Showing papers by "Claude Samson published in 1983"
TL;DR: An approach for studying stability of adaptively controlled systems subject to bounded disturbances with unknown statistics is given and uniform boundedness of all signals is proven under a condition that is discussed.
161 citations
TL;DR: In this article, the fixed point error performance of the normalized ladder algorithm, for autoregressive system identification, assuming rounding arithmetic, was analyzed and a simplified theoretical expression for predicting the average bias in the estimated reflection coefficients at any stage was derived.
Abstract: An attempt is made to analyze the fixed point error performance of the normalized ladder algorithm, for autoregressive system identification, assuming rounding arithmetic. A preliminary simulation study of this algorithm has shown that the bias in the estimated reflection coefficients is much more predominant than the variance of the error in the estimate. The study, therefore, is directed to find a model for predicting the bias in the estimated reflection coefficients. The analysis shows that the roundoff errors associated with the square root operations in one of the algorithm equations are mainly responsible for the bias in the estimated reflection coefficients. These errors arise because of the normalization procedure that makes the quantities under the square root operations very close to one. Two main results are presented in the paper. 1) A simplified theoretical expression for predicting the average bias in the estimated reflection coefficients at any stage is derived. 2) A recursive relation for the average error, arising from the finite precision arithmetic in the squared residuals, is derived. This relation illustrates how the errors made in one stage affect the errors in the succeeding stages. Simulations are performed to check the theoretical models. The experimental results agree very closely with the theoretical predictions.
139 citations
01 Dec 1983
TL;DR: In this article, a preliminary theoretical study is conducted so as to determine a large set of stable and robust controls for non-linear systems whose equations encompass the dynamic equations of any rigid manipulator.
Abstract: This article addresses the problem of controlling robotic manipulators. A preliminary theoretical study is conducted so as to determine a large set of stable and robust controls for non-linear systems whose equations encompass the dynamic equations of any rigid manipulator. Sufficient conditions for obtaining a good tracking of a linear time-invariant model of reference are derived. The local stability of several well known control methods is rigourously established while it is shown that global stability requires the use of non-linear gains in the control expression. An interesting property is that the determination of such gains does not necessarily require an important knowledge of the system; which justifies the use of very simple control schemes in practice. However, a control better conditioned with respect to measurement noises is obtained when a good model of the system is used in the control derivation. Between these two alternatives lies the idea of using adjustable control gains that become large when needed and stay small otherwise. In light of this study, several control schemes proposed in the literature on the subject (including adaptive control schemes) are discussed and conclusions are drawn with a view to future studies.
32 citations