Showing papers in "IEEE Transactions on Automatic Control in 1995"
TL;DR: A new dynamic model for friction is proposed that captures most of the friction behavior that has been observed experimentally, including the Stribeck effect, hysteresis, spring-like characteristics for stiction, and varying break-away force.
Abstract: In this paper we propose a new dynamic model for friction. The model captures most of the friction behavior that has been observed experimentally. This includes the Stribeck effect, hysteresis, spring-like characteristics for stiction, and varying break-away force. Properties of the model that are relevant to control design are investigated by analysis and simulation. New control strategies, including a friction observer, are explored, and stability results are presented. >
3,416 citations
TL;DR: The approach to failure diagnosis presented in this paper is applicable to systems that fall naturally in the class of DES's; moreover, for the purpose of diagnosis, most continuous variable dynamic systems can be viewed as DES's at a higher level of abstraction.
Abstract: Fault detection and isolation is a crucial and challenging task in the automatic control of large complex systems We propose a discrete-event system (DES) approach to the problem of failure diagnosis We introduce two related notions of diagnosability of DES's in the framework of formal languages and compare diagnosability with the related notions of observability and invertibility We present a systematic procedure for detection and isolation of failure events using diagnosers and provide necessary and sufficient conditions for a language to be diagnosable The diagnoser performs diagnostics using online observations of the system behavior; it is also used to state and verify off-line the necessary and sufficient conditions for diagnosability These conditions are stated on the diagnoser or variations thereof The approach to failure diagnosis presented in this paper is applicable to systems that fall naturally in the class of DES's; moreover, for the purpose of diagnosis, most continuous variable dynamic systems can be viewed as DES's at a higher level of abstraction >
1,599 citations
TL;DR: Extensions of H/sub /spl infin// synthesis techniques to allow for controller dependence on time-varying but measured parameters are discussed and simple heuristics are proposed to compute robust time-invariant controllers.
Abstract: An important class of linear time-varying systems consists of plants where the state-space matrices are fixed functions of some time-varying physical parameters /spl theta/. Small gain techniques can be applied to such systems to derive robust time-invariant controllers. Yet, this approach is often overly conservative when the parameters /spl theta/ undergo large variations during system operation. In general, higher performance can be achieved by control laws that incorporate available measurements of /spl theta/ and therefore "adjust" to the current plant dynamics. This paper discusses extensions of H/sub /spl infin// synthesis techniques to allow for controller dependence on time-varying but measured parameters. When this dependence is linear fractional, the existence of such gain-scheduled H/sub /spl infin// controllers is fully characterized in terms of linear matrix inequalities. The underlying synthesis problem is therefore a convex program for which efficient optimization techniques are available. The formalism and derivation techniques developed here apply to both the continuous- and discrete-time problems. Existence conditions for robust time-invariant controllers are recovered as a special case, and extensions to gain-scheduling in the face of parametric uncertainty are discussed. In particular, simple heuristics are proposed to compute such controllers. >
1,229 citations
TL;DR: Application to the control of nonholonomic wheeled mobile robots is described by considering the case of a car pulling trailers, and globally stabilizing time-varying feedbacks are derived.
Abstract: Chain form systems have recently been introduced to model the kinematics of a class of nonholonomic mechanical systems. The first part of the study is centered on control design and analysis for nonlinear systems which can be converted to the chain form. Solutions to various control problems (open-loop steering, partial or complete state feedback stabilization) are either recalled, generalized, or developed. In particular, globally stabilizing time-varying feedbacks are derived, and a discussion of their convergence properties is provided. Application to the control of nonholonomic wheeled mobile robots is described in the second part of the study by considering the case of a car pulling trailers. >
1,094 citations
TL;DR: Two serial and parallel algorithms for solving a system of equations that arises from the discretization of the Hamilton-Jacobi equation associated to a trajectory optimization problem of the following type are presented.
