Showing papers in "IEEE Transactions on Automatic Control in 1997"

Neuro-Fuzzy and Soft Computing-A Computational Approach to Learning and Machine Intelligence [Book Review]

Abstract: Interestingly, neuro fuzzy and soft computing a computational approach to learning and machine intelligence that you really wait for now is coming. It's significant to wait for the representative and beneficial books to read. Every book that is provided in better way and utterance will be expected by many peoples. Even you are a good reader or not, feeling to read this book will always appear when you find it. But, when you feel hard to find it as yours, what to do? Borrow to your friends and don't know when to give back it to her or him.

Multiobjective output-feedback control via LMI optimization

Abstract: This paper presents an overview of a linear matrix inequality (LMI) approach to the multiobjective synthesis of linear output-feedback controllers. The design objectives can be a mix of H/sub /spl infin// performance, H/sub 2/ performance, passivity, asymptotic disturbance rejection, time-domain constraints, and constraints on the closed-loop pole location. In addition, these objectives can be specified on different channels of the closed-loop system. When all objectives are formulated in terms of a common Lyapunov function, controller design amounts to solving a system of linear matrix inequalities. The validity of this approach is illustrated by a realistic design example.

A cone complementarity linearization algorithm for static output-feedback and related problems

Abstract: This paper describes a linear matrix inequality (LMI)-based algorithm for the static and reduced-order output-feedback synthesis problems of nth-order linear time-invariant (LTI) systems with n/sub u/ (respectively, n/sub y/) independent inputs (respectively, outputs). The algorithm is based on a "cone complementarity" formulation of the problem and is guaranteed to produce a stabilizing controller of order m/spl les/n-max(n/sub u/,n/sub y/), matching a generic stabilizability result of Davison and Chatterjee (1971). Extensive numerical experiments indicate that the algorithm finds a controller with order less than or equal to that predicted by Kimura's generic stabilizability result (m/spl les/n-n/sub u/-n/sub y/+1). A similar algorithm can be applied to a variety of control problems, including robust control synthesis.

System analysis via integral quadratic constraints

Abstract: This paper introduces a unified approach to robustness analysis with respect to nonlinearities, time variations, and uncertain parameters. From an original idea by Yakubovich (1967), the approach has been developed under a combination of influences from the Western and Russian traditions of control theory. It is shown how a complex system can be described, using integral quadratic constraints (IQC) for its elementary components. A stability theorem for systems described by IQCs is presented that covers classical passivity/dissipativity arguments but simplifies the use of multipliers and the treatment of causality. A systematic computational approach is described, and relations to other methods of stability analysis are discussed. Last, but not least, the paper contains a summarizing list of IQCs for important types of system components.

Adaptive control using multiple models

Abstract: Intelligent control may be viewed as the ability of a controller to operate in multiple environments by recognizing which environment is currently in existence and servicing it appropriately. An important prerequisite for an intelligent controller is the ability to adapt rapidly to any unknown but constant operating environment. This paper presents a general methodology for such adaptive control using multiple models, switching, and tuning. The approach was first introduced by Narendra et al. (1992) for improving the transient response of adaptive systems in a stable fashion. This paper proposes different switching and tuning schemes for adaptive control which combine fixed and adaptive models in novel ways. The principal mathematical results are the proofs of stability when these different schemes are used in the context of model reference control of an unknown linear time-invariant system. A variety of simulation results are presented to demonstrate the efficacy of the proposed methods.

An analysis of temporal-difference learning with function approximation

Abstract: We discuss the temporal-difference learning algorithm, as applied to approximating the cost-to-go function of an infinite-horizon discounted Markov chain. The algorithm we analyze updates parameters of a linear function approximator online during a single endless trajectory of an irreducible aperiodic Markov chain with a finite or infinite state space. We present a proof of convergence (with probability one), a characterization of the limit of convergence, and a bound on the resulting approximation error. Furthermore, our analysis is based on a new line of reasoning that provides new intuition about the dynamics of temporal-difference learning. In addition to proving new and stronger positive results than those previously available, we identify the significance of online updating and potential hazards associated with the use of nonlinear function approximators. First, we prove that divergence may occur when updates are not based on trajectories of the Markov chain. This fact reconciles positive and negative results that have been discussed in the literature, regarding the soundness of temporal-difference learning. Second, we present an example illustrating the possibility of divergence when temporal difference learning is used in the presence of a nonlinear function approximator.

