in these controllers (we will show how to choose the free parameters to produce all covariance controllers and all H ∞ controllers of fixed order). These results also apply to robustness analysis, and provide a closed form expression for the set of all stabilizing real structured perturbations. Due to the assignment of a matrix property to the system (e.g. covaria...
TL;DR: In this paper, an identification method for highly nonlinear processes is proposed based on a multi-model approach and Kolmogorov-Gabor polynomials, where significant terms are selected by several statistical test procedures leading automatically to a minimal-order model realization.
Abstract: An identification method for highly nonlinear processes is proposed based on a multi-model approach and Kolmogorov-Gabor polynomials. Owing to the large number of possible terms in this general model structure, the significant terms are selected by several statistical test procedures leading automatically to a minimal-order model realization. The performance of this method is evaluated in an in-depth case study using a simulated pH neutralization process. The effects of important variables such as range of operating conditions, signal-/noise-ratio, and data length are discussed.
TL;DR: In this paper, a decentralized controller design for large-scale uncertain systems with higher-order uncertainties is investigated, where uncertainties are assumed to be bounded by a known or unknown pth-order polynomial in states.
Abstract: Decentralized controller design for large-scale uncertain systems with higher-order uncertainties is investigated. The uncertainties are assumed to be bounded by a known or unknown pth-order polynomial in states. A non-adaptive controller is proposed to handle the case when the pth-order polynomial is known. An adaptive controller is proposed to deal with the unknown case. The effectiveness of the proposed decentralized control schemes is demonstrated by a numerical simulation of two inverted pendulums on carts.
TL;DR: An optimal dynamic output feedback controller design approach is proposed for systems which are required to have an overlapping feedback structure and it is shown that if the controller designed for the expanded system achieves stability and satisfies the necessary conditions of optimality for the original system, then the contracted controller achieves stability
Abstract: An optimal dynamic output feedback controller design approach is proposed for systems which are required to have an overlapping feedback structure. Such a structure may be either imposed due to some design considerations or selected to match the overlapping structure of the given system. The proposed approach first involves transforming the given system into a larger dimensional system. Decentralized optimal controllers are then designed for this expanded system. These controllers are contracted for implementation on the original system in the final phase. It is shown that if the controller designed for the expanded system achieves stability and satisfies the necessary conditions of optimality for the expanded system, then the contracted controller achieves stability and satisfies the necessary conditions of optimality for the original system. Furthermore, the costs for the original and the expanded systems are equal. The details of overlapping controller design for a particular pattern of overla...
TL;DR: In this paper, the local linearization approach to nonlinear filtering of time series generated from continuous time stochastic dynamical systems is discussed and a simple and powerful method for the non-linear filtering is introduced.
Abstract: The local linearization approach to nonlinear filtering of time series generated from continuous time stochastic dynamical systems is discussed and a simple and powerful method for the nonlinear filtering is introduced Some numerical results of applications of the filter are shown
TL;DR: In this article, a simplified model of a crane is presented, which exhibits such a description of control derivatives as shown in Fig. 1 : A simplified model for a crane with control derivatives.
Abstract: Recent theoretical advances in nonlinear systems theory insist on the relevance of dynamics where control derivatives appear. We discuss here a simplified model of a crane which exhibits such a description.
TL;DR: In this article, a robust output tracking controller for MIMO nonlinear systems with weakly non-minimum phase is proposed, where the controller design is divided into two phases: fast feedback control and slow feedback control, so that a final composite control is obtained.
Abstract: This paper is concerned with the problem of designing a robust output tracking controller for MIMO nonlinear systems with weakly non-minimum phase. Based on our system formulation, control plants with uncertainties and/or with actuator dynamics fall into the class under consideration. The controller design here is divided into two phases: fast feedback control and slow feedback control, so that a final composite control is obtained. The former is chosen to stabilize the boundary layer system, whereas the latter essentially handles the mismatched uncertainties after the system is reformulated. Under some mild assumptions, it is shown that the overall states are bounded and the tracking errors converge to a residual set whose size is a class k function of e. As e → 0, the residual set shrinks to the origin. An interesting application to a simplified aircraft model with fast actuator dynamics, which turns out to be weakly non-minimum phase, is given. The computer simulation has verified the expected satisfac...
TL;DR: This paper introduces a trajectory interpolation algorithm, discusses a method for trajectory optimization, and includes simulation examples.
Abstract: Interpolation of a robot joint trajectory is realized using trigonometric splines This method is based on the assumption that joint-space knots have been generated from cartesian knots by an inverse kinematics algorithm The use of trigonometric splines results in smooth joint trajectories and is amenable to real-time obstacle avoidance Some of the spline parameters can be chosen to minimize an objective function (eg jerk or energy) If the objective function is minimum jerk, a closed-form solution is obtained This paper introduces a trajectory interpolation algorithm, discusses a method for trajectory optimization, and includes simulation examples
TL;DR: In this paper, a generalization of polynomial interpolation to the matrix case is introduced and applied to problems in systems and control, and it is shown that this generalization is most general and it includes all other such interpolation schemes that have appeared in the literature.
Abstract: A generalization of polynomial interpolation to the matrix case is introduced and applied to problems in systems and control. It is shown that this generalization is most general and it includes all other such interpolation schemes that have appeared in the literature. The polynomial matrix interpolation theory is developed and then applied to solving matrix equations; solutions to the diophantine equation are also derived. The relation between a polynomial matrix and its characteristic values and vectors is established and it is used in pole assignment and other control problems. Rational matrix interpolation is discussed; it can be seen as a special case of polynomial matrix interpolation. It is then used to solve rational matrix equations including the model matching problem.
TL;DR: In this paper, the authors present a design methodology for state estimation of nonlinear stochastic systems and measurement models with coloured noise processes based on the extension of variable structure observer schemes.
Abstract: We present a design methodology for state estimation of nonlinear stochastic systems and measurement models with coloured noise processes. The method is based on the extension of variable structure observer schemes. The deterministic versions of these results are also included, a new approach for obtaining the required parameters in the observer design is provided, together with the design of a dynamic feedback controller to minimize the effect of known waveform-type disturbances with unknown magnitudes and arrival times. Two simulation examples illustrate the design procedures.