Abstract: We present serial and parallel algorithms for solving a system of equations that arises from the discretization of the Hamilton-Jacobi equation associated to a trajectory optimization problem of the following type. A vehicle starts at a prespecified point x/sub o/ and follows a unit speed trajectory x(t) inside a region in /spl Rscr//sup m/ until an unspecified time T that the region is exited. A trajectory minimizing a cost function of the form /spl int//sub 0//sup T/ r(x(t))dt+q(x(T)) is sought. The discretized Hamilton-Jacobi equation corresponding to this problem is usually solved using iterative methods. Nevertheless, assuming that the function r is positive, we are able to exploit the problem structure and develop one-pass algorithms for the discretized problem. The first algorithm resembles Dijkstra's shortest path algorithm and runs in time O(n log n), where n is the number of grid points. The second algorithm uses a somewhat different discretization and borrows some ideas from a variation of Dial's shortest path algorithm (1969) that we develop here; it runs in time O(n), which is the best possible, under some fairly mild assumptions. Finally, we show that the latter algorithm can be efficiently parallelized: for two-dimensional problems and with p processors, its running time becomes O(n/p), provided that p=O(/spl radic/n/log n). >
816 citations
TL;DR: This paper presents a computational technique for optimal control problems including state and control inequality constraints based on spectral collocation methods used in the solution of differential equations that is easy to implement, capable of handling various types of constraints, and yields very accurate results.
Abstract: This paper presents a computational technique for optimal control problems including state and control inequality constraints. The technique is based on spectral collocation methods used in the solution of differential equations. The system dynamics are collocated at Legendre-Gauss-Lobatto points. The derivative x/spl dot/(t) of the state x(t) is approximated by the analytic derivative of the corresponding interpolating polynomial. State and control inequality constraints are collocated at Legendre-Gauss-Lobatto nodes. The integral involved in the definition of the performance index is discretized based on the Gauss-Lobatto quadrature rule. The optimal control problem is thereby converted into a mathematical programming program. Thus existing, well-developed optimization algorithms may be used to solve the transformed problem. The method is easy to implement, capable of handling various types of constraints, and yields very accurate results. Illustrative examples are included to demonstrate the capability of the proposed method, and a comparison is made with existing methods in the literature. >
703 citations
TL;DR: Simulations show that the use of the adaptive hysteresis inverse leads to major improvements of system performance.
Abstract: For a system with hysteresis, the authors present a parameterized hysteresis model and develop a hysteresis inverse. The authors then design adaptive controllers with an adaptive hysteresis inverse for plants with unknown hysteresis. A new adaptive controller structure is introduced which is capable of achieving a linear parameterization and a linear error model in the presence of a hysteresis nonlinearity. A robust adaptive law is used to update the controller parameters and hysteresis inverse parameters, which ensures the global boundedness of the closed-loop signals for a wide class of of hysteresis models. Simulations show that the use of the adaptive hysteresis inverse leads to major improvements of system performance. >
621 citations
TL;DR: This paper presents a feedback control scheme for the stabilization of two-input, driftless, chained nonholonomic systems, also called chained form, which are controllable but not asymptotically stabilizable by a smooth static-state feedback control law.
Abstract: This paper presents a feedback control scheme for the stabilization of two-input, driftless, chained nonholonomic systems, also called chained form. These systems are controllable but not asymptotically stabilizable by a smooth static-state feedback control law. In addition, exponential stability cannot be obtained with a smooth, time-varying feedback control law. Here, global, asymptotical stability with exponential convergence is achieved about any desired configuration by using a nonsmooth, time-varying feedback control law. The control law depends, in addition to the state and time, on a function which is constant except at predefined instants of time where the function is recomputed as a nonsmooth function of the state. The inputs are differentiable with respect to time and tend exponentially toward zero. For use in the analysis, a lemma on the exponential convergence of a stable time-varying nonlinear system perturbed by an exponentially decaying signal is presented. Simulation results are also shown. >
591 citations
TL;DR: The result says that, for any bounded initial conditions of the plant, if the neural network model contains enough number of nonlinear hidden neurons and if the initial guess of the network weights is sufficiently close to the correct weights, then the tracking error between the plant output and the reference command will converge to a bounded ball, whose size is determined by a dead-zone nonlinearity.
