Showing papers by "Dennis S. Bernstein published in 2003"
TL;DR: The results use a novel condition based on nontangency between the vector field and invariant or negatively invariant subsets of the level or sublevel sets of the Lyapunov function or its derivative and represent extensions of previously known stability results involving semidefinite Lyap unov functions.
Abstract: This paper focuses on the stability analysis of systems having a continuum of equilibria. Two notions that are of particular relevance to such systems are convergence and semistability. Convergence is the property whereby every solution converges to a limit point that may depend on the initial condition. Semistability is the additional requirement that all solutions converge to limit points that are Lyapunov stable. We give new Lyapunov-function-based results for convergence and semistability of nonlinear systems. These results do not make assumptions of sign definiteness on the Lyapunov function. Instead, our results use a novel condition based on nontangency between the vector field and invariant or negatively invariant subsets of the level or sublevel sets of the Lyapunov function or its derivative and represent extensions of previously known stability results involving semidefinite Lyapunov functions. To illustrate our results we deduce convergence and semistability of the kinetics of the Michaelis--Menten chemical reaction and the closed-loop dynamics of a scalar system under a universal adaptive stabilizing feedback controller.
137 citations
TL;DR: This work writes the least-squares optimization problem as a convex linear programming problem with mixed equality, quadratic, and positive-semidefinite constraints suitable for existing convex optimization codes such as SeDuMi.
Abstract: In system identification, the true system is often known to be stable. However, due to finite sample constraints, modeling errors, plant disturbances and measurement noise, the identified model may be unstable. We present a constrained optimization method to ensure asymptotic stability of the identified model in the context of subspace identification methods. In subspace identification, we first obtain an estimate of the state sequence or extended observability matrix and then solve a least squares optimization problem to estimate the system parameters. To ensure asymptotic stability of the identified model, we write the least-squares optimization problem as a convex linear programming problem with mixed equality, quadratic, and positive-semidefinite constraints suitable for existing convex optimization codes such as SeDuMi. We present examples to illustrate the method and compare to existing approaches.
124 citations
TL;DR: In this article, the verge and foliot escapement mechanism of a mechanical clock is analyzed from a feedback perspective, and conditions under which the system possesses a limit cycle are determined using impulsive differential equations and Poincare maps.
Abstract: The verge and foliot escapement mechanism of a mechanical clock is a classical example of a feedback regulator. In this paper we analyse the dynamics of this mechanism to understand its operation from a feedback perspective. Using impulsive differential equations and Poincare maps to model the dynamics of this closed-loop system, we determine conditions under which the system possesses a limit cycle, and we analyse the period and amplitude of the oscillations in terms of the inertias of the colliding masses and their coefficient of restitution.
52 citations
TL;DR: In this paper, the authors identify single-input single-output (SISO) Wiener systems with finite impulse response dynamics and polynomial output nonlinearities using multi-index notation.
Abstract: Wiener systems consist of a linear dynamic system whose output is measured through a static non-linearity. In this paper we study the identification of single-input single-output Wiener systems with finite impulse response dynamics and polynomial output non-linearities. Using multi-index notation, we solve a least squares problem to estimate products of the coefficients of the non-linearity and the impulse response of the linear system. We then consider four methods for extracting the coefficients of the non-linearity and impulse response: direct algebraic solution, singular value decomposition, multi-dimensional singular value decomposition and prediction error optimization.
42 citations
04 Jun 2003
TL;DR: It is shown that a system is convergent if all of its orbits have finite arc length, while an equilibrium is Lyapunov stable if the arc length is continuous at the equilibrium, and semistable if the arcs are continuous in a neighborhood of the equilibrium.
