Showing papers by "Brian D. O. Anderson published in 2000"

Model Reduction for Control System Design

Abstract: 1 Methods for Model Reduction.- 2 Multiplicative Approximation.- 3 Low Order Controller Design.- 4 Model and Controller Reduction Based On Coprime Factorizations.

Multiple model adaptive control. Part 1: Finite controller coverings

Abstract: We consider the problem of determining an appropriate model set on which to design a set of controllers for a multiple model switching adaptive control scheme. We show that, given mild assumptions on the uncertainty set of linear time-invariant plant models, it is possible to determine a "nite set of controllers such that for each plant in the uncertainty set, satisfactory performance will be obtained for some controller in the "nite set. We also demonstrate how such a controller set may be found. The analysis exploits the Vinnicombe metric and the fact that the set of approximately bandand time-limited transfer functions is approximately "nite-dimensional. Copyright ( 2000 John Wiley & Sons, Ltd.

Minimal positive realizations of transfer functions with positive real poles

Abstract: A standard result of linear-system theory states that a SISO rational nth-order transfer function always has an nth-order realization. In some applications, one is interested in having a realization with nonnegative entries (i.e., a positive system) and it is known that a positive system may not be minimal in the usual sense. In this paper, we give an explicit necessary and sufficient condition for a third-order transfer function with distinct real positive poles to have a third-order positive realization. The proof is constructive so that it is straightforward to obtain a minimal positive realization.

Complete solution of the 4-block H∞ Control problem with infinite and finite α-axis zeros

Abstract: This paper discusses the 4-block H∞ control problem with infinite and finite jω-axis invariant zeros in the state-space realizations of the transfer functions from the control input to the controlled output and from the disturbance input to the measurement output, where these realizations are induced from a stabilizable and detectable realization of the generalized plant. This paper extends the DGKF approach to the H∞ control problem but permitting infinite and finite jω-axis invariant zeros by using the eigenstructures related to these zeros. Necessary and sufficient conditions are presented for checking solvability through checking the stabilizing solutions of two reduced-order Riccati equations and examining matrix norm conditions related to the jω-axis zeros. The parameterization of all suitable controllers is given in terms of a linear fractional transformation involving a certain fixed transfer function matrix and together with a stable transfer function matrix with gain less than 1 which is free apart from satisfying certain interpolation conditions. Copyright © 2000 John Wiley & Sons, Ltd.

Asymptotic smoothing errors for hidden Markov models

Abstract: In this paper, the asymptotic smoothing error for hidden Markov models (HMMs) is investigated using hypothesis testing ideas. A family of HMMs is studied parametrised by a positive constant /spl epsiv/, which is a measure of the frequency of change. Thus, when /spl epsiv//spl rarr/0, the HMM becomes increasingly slower moving. We show that the smoothing error is O(/spl epsiv/). These theoretical predictions are confirmed by a series of simulations.

Robust disturbance suppression for nonlinear systems based on H/sub /spl infin// control

Abstract: The disturbance suppression problem for nonlinear systems is examined. We review the so-called nonstandard mixed sensitivity problem, which introduces an integrator to a selected weight, as well as the linear classical disturbance suppression problem and the linear H/sub /spl infin// disturbance suppression problem. We extend this H/sub /spl infin// problem to the nonlinear case, and present a method to reduce the order of the state feedback Hamilton-Jacobi partial differential equation for this nonlinear H/sub /spl infin// problem by extending the concept of comprehensive stability. Finally, we investigate the structure of the output feedback H/sub /spl infin// controller for disturbance suppression, and draw the conclusion that, as in the linear case, there must also be an integrator in the controller.

Differentially coprime kernel representations and closed-loop identification of nonlinear systems

Abstract: We utilize the differential kernel representation concept to convert a nonlinear closed-loop identification problem into one of open-loop identification utilizing a nonlinear version of the Youla parametrization. The main advantage of our approach using kernel representations over fractional descriptions is that we address a larger class of nonlinear systems.