Abstract: Layered neural networks are used in a nonlinear self-tuning adaptive control problem. The plant is an unknown feedback-linearizable discrete-time system, represented by an input-output model. To derive the linearizing-stabilizing feedback control, a (possibly nonminimal) state-space model of the plant is obtained. This model is used to define the zero dynamics, which are assumed to be stable, i.e., the system is assumed to be minimum phase. A linearizing feedback control is derived in terms of some unknown nonlinear functions. A layered neural network is used to model the unknown system and generate the feedback control. Based on the error between the plant output and the model output, the weights of the neural network are updated. A local convergence result is given. The result says that, for any bounded initial conditions of the plant, if the neural network model contains enough number of nonlinear hidden neurons and if the initial guess of the network weights is sufficiently close to the correct weights, then the tracking error between the plant output and the reference command will converge to a bounded ball, whose size is determined by a dead-zone nonlinearity. Computer simulations verify the theoretical result. >
542 citations
TL;DR: This work considers the problem of characterizing possible supply functions for a given dissipative nonlinear system and provides a result which allows some freedom in the modification of such functions.
Abstract: We consider the problem of characterizing possible supply functions for a given dissipative nonlinear system and provide a result which allows some freedom in the modification of such functions. >
463 citations
TL;DR: Stability of a composite moving horizon system, comprising aMoving horizon regulator and a moving horizon observer, is established and the utility of the estimator for receding horizon control is explored.
Abstract: In this paper two topics are explored. A new approach to the problem of obtaining an estimate of the state of a nonlinear system is proposed. The moving horizon observer produces an estimate of the state of the nonlinear system at time t either by minimizing, or approximately minimizing, a cost function over the preceding interval (horizon) [t-T,t]; as t advances, so does the horizon. Convergence of the estimator is established under the assumption that the corresponding global optimization problem can be (approximately) solved and a uniform reconstructability condition is satisfied; the latter condition is automatically satisfied for linear observable systems. The utility of the estimator for receding horizon control is explored. In particular, stability of a composite moving horizon system, comprising a moving horizon regulator and a moving horizon observer, is established. >
TL;DR: A new adaptive nonlinear control design which achieves a complete controller-identifier separation and is more flexible than the Lyapunov-based design because the identifier can employ any standard update law gradient and least-squares, normalized and unnormalized.
Abstract: We present a new adaptive nonlinear control design which achieves a complete controller-identifier separation. This modularity is made possible by a strong input-to-state stability property of the new controller with respect to the parameter estimation error and its derivative as inputs. These inputs are independently guaranteed to be bounded by the identifier. The new design is more flexible than the Lyapunov-based design because the identifier can employ any standard update law gradient and least-squares, normalized and unnormalized. A key ingredient in the identifier design and convergence analysis is a nonlinear extension of the well-known linear swapping lemma. >
TL;DR: It is shown that the discrete Newton method, properly interpreted, yields an asymptotic observer for a large class of discrete-time systems, while the continuous Newton method may be employed to obtain a global observer.
Abstract: This paper focuses on the development of asymptotic observers for nonlinear discrete-time systems. It is argued that instead of trying to imitate the linear observer theory, the problem of constructing a nonlinear observer can be more fruitfully studied in the context of solving simultaneous nonlinear equations. In particular, it is shown that the discrete Newton method, properly interpreted, yields an asymptotic observer for a large class of discrete-time systems, while the continuous Newton method may be employed to obtain a global observer. Furthermore, it is analyzed how the use of Broyden's method in the observer structure affects the observer's performance and its computational complexity. An example illustrates some aspects of the proposed methods; moreover, it serves to show that these methods apply equally well to discrete-time systems and to continuous-time systems with sampled outputs. >
TL;DR: It is shown how to exploit these generalized basis functions to increase the speed of convergence in a series expansion, i.e., to obtain a good approximation by retaining only a finite number of expansion coefficients.
Abstract: In many areas of signal, system, and control theory, orthogonal functions play an important role in issues of analysis and design. In this paper, it is shown that there exist orthogonal functions that, in a natural way, are generated by stable linear dynamical systems and that compose an orthonormal basis for the signal space l/sub 2sup n/. To this end, use is made of balanced realizations of inner transfer functions. The orthogonal functions can be considered as generalizations of, for example, the pulse functions, Laguerre functions, and Kautz functions, and give rise to an alternative series expansion of rational transfer functions. It is shown how we can exploit these generalized basis functions to increase the speed of convergence in a series expansion, i.e., to obtain a good approximation by retaining only a finite number of expansion coefficients. Consequences for identification of expansion coefficients are analyzed, and a bound is formulated on the error that is made when approximating a system by a finite number of expansion coefficients. >
TL;DR: A programmatic procedure for establishing the stability of queueing networks and scheduling policies that establishes not only positive recurrence and the existence of a steady-state probability distribution, but also the geometric convergence of an exponential moment.