Abstract: This paper focuses on the stability analysis of systems having a continuum of equilibria. Two notions that are of particular relevance to such systems are convergence and semistability. Convergence is the property whereby every solution converges to a limit point that may depend on the initial condition. Semistability is the additional requirement that all solutions converge to limit point that are Lyapunov stable. In this paper, we relate convergence and stability to arc length of the orbits. More specifically, we show that a system is convergent if all of its orbits have finite arc length, while an equilibrium is Lyapunov stable if the arc length (considered as a function of the initial condition) is continuous at the equilibrium, and semistable if the arc length is continuous in a neighborhood of the equilibrium. Next we derive arc-length-base Lyapunov results for convergence and stability. These results do not require the Lyapunov function to be positive definite. Instead, these results involve an inequality relating the righthand side of the differential equation and the Lyapunov function derivative. The inequality makes it possible to deduce properties of the arc length function and this leads to sufficient conditions for convergence and stability. Finally, we give additional assumptions under which the converses of all the main results hold.
37 citations
TL;DR: In this article, a discrete-time adaptive stabilization algorithm based on a one-step backward-horizon cost criterion was developed to obtain a gain update law that guarantees convergence of the plant states.
Abstract: In this paper we develop a discrete-time adaptive stabilization algorithm based on a one-step backward-horizon cost criterion. By optimizing the cost with respect to the update step size, we obtain a gain update law that guarantees convergence of the plant states. The convergence proof is based on a modified Lyapunov technique. We extend the algorithm to include integral control for rejecting constant disturbances and we present an experimental application to DC motor positioning system. Copyright © 2003 John Wiley & Sons, Ltd.
26 citations
TL;DR: Control algorithms for stabilization and asymptotic disturbance rejection for Hammerstein systems with positive real linear dynamics are presented and constructed that guarantee convergence of the plant output while accounting for input nonlinearities.
Abstract: We present control algorithms for stabilization and asymptotic disturbance rejection for Hammerstein systems with positive real linear dynamics. To do this, we extend the nonlinear controller modification technique of Bernstein and Haddad (1994) to include matched plant disturbances. The controller is based on a Lyapunov function that estimates the disturbance bound. These estimates are then used to construct high-gain switching controllers that guarantee convergence of the plant output while accounting for input nonlinearities.
19 citations
09 Dec 2003
TL;DR: An adaptive controller is developed for a planar rotating body tracking a desired angular velocity command and Lyapunov analysis is used to show boundedness of the angular velocity and inertia estimate errors.
Abstract: The problem of a rigid body tracking a desired angular velocity trajectory is addressed using adaptive feedback control. An adaptive controller is developed for a planar rotating body tracking a desired angular velocity command. Lyapunov analysis is used to show that tracking is achieved globally. A periodic angular velocity command is then used to identify the inertia parameter. The adaptive controller is implemented on a triaxial attitude control testbed with fan thrusters. A piecewise linear approximation of an observed input nonlinearity is inverted to obtain improved angular velocity tracking and inertia identification. To eliminate residual tracking error, an adaptive algorithm is used for improved feedback linearization. Lyapunov analysis is used to show boundedness of the angular velocity and inertia estimate errors. The approach is validated by numerical simulation.
18 citations
11 Aug 2003
TL;DR: In this article, the ARMARKOV adaptive disturbance rejection algorithm is used to reject single and dual-tone disturbances without knowledge of the disturbance spectrum and with limited modeling of the membrane dynamics.
Abstract: Flexible membranes are envisioned as a key component of large, lightweight, space-based systems. This paper focuses on the problem of adaptive disturbance rejection, that is, the rejection of external disturbances with unknown spectral content. It describes the design and operation of a laboratory testbed involving a exible membrane with acoustic excitation and optical sensing. The ARMARKOV adaptive disturbance rejection algorithm is used to reject single- and dual-tone disturbances without knowledge of the disturbance spectrum and with limited modeling of the membrane dynamics.
14 citations
TL;DR: The author offers helpful advice based on his own experience, much of it learned by sometimes painful trial and error, in the hope that this advice will help him avoid some of the difficulties that he might otherwise encounter.