Robust, fragile, or optimal?

Abstract: We show by examples that optimum and robust controllers, designed by using the H/sub 2/, H/sub /spl infin//, l/sup 1/, and /spl mu/ formulations, can produce extremely fragile controllers, in the sense that vanishingly small perturbations of the coefficients of the designed controller destabilize the closed-loop control system. The examples show that this fragility usually manifests itself as extremely poor gain and phase margins of the closed-loop system. The calculations given here should raise a cautionary note and draw attention to the larger issue of controller sensitivity which may be important in other nonoptimal design techniques as well.

Asymptotic controllability implies feedback stabilization

Abstract: It is shown that every asymptotically controllable system can be globally stabilized by means of some (discontinuous) feedback law. The stabilizing strategy is based on pointwise optimization of a smoothed version of a control-Lyapunov function, iteratively sending trajectories into smaller and smaller neighborhoods of a desired equilibrium. A major technical problem, and one of the contributions of the present paper, concerns the precise meaning of "solution" when using a discontinuous controller.

The unfalsified control concept and learning

Abstract: Without a plant model or other prejudicial assumptions, a theory is developed for identifying control laws which are consistent with performance objectives and past experimental data-possibly before the control laws are ever inserted in the feedback loop. The theory complements model-based methods such as H/sup /spl infin//-robust control theory by providing a precise characterization of how the set of suitable controllers shrinks when new experimental data is found to be inconsistent with prior assumptions or earlier data. When implemented in real time, the result is an adaptive switching controller. An example is included.

Systems with finite communication bandwidth constraints. I. State estimation problems

Abstract: In this paper, we investigate a state estimation problem involving finite communication capacity constraints. Unlike classical estimation problems where the observation is a continuous process corrupted by additive noises, there is a constraint that the observations must be coded and transmitted over a digital communication channel with finite capacity. This problem is formulated mathematically, and some convergence properties are defined. Moreover, the concept of a finitely recursive coder-estimator sequence is introduced. A new upper bound for the average estimation error is derived for a large class of random variables. Convergence properties of some coder-estimator algorithms are analyzed. Various conditions connecting the communication data rate with the rate of change of the underlying dynamics are established for the existence of stable and asymptotically convergent coder-estimator schemes.

Nonlinear control of constrained linear systems via predictive reference management

Abstract: A method based on conceptual tools of predictive control is described for solving set-point tracking problems wherein pointwise-in-time input and/or state inequality constraints are present. It consists of adding to a primal compensated system a nonlinear device, called command governor (CG), whose action is based on the current state, set-point, and prescribed constraints. The CG selects at any time a virtual sequence among a family of linearly parameterized command sequences, by solving a convex constrained quadratic optimization problem, and feeds the primal system according to a receding horizon control philosophy. The overall system is proved to fulfill the constraints, be asymptotically stable, and exhibit an offset-free tracking behavior, provided that an admissibility condition on the initial state is satisfied. Though the CG can be tailored for the application at hand by appropriately choosing the available design knobs, the required online computational load for the usual case of affine constraints is well tempered by the related relatively simple convex quadratic programming problem.

Delay-dependent robust stability and stabilization of uncertain linear delay systems: a linear matrix inequality approach

Abstract: This paper considers the problems of robust stability analysis and robust control design for a class of uncertain linear systems with a constant time-delay. The uncertainty is assumed to be norm-bounded and appears in all the matrices of the state-space model. We develop methods for robust stability analysis and robust stabilization. The proposed methods are dependent on the size of the delay and are given in terms of linear matrix inequalities.