Abstract: We develop a programmatic procedure for establishing the stability of queueing networks and scheduling policies. The method uses linear or nonlinear programming to determine what is an appropriate quadratic functional to use as a Lyapunov function. If the underlying system is Markovian, our method establishes not only positive recurrence and the existence of a steady-state probability distribution, but also the geometric convergence of an exponential moment. We illustrate this method on several example problems. >
TL;DR: This work provides a solid foundation for performance analysis either by analytical methods or by simulation of open multiclass queueing networks, which are common models of communication networks, and complex manufacturing systems such as wafer fabrication facilities.
Abstract: The subject of this paper is open multiclass queueing networks, which are common models of communication networks, and complex manufacturing systems such as wafer fabrication facilities. We provide sufficient conditions for the existence of bounds on long-run average moments of the queue lengths at the various stations, and we bound the rate of convergence of the mean queue length to its steady-state value. Our work provides a solid foundation for performance analysis either by analytical methods or by simulation. These results are applied to several examples including re-entrant lines, generalized Jackson networks, and a general polling model as found in computer networks applications. >
TL;DR: The adaptive observers presented in this note guarantee arbitrarily fast exponential convergence both of parameter and state estimates to actual parameters and states, while previous adaptive observers guarantee only exponential (not arbitrarily fast) convergence.
Abstract: Concerns the same class of linearly parameterized single-output nonlinear systems that the authors previously identified in (1992) in terms of differential geometric conditions. When persistency of excitation conditions are satisfied, the adaptive observers presented in this note guarantee arbitrarily fast exponential convergence both of parameter and state estimates to actual parameters and states, while previous adaptive observers guarantee only exponential (not arbitrarily fast) convergence. This extends earlier results for linear systems. >
TL;DR: The solution of the problem of (local) disturbance attenuation via measurement feedback, with internal stability, can be solved for a nonlinear system of rather general structure thanks to the existence of solutions of a pair of Hamilton-Jacobi inequalities in n independent variables.
Abstract: This paper shows how the problem of (local) disturbance attenuation via measurement feedback, with internal stability, can be solved for a nonlinear system of rather general structure. The solution of the problem is shown to be related to the existence of solutions of a pair of Hamilton-Jacobi inequalities in n independent variables, which are associated with state-feedback and, respectively, output-injection design. >
TL;DR: A nonlinear control law which uses the feedback of the unit quaternion and the measured angular velocities is proposed and is shown to provide global asymptotic stability.
Abstract: This paper considers the problem of three-axis attitude stabilization of a rigid spacecraft. A nonlinear control law which uses the feedback of the unit quaternion and the measured angular velocities is proposed and is shown to provide global asymptotic stability. The control law does not require the knowledge of the system parameters and is, therefore, robust to modeling errors. The significance of the control law is that it can be used for large-angle maneuvers with guaranteed stability. >
TL;DR: In this note simple and straightforward methods to design full- and reduced-order observers for linear time-invariant descriptor systems are presented.
Abstract: In this note simple and straightforward methods to design full- and reduced-order observers for linear time-invariant descriptor systems are presented. The approach for the reduced-order observer design is based on the generalized Sylvester equation. Sufficient conditions for the existence of the observers are given. An illustrative example is included. >
TL;DR: It is shown that with state feedback, MPC is globally asymptotically stabilizing if and only if all the eigenvalues of the open loop system are in the closed unit disk.
Abstract: We derive stability conditions for model predictive control (MPC) with hard constraints on the inputs and "soft" constraints on the outputs for an infinitely long output horizon. We show that with state feedback, MPC is globally asymptotically stabilizing if and only if all the eigenvalues of the open loop system are in the closed unit disk. With output feedback, we show that the results hold if all the eigenvalues are strictly inside the unit circle. The online optimization problem defining MPC can be posed as a finite dimensional quadratic program even though the output constraints are specified over an infinite horizon. >
TL;DR: The authors present an algorithm for finding a family of transformations which will convert the system of rolling constraints on the wheels of the robot with n trailers into the Goursat canonical form, and study two of these transformations in detail.
