Showing papers in "Ima Journal of Mathematical Control and Information in 1984"
TL;DR: In this paper, the authors study the analysis involved with Volterra series operators, and prove a general Steady-state theorem for the spectrum of the output of a VOLTERRA series operator in terms of a periodic input.
Abstract: In this paper we carefully study the analysis involved with Volterra series. We address system-theoretic issues ranging from bounds on the gain and incremental gain of Volterra series operators to the existence of Volterra series operator inverses, and mathematical topics such as the relation between Volterra series operators and Taylor series. The proofs are complete, and use only the basic facts of analysis. We prove a general Steady-state theorem for Volterra series operators, and then establish a general formula for the spectrum of the output of a Volterra series operator in terms of the spectrum of a periodic input. This paper is meant to complement recent work on Volterra series expansions for dynamical systems.
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TL;DR: In this article, the stability, parameter convergence and robustness aspects of single input-single output model reference adaptive systems were studied, and conditions on the exogenous input to the adaptive loop, the reference signal, to guarantee exponential para meter and error convergence.
Abstract: We study stability, parameter convergence and robustness aspects of single input-single output model reference adaptive systems. We begin by establishing a framework for studying parametrizable and unparametrizable uncertainty in the plant to be controlled. Using the standard assumptions on the parametrizable part of the plant dynamics we give a corrected proof (of Narendra, Lin and Valavani) of the stability of the nominal adaptive scheme. Next, we give conditions on the exogenous input to the adaptive loop, the reference signal, to guarantee exponential para meter and error convergence. Using our framework for studying unmodelled (unparametrized) dynamics; we show how the model should be chosen, and the update law modified (by a deadzone in the update law) to preserve stability of the adaptive loop in the presence of output disturbances and unmodelled dynamics. Finally, we compare adaptive and non-adaptive con trol and list directions of ongoing research.
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TL;DR: Black-Box Identification of Transfer Functions: Asymptotic Results for Increasing Model Order and Data Records as discussed by the authors, is a black-box identification of transfer functions for increasing model order and data records.
Abstract: Black-Box Identification of Transfer Functions : Asymptotic Results for Increasing Model Order and Data Records
TL;DR: In this article, the authors considered many of the self-tuning algorithms, both state-space and polynomial, presently in use, and by starting from first principles developed the observers which are, effectively, used in each case.
Abstract: In the last few years a state-space formulation has been introduced into self-tuning control. This has not only allowed for a wider choice of possible control actions, but has also provided an insight into the theory underlying—and hidden by—that used in the polynomial description.
This paper considers many of the self-tuning algorithms, both state-space and polynomial, presently in use, and by starting from first principles develops the observers which are, effectively, used in each case.
At any specific time instant the state estimator can be regarded as taking one of two forms. In the first case the most recently available output measurement is excluded, and here an optimal and conditionally stable observer is obtained. In the second case the present output signal is included, and here it is shown that although the observer is once again conditionally stable, it is no longer optimal. This result is of significance, as many of the popular self-tuning controllers lie in the second, rather than first, category.
TL;DR: In this article, the nonlinear variation of constants formula is generalized to infinite dimensional systems and applied to the stability problem and to obtain bounds on the states of a nonlinear control system when the controls are bounded.
Abstract: The nonlinear variation of constants formula is generalised to infinite dimensional systems and applied to the stability problem and to obtain bounds on the states of a nonlinear control system when the controls are bounded. The theory is illustrated by a simple model from nuclear reactor dynamics