A unifying construction of orthonormal bases for system identification

Abstract: This paper develops a general and very simple construction for complete orthonormal bases for system identification. This construction provides a unifying formulation of many previously studied orthonormal bases since the common FIR and recently popular Laguerre and two-parameter Kautz model structures are restrictive special cases of the construction presented here. However, in contrast to these special cases, the basis vectors in the unifying construction of this paper can have arbitrary placement of pole position according to the prior information the user wishes to inject. Results characterizing the completeness of the bases and the accuracy properties of models estimated using the bases are provided.

Exponential stabilization of driftless nonlinear control systems using homogeneous feedback

Abstract: This paper focuses on the problem of exponential stabilization of controllable, driftless systems using time-varying, homogeneous feedback. The analysis is performed with respect to a homogeneous norm in a nonstandard dilation that is compatible with the algebraic structure of the control Lie algebra. It can be shown that any continuous, time-varying controller that achieves exponential stability relative to the Euclidean norm is necessarily non-Lipschitz. Despite these restrictions, we provide a set of constructive, sufficient conditions for extending smooth, asymptotic stabilizers to homogeneous, exponential stabilizers. The modified feedbacks are everywhere continuous, smooth away from the origin, and can be extended to a large class of systems with torque inputs. The feedback laws are applied to an experimental mobile robot and show significant improvement in convergence rate over smooth stabilizers.

Supervisory control of families of linear set-point controllers. 2. Robustness

Abstract: A simply structured high-level controller, called a "supervisor", has recently been proposed in part I of this article (ibid., vol.41, 1996) for the purpose of orchestrating the switching of a sequence of candidate set-point controllers into feedback with an imprecisely modeled SISO process so as to cause the output of the process to approach and track a constant reference input. The process is assumed to be modeled by an SISO linear system whose transfer function is in the union of a number of subclasses, each subclass being small enough so that one of the candidate controllers would solve the set-point tracking problem, if the process transfer function was to be one of the subclass members. This paper proves that without any further modification, the same supervisor described in Part I can also perform this function in the face of norm-bounded unmodeled dynamics, and moreover that none of the signals within the overall system can grow without bound in response to bounded disturbance and noise inputs, whether they are constant or not.

A small-gain control method for nonlinear cascaded systems with dynamic uncertainties

Abstract: Some robust control problems for a class of nonlinear cascaded systems in the presence of state and input driven unmeasured dynamics are analyzed. A stepwise constructive control methodology is proposed on the basis of the nonlinear small-gain theorem. The flexibility of the approach in tackling dynamic uncertainties is illustrated by demonstrating that several results for special classes of cascaded systems, considered previously in the literature, may be viewed as special instances of the present results.

On interconnections, control, and feedback

Abstract: The purpose of this paper is to study interconnections and control of dynamical systems in a behavioral context. We start with an extensive physical example which serves to illustrate that the familiar input-output feedback loop structure is not as universal as we have been taught to believe. This leads to a formulation of control problems in terms of interconnections. Subsequently, we study interconnections of linear time-invariant systems from this vantage point. Let us mention two of the results obtained. The first one states that any polynomial can be achieved as the characteristic polynomial of the interconnection with a given plant, provided the plant is not autonomous. The second result states that any subsystem of a controllable system can be implemented by means of a singular feedback control law. These results yield pole placement and stabilization of controllable plants as a special case. These ideas are finally applied to the stabilization of a nonlinear system around an operating point.

A systematic approach to adaptive observer synthesis for nonlinear systems

Abstract: Geometric techniques of controller design for nonlinear systems have enjoyed great success. A serious shortcoming, however, has been the need for access to full-state feedback. This paper addresses the issue of state estimation from limited sensor measurements in the presence of parameter uncertainty. An adaptive nonlinear observer is suggested for Lipschitz nonlinear systems, and the stability of this observer is shown to be related to finding solutions to a quadratic inequality involving two variables. A coordinate transformation is used to reformulate this inequality as a linear matrix inequality. A systematic algorithm is presented, which checks for feasibility of a solution to the quadratic inequality and yields an observer whenever the solution is feasible. The state estimation errors then are guaranteed to converge to zero asymptotically. The convergence of the parameters, however, is determined by a persistence-of-excitation-type constraint.