Abstract: Develops the machinery of exterior differential forms, more particularly the Goursat normal form for a Pfaffian system, for solving nonholonomic motion planning problems, i.e., motion planning for systems with nonintegrable velocity constraints. The authors use this technique to solve the problem of steering a mobile robot with n trailers. The authors present an algorithm for finding a family of transformations which will convert the system of rolling constraints on the wheels of the robot with n trailers into the Goursat canonical form. Two of these transformations are studied in detail. The Goursat normal form for exterior differential systems is dual to the so-called chained-form for vector fields that has been studied previously. Consequently, the authors are able to give the state feedback law and change of coordinates to convert the N-trailer system into chained-form. Three methods for planning trajectories for chained-form systems using sinusoids, piecewise constants, and polynomials as inputs are presented. The motion planning strategy is therefore to first convert the N-trailer system into Goursat form, use this to find the chained-form coordinates, plan a path for the corresponding chained-form system, and then transform the resulting trajectory back into the original coordinates. Simulations and frames of movie animations of the N-trailer system for parallel parking and backing into a loading dock using this strategy are included. >
TL;DR: This work considers specifically the notion of asymptotic stability independent of delay, and presents for each class of systems a necessary and sufficient condition in terms of structured singular values, and demonstrates how these conditions may be extended to study stabilityIndependent of delay for uncertain systems.
Abstract: In this paper we study the stability properties of linear time-invariant delay systems given in a state space form. We consider specifically the notion of asymptotic stability independent of delay. Systems with both commensurate and noncommensurate delays are investigated. We present for each class of systems a necessary and sufficient condition in terms of structured singular values, and further we demonstrate how these conditions may be extended to study stability independent of delay for uncertain systems. Our results consist of several frequency sweeping tests that can be systematically implemented and that should complement the previous work. >
TL;DR: This paper analyzes the generic local bifurcations including those which are directly related to the singularity, and introduces the notion of a feasibility region, which consists of all equilibrium states that can be reached quasistatically from the current operating point without loss of local stability.
Abstract: The dynamics of a large class of physical systems such as the general power system can be represented by parameter-dependent differential-algebraic models of the form x/spl dot/=f and 0=g. Typically, such constrained models have singularities. This paper analyzes the generic local bifurcations including those which are directly related to the singularity. The notion of a feasibility region is introduced and analyzed. It consists of all equilibrium states that can be reached quasistatically from the current operating point without loss of local stability. It is shown that generically loss of stability at the feasibility boundary is caused by one of three different local bifurcations, namely the saddle-node and Hopf bifurcations and a new bifurcation called the singularity induced bifurcation which is analyzed precisely here for the first time. The latter results when an equilibrium point is at the singular surface. Under certain transversality conditions, the change in the eigenstructure of the system Jacobian at the equilibrium is established and the local dynamical structure of the trajectories near this bifurcation point is analyzed.
TL;DR: A recursive formulation of discounted costs for a linear quadratic exponential Gaussian linear regulator problem which implies time-invariant linear decision rules in the infinite horizon case is described.
Abstract: In this note, we describe a recursive formulation of discounted costs for a linear quadratic exponential Gaussian linear regulator problem which implies time-invariant linear decision rules in the infinite horizon case. Time invariance in the discounted case is attained by surrendering state-separability of the risk-adjusted costs. >
TL;DR: An extension of a Lyapunov equation result is derived for the countably infinite Markov state-space case and guarantees existence and uniqueness of a stationary measure and consequently existence of an optimal stationary control policy.
Abstract: Optimal control problems for discrete-time linear systems subject to Markovian jumps in the parameters are considered for the case in which the Markov chain takes values in a countably infinite set. Two situations are considered: the noiseless case and the case in which an additive noise is appended to the model. The solution for these problems relies, in part, on the study of a countably infinite set of coupled algebraic Riccati equations (ICARE). Conditions for existence and uniqueness of a positive semidefinite solution to the ICARE are obtained via the extended concepts of stochastic stabilizability (SS) and stochastic detectability (SD), which turn out to be equivalent to the spectral radius of certain infinite dimensional linear operators in a Banach space being less than one. For the long-run average cost, SS and SD guarantee existence and uniqueness of a stationary measure and consequently existence of an optimal stationary control policy. Furthermore, an extension of a Lyapunov equation result is derived for the countably infinite Markov state-space case.