Thermal Noise Behavior of the Bridge Circuit

Abstract: Supported by the National Science Foundation under Grant 94-23221, by DARPA/ARO under Contract DAAH04-94-G-0342, and by the NEC Research Institute, Princeton, New Jersey.

Limits to the fluctuation-dissipation theorem for nonlinear circuits

Abstract: It is well known that the equilibrium thermal noise behavior at the terminals of any linear time-invariant (LTI) RLC circuit can be predicted from knowledge of the driving-point impedance and temperature alone. This paper examines the conjecture that similar results hold if the capacitors and inductors are nonlinear. We refine the conjecture by analyzing the behavior of an RLC bridge circuit with the nonlinear inductor and capacitor carefully matched so the terminal behavior reduces to that of a linear resistor R. We show that the terminal noise current is not that predicted by the Nyquist-Johnson model for R if the driving voltage is time dependent or the inductor and capacitor are time varying. This counterexample disproves the conjecture, which does hold, however, for the bridge circuit with nonlinear (but time invariant) devices if the driving voltage is zero or constant. This paper makes exact calculations using techniques from stochastic differential equations and using reversibility arguments.

Identification and validation for robust control: design issues

Abstract: Model validation is the exercise of assessing whether a model of some underlying system is good enough. The assessment of the quality of a model cannot be decoupled from the purpose for which the model is to be used. And just as the research on system identification has, in the last 10 years, focused on issues of design in order to obtain a nominal model that suited the objective, so must the validation experiment similarly be designed in such a way that the model is guaranteed to deliver what the model is supposed to deliver. Thus, one must think in terms of "goal-oriented validation". This presentation focuses on model validation for robust control. The validation step is the ultimate quality control station that allows the model builder to provide the user with certified guarantees about the quality of his/her model. Without such certification the user cannot confidently use the model for his particular application, since he has no guarantees about whether the model is able to achieve its purpose.

Parametrization of all internally stabilizing plant and controller pairs via differentially coprime kernel representations

Abstract: In this paper, we use the notion of a differentially coprime kernel representation to parametrize the set of all internally stabilizing nonlinear plant and controller pairs using a Youla parameter and to unify understanding of some stability concepts for nonlinear systems. The idea of a differential kernel representation allows us to clarify the relationship between three different notions of internal stability available in the literature. Furthermore the parametrization derived here is applicable to nonlinear closed-loop identification problems.

Thermal noise behavior of a nonlinear bridge circuit

Abstract: It is well known that the thermal noise behavior at the terminals of any LTI RLC circuit can be predicted from knowledge of the driving-point impedance and temperature alone. This paper offers the conjecture that similar results hold if the capacitors and inductors are nonlinear. We refine the conjecture by analyzing the behavior of an RLC bridge circuit with the nonlinear inductor and capacitor carefully matched so the terminal behavior reduces to that of a linear resistor R. We show that the terminal noise current is precisely that predicted by the Nyquist-Johnson model for R if the driving voltage is zero or constant, but not if the driving voltage is time-dependent or the inductor and capacitor are time-varying. This paper makes exact calculations using techniques from stochastic differential equations and using reversibility arguments.

Closed-loop output error identification of nonlinear plants using kernel representations

Abstract: In this paper, the family of algorithms presented previously by the authors (1999) is extended for the identification of continuous time nonlinear plants operating in closed-loop. The main novelty is that the identification of unstable plants is covered in its generality.

Brief Paper Extended H = control * H = control with unstable weights q

Abstract: This paper presents a complete solution to an extended H = control problem for a generalized plant comprising a physical system cascaded with weights containing poles in the closed right half-plane. Necessary and su$cient conditions for a solution to exist are obtained which guarantee closed-loop stability of the physical system and controller as well as achieving the H = norm constraint on the closed loop of the transfer function matrix of the generalized plant and controller interconnection. The set of all feasible controllers is characterized. Conditions for solvability are a minimal variation on those appearing in the standard H = control problem. ( 2000 Elsevier Science Ltd. All rights reserved.