Convergence analysis of the extended Kalman filter used as an observer for nonlinear deterministic discrete-time systems

Abstract: In this paper, convergence analysis of the extended Kalman filter (EKF), when used as an observer for nonlinear deterministic discrete-time systems, is presented. Based on a new formulation of the first-order linearization technique, sufficient conditions to ensure local asymptotic convergence are established. Furthermore, it is shown that the design of the arbitrary matrix plays an important role in enlarging the domain of attraction and then improving the convergence of the modified EKF significantly. The efficiency of this approach, compared to the classical version of the EKF, is shown through a nonlinear identification problem as well as a state and parameter estimation of nonlinear discrete-time systems.

Decentralized adaptive control of a class of large-scale interconnected nonlinear systems

Abstract: Decentralized adaptive control design for a class of large-scale interconnected nonlinear systems with unknown interconnections is considered. The motivation behind this work is to develop decentralized control for a class of large-scale systems which do not satisfy the matching condition requirement. To this end, large-scale nonlinear systems transformable to the decentralized strict feedback form are considered. Coordinate-free geometric conditions under which any general interconnected nonlinear system can be transformed to this form are obtained. The interconnections are assumed to be bounded by polynomial-type nonlinearities. Global stability and asymptotic regulation are established using classical Lyapunov techniques. The controller is shown to maintain robustness for a wide class of systems obtained by perturbation in the dynamics of the original system. Furthermore, appending additional subsystems does not require controller redesign for the original subsystems. Finally, the scheme is extended to the model reference tracking problem when global uniform boundedness of the tracking error to a compact set is established.

A simple alternative to the Barbalat lemma

Abstract: This paper gives a simple proof of the property that if a signal is square integrable and has a bounded derivative, then the signal converges to zero asymptotically.

Perturbation realization, potentials, and sensitivity analysis of Markov processes

Abstract: Two fundamental concepts and quantities, realization factors and performance potentials, are introduced for Markov processes. The relations among these two quantities and the group inverse of the infinitesimal generator are studied. It is shown that the sensitivity of the steady-state performance with respect to the change of the infinitesimal generator can be easily calculated by using either of these three quantities and that these quantities can be estimated by analyzing a single sample path of a Markov process. Based on these results, algorithms for estimating performance sensitivities on a single sample path of a Markov process can be proposed. The potentials in this paper are defined through realization factors and are shown to be the same as those defined by Poisson equations. The results provide a uniform framework of perturbation realization for infinitesimal perturbation analysis (IPA) and non-IPA approaches to the sensitivity analysis of steady-state performance; they also provide a theoretical background for the PA algorithms developed in recent years.

Robustness analysis of nonlinear feedback systems: an input-output approach

Abstract: This paper presents an approach to robustness analysis for nonlinear feedback systems. We pursue a notion of model uncertainty based on the closeness of input-output trajectories which is not tied to a particular uncertainty representation, such as additive, parametric, structured, etc. The basic viewpoint is to regard systems as operators on signal spaces. We present two versions of a global theory where stability is captured by induced norms or by gain functions. We also develop local approaches (over bounded signal sets) and give a treatment for systems with potential for finite-time escape. We compute the relevant stability margin for several examples and demonstrate robustness of stability for some specific perturbations, e.g., small-time delays. We also present examples of nonlinear control systems which have zero robustness margin and are destabilized by arbitrarily small gap perturbations. The paper considers the case where uncertainty is present in the controller as well as the plant and the generalization of the approach to the case where uncertainty occurs in several subsystems in an arbitrary interconnection.

Time-varying exponential stabilization of a rigid spacecraft with two control torques

Abstract: Rigid body models with two controls cannot be locally asymptotically stabilized by continuous feedbacks which are functions of the state only. This impossibility no longer holds when the feedback is also a function of time, and time-varying asymptotically stabilizing feedbacks have already been proposed. However, due to the smoothness of the feedbacks, the convergence rate is only polynomial. In this paper, exponential convergence is obtained by considering time-varying feedbacks which are only continuous.