TL;DR: The author provides a theoretical justification for the fuzzy identifiers by proving that they are capable of following the output of a general nonlinear dynamic system to arbitrary accuracy in any finite time interval.
Abstract: Uses fuzzy systems as identifiers for nonlinear dynamic systems. The author provides a theoretical justification for the fuzzy identifiers by proving that they are capable of following the output of a general nonlinear dynamic system to arbitrary accuracy in any finite time interval. The fuzzy identifiers are constructed from a set of adaptable fuzzy IF-THEN rules and can combine both numerical information (in the form of input-output pairs obtained by exciting the system with an input signal and measuring the corresponding outputs) and linguistic information (in the form of IF-THEN rules about the behavior of the system in terms of vague and fuzzy words) into their designs in a uniform fashion. The author develops two fuzzy identifiers. The first one is designed through the following four steps: 1) define some fuzzy sets in the state space U/spl sub/R/sup n/ of the system; these fuzzy sets do not change; 2) construct fuzzy rule bases of the fuzzy identifier which comprise rules whose IF parts constitute all the possible combinations of the fuzzy sets defined in 1); 3) design the fuzzy systems in the fuzzy identifier based on the fuzzy rule bases of 2); and 4) develop an adaptive law for the free parameters in the fuzzy identifier. The second fuzzy identifier is designed in a similar way as the first one except that: a) the parameters characterizing the fuzzy sets in the state space change during the adaptation procedure; and b) the fuzzy systems and the adaptive law are different. The author proves that: 1) both fuzzy identifiers are globally stable in the sense that all variables in the fuzzy identifiers are uniformly bounded, and 2) under some conditions the identification errors of both fuzzy identifiers converge to zero asymptotically. Finally, the author simulates the fuzzy identifiers for identifying the chaotic glycolytic oscillator, and the results show that: 1) the fuzzy identifiers can approximate the chaotic system at a reasonable speed and accuracy without using any linguistic information, and 2) by incorporating some fuzzy linguistic IF-THEN rules about the behavior of the system into the fuzzy identifiers, the speed and accuracy of the fuzzy identifiers are greatly improved. >
TL;DR: A survey of the matrix sign function is presented including some historical background, definitions and properties, approximation theory and computational methods, and condition theory and estimation procedures.
Abstract: A survey of the matrix sign function is presented including some historical background, definitions and properties, approximation theory and computational methods, and condition theory and estimation procedures, Applications to areas such as control theory, eigendecompositions, and roots of matrices are outlined, and some new theoretical results are also given. >
TL;DR: This paper shows how the pth-order average formula can be used to construct open-loop controls for point-to-point maneuvering of systems which require up to (p-1) iterations of Lie brackets to satisfy the Lie algebra controllability rank condition.
Abstract: In this paper we address the constructive controllability problem for drift-free, left-invariant systems on finite-dimensional Lie groups with fewer controls than state dimension. We consider small (/spl epsiv/) amplitude, low-frequency, periodically time-varying controls and derive average solutions for system behavior. We show how the pth-order average formula can be used to construct open-loop controls for point-to-point maneuvering of systems which require up to (p-1) iterations of Lie brackets to satisfy the Lie algebra controllability rank condition. In the cases p=2,3, we give algorithms for constructing these controls as a function of structure constants that define the control authority, i.e., the actuator capability, of the system. The algorithms are based on a geometric interpretation of the average formulas and produce sinusoidal controls that solve the constructive controllability problem with O(/spl epsiv//sup P/) accuracy in general (exactly if the Lie algebra is nilpotent). The methodology is applicable to a variety of control problems and is illustrated for the motion control problem of an autonomous underwater vehicle with as few as three control inputs. >
TL;DR: The nonlinear /spl Hscr//sub /spl infin//-control problem is considered with an emphasis on developing machinery with promising computational properties and the solutions are characterized in terms of nonlinear matrix inequalities which result in convex problems.
Abstract: The nonlinear /spl Hscr//sub /spl infin//-control problem is considered with an emphasis on developing machinery with promising computational properties. The solutions to /spl Hscr//sub /spl infin//-control problems for a class of nonlinear systems are characterized in terms of nonlinear matrix inequalities which result in convex problems. The computational implications for the characterization are discussed. >