Abstract: Setting up and managing a control research laboratory can be a time-consuming and labor-intensive undertaking. The author offers helpful advice based on his own experience, much of it learned by sometimes painful trial and error, in the hope that this advice will help you avoid some of the difficulties that you might otherwise encounter. Questions addressed are whether to build or to buy; how much space is needed; how much money is needed; the best way to design a control experiment; PCs and software maintenance; electrical problems; filters; power amplifiers; batteries; documentation of results; choice of vendors; and lab safety.
13 citations
TL;DR: In this paper, an alternative technology for attitude control called shape change actuation and control (SCC) is proposed, which is intended for efficient, low-authority attitude control, possibly as a backup for thrusters and reaction wheels.
Abstract: This article focuses on an alternative technology for attitude control called shape change actuation and control. The objective is to control the spacecraft attitude by purposefully changing the mass distribution of the spacecraft. Shape change actuation and control is not useful for momentum dumping or storage. Rather, it is intended for efficient, low-authority attitude control, possibly as a backup for thrusters and reaction wheels.
09 Dec 2003
TL;DR: This paper develops additional criteria for input signal selection, in particular, the input at each time step is chosen to minimize the predicted variance of the system estimate at the next time step.
Abstract: The accuracy of an identified model depends on the choice of input signal. Persistency of excitation is a necessary criterion for such signals. In this paper we develop additional criteria for input signal selection, in particular, the input at each time step is chosen to minimize the predicted variance of the system estimate at the next time step. We extend the method to the finite-horizon input selection problem and demonstrate the method in simulation.
04 Jun 2003
TL;DR: This paper presents a method based on continuous-time modeling of a scalar nth-order system whose dynamics are represented as a map of integrals and derivatives of the available signal that is able to reproduce a periodic signal as a limiting trajectory.
Abstract: Limit cycle oscillations occur in a wide range of electrical, mechanical, and aerospace applications. In this paper we present a method for constructing system models that are able to reproduce a periodic signal as a limiting trajectory. Our approach is based on continuous-time modeling of a scalar nth-order system whose dynamics are represented as a map of integrals and derivatives of the available signal. The method is demonstrated on the classical Van der Pol oscillator and a nonlinear oscillator with piecewise linear damping.
04 Jun 2003
TL;DR: This paper shows that a linear system is output-reversible if and only if its non-imaginary spectrum is symmetric with respect to the imaginary axis, and suggests that stability and instability play a key role in the arrow of time.
Abstract: In the present paper we consider the free response of a linear system involving dynamics and an output map. A second system is an output reversal of the original system if it can produce a time-reversed image every output of the original system. As a special case, a system is output reversible if it can produce time-reversed image of every one of its free output responses. Our main result is a spectral symmetry condition that provides a complete characterization of single-input, single-output, output-reversible systems. In particular, we show that a linear system is output-reversible if and only if its non-imaginary spectrum is symmetric with respect to the imaginary axis. As special cases, the class of output-reversible systems includes rigid body and Hamiltonian systems. This result suggests that stability and instability play a key role in the arrow of time, independently of dimensionality, continue, and sensitivity.
TL;DR: In this paper, the authors discuss the effect of their experimental activities on the development of control ideas and their contribution to improving our understanding of the role of control experiments in control research.
Abstract: I n the past decade, there has been an explosion of activity in what we commonly call control experimentation. Even without a definitive statement of what constitutes a control experiment, there can be little doubt that the implementation of control theory on control hardware can have only a positive impact on control engineering and control education. Since the ultimate goal of control theory is to enhance the performance and reliability of operational systems, control experiments provide a valuable link between theory and practice. The articles in this issue were selected largely for their contribution to improving our understanding of the role of control experiments in control research. Consequently, each article includes perspective on the conceptualization, design, construction, and operation of laboratory experiments. In addition, the authors of each article make a conscious effort to discuss the effect of their experimental activities on the development of control ideas. Although there is less emphasis on how these experiments might impact control practice, it is only a small step to drawing conclusions in that direction as well. © M A S T E R S E R IE S & E Y E W IR E Introduction to the special section. G U E S T E D I T O R I A L I I
04 Jun 2003
TL;DR: A discontinuous control algorithm is used to stabilize SISO minimum-phase relative-degreeone linear systems in the presence of external disturbances and Lyapunov methods are used to prove stability of the closed-loop system and convergence to zero of the measurement.