On the rank minimization problem over a positive semidefinite linear matrix inequality

Abstract: We consider the problem of minimizing the rank of a positive semidefinite matrix, subject to the constraint that an affine transformation of it is also positive semidefinite. Our method for solving this problem employs ideas from the ordered linear complementarity theory and the notion of the least element in a vector lattice. This problem is of importance in many contexts, for example in feedback synthesis problems, and such an example is also provided.

Decentralized adaptive output feedback design for large-scale nonlinear systems

Abstract: In this paper, we present a global, decentralized adaptive design procedure for a class of large-scale nonlinear systems, which utilizes only local output feedback. The advocated scheme guarantees robustness to parametric and dynamic uncertainties in the interconnections and also rejects any bounded disturbances entering the system. The systems belonging to this class are those which can be transformed using a global diffeomorphism to the output feedback canonical form, where the interconnections are a function of subsystem outputs only. The uncertainties are assumed to be bounded by an unknown pth-order polynomial in the outputs. The resulting controller maintains global robustness and disturbance rejection properties. The output tracking error is shown to be bounded within a compact set, the size of which can be made arbitrarily small by appropriate choice of the control gains. For the case where the objective is regulation, global asymptotic regulation of all the states of the closed-loop system is achieved.

Polynomial-complexity deadlock avoidance policies for sequential resource allocation systems

Abstract: The development of efficient deadlock avoidance policies (DAPs) for sequential resource allocation systems (RASs) is a problem of increasing interest in the scientific community, largely because of its relevance to the design of large-scale flexibly automated manufacturing systems. Much of the work on this problem existing in the literature is focused on the so-called single-unit RAS model, which is the simplest model in the considered class of RASs. Furthermore, due to a well-established result stating that, even for single-unit RASs, the computation of the maximally permissive DAP is intractable (NP-hard), many researchers (including our group) have focused on obtaining good suboptimal policies which are computationally tractable (scalable) and provably correct. In the first part of the paper, it is shown, however, that for a large subset (in fact, a majority) of single-unit RASs, the optimal DAP can be obtained in real-time with a computational cost which is a polynomial function of the system size (i.e., the number of resource types and the distinct route stages of the processes running through the system). The implications of this result for the entire class of single-unit RASs are also explored. With a result on the design of optimal DAPs for single-unit RASs, the second part of the paper concentrates on the development of scalable and provably correct DAPs for the more general case of conjunctive RASs.

On the control of finite-dimensional mechanical systems with unilateral constraints

Abstract: This paper focuses on the problem of the control of a class of mechanical systems with a finite number of degrees-of-freedom, subject to unilateral constraints on the position. Roughly speaking, those systems are described by a set of ordinary differential equations that represent smooth dynamics, together with an algebraic inequality condition F(q)/spl ges/0 (where q is the vector of generalized coordinates) and an impact rule relating the interaction impulse and the velocity. Nonsmooth dynamics is at the core of the study of such systems. This implies that one can suitably define solutions and stability concepts that fit with the considered model. We then discuss the closed-loop control problem, and analyze various switching control strategies.

Capacity allocation under noncooperative routing

Abstract: The capacity allocation problem in a network that is to be shared by noncooperative users is considered. Each user decides independently upon its routing strategy so as to optimize its individual performance objective. The operating points of the network are the Nash equilibria of the underlying routing game,. The network designer aims to allocate link capacities, so that the resulting Nash equilibria are efficient, according to some systemwide performance criterion. In general, the solution of such design problems is complex and at times counterintuitive, since adding link capacity might lead to degradation of user performance. For systems of parallel links, we show that such paradoxes do not occur and that the capacity allocation problem has a simple and intuitive optimal solution that coincides with the solution in the single-user case.

Frequency domain system identification using arbitrary signals

Abstract: It is the common conviction that frequency domain system identification suffers from the drawback that it cannot handle arbitrary signals without introducing systematic errors. This paper shows that it is possible to deal with nonperiodic signals without any approximation and under the same assumptions as in the time domain, by estimating simultaneously some initial conditions and the system model parameters.