Abstract: We use a discontinuous control algorithm to adap tively stabilize SISO minimum-phase relative-degreeone linear systems in the presence of external disturbances. Lyapunov methods are used to prove stability of the closed-loop system and convergence to zero of the measurement. By proving Lyapunov stability, these results complement existing convergence results that utilize adaptive algorithms with discontinuous feedback.
04 Jun 2003
TL;DR: The problem of discrete-time adaptive stabilization under full-state feedback control is considered under weaker assumptions than the prior literature and the main result is based on a gain update law involving a step-size function.
Abstract: The problem of discrete-time adaptive stabilization under full-state feedback control is considered under weaker assumptions than the prior literature. The main result is based on a gain update law involving a step-size function. The formulation generalizes and unifies prior results based on quadratic and logarithmic Lyapunov functions.
TL;DR: In this paper, a constrained least squares method is developed to identify the hysteresis map using the semilinear Duhem model, where the input-output map of the model is rate-independent, thus yielding persistent phase shift at arbitrarily low frequency.
TL;DR: In this paper, an adaptive controller is developed for a planar rotating body tracking a desired angular velocity command, and Lyapunov analysis is used to show that tracking is achieved globally.
TL;DR: Signals, systems, and control provide a powerful paradigm for intellectual thought in science and technology, yet these ideas have had virtually no penetration into grades K through 12 education.
Abstract: Signals, systems, and control provide a powerful paradigm for intellectual thought in science and technology, yet these ideas have had virtually no penetration into grades K through 12 education. In this article the author provides some suggestions for introducing these concepts into primary and secondary education, thus promoting their diffusion throughout the academic disciplines.
09 Dec 2003
TL;DR: In this article, the authors considered a generalized Duhem model for hysteresis and provided a sufficient condition for the existence of hystresis in the input-output map.
Abstract: In this paper we consider a generalized Duhem model for hysteresis and provide a sufficient condition for the existence of hysteresis in the input-output map. Hysteresis is defined to be persistent phase shift at arbitrarily low frequency. The rate dependence of the hysteresis is also discussed, and we develop a rate-independent semilinear Duhem model with provable convergence properties. We also discuss the reversal behavior and orientation of the hysteretic map.
Journal Article•
01 Jan 2003
TL;DR: In this paper, a constrained least squares method is developed to identify the hysteresis map using the semilinear Duhem model, where the input-output map of the model is rate-independent, thus yielding persistent phase shift at arbitrarily low frequency.
Abstract: In this paper we consider a semilinear Duhem model. The input-output map of the model is rate-independent, thus yielding persistent phase shift (that is, hysteresis) at arbitrarily low frequency. For the semilinear Duhem model we reparameterize the response in terms of the control input, and we provide su-cient conditions for convergence to a hysteresis map. A constrained least squares method is developed to identify the hysteresis map using the semilinear Duhem model. Copyright c ∞ 2003 IFAC
04 Jun 2003
TL;DR: This work considers the adaptive output convergence for a class of unstable non-minimum-phase second-order relative-degree-one linear systems with unknown constant coefficients and illustrates the use of the controller.
Abstract: We consider the adaptive output convergence for a class of unstable non-minimum-phase second-order relative-degree-one linear systems with unknown constant coefficients. The coefficient uncertainty bounds are required to be known and to satisfy an inequality constraint. We illustrate the use of the controller with several example systems.