Journal ArticleDOI
Bilinear approximation of general non-linear dynamic systems with linear inputs
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TLDR
In this article, two methods are developed by which control systems that are non-linear in the state variables but linear in the inputs may be approximated by bilinear systems in the neighbourhood of a steady state.Abstract:
Two methods are developed by which control systems that are non-linear in the state variables but linear in the inputs may be approximated by bilinear systems in the neighbourhood of a steady state. For both methods the approximations can be made successively more accurate at the expense of higher dimensionality, and can be a considerable improvement over the linear approximation. The resulting dimensionalities are determined as functions of the accuracy. Illustrative examples are given, and finally the two models are compared. Both are found to have considerable merit.read more
Citations
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Journal ArticleDOI
Hierarchical parameter and state estimation for bilinear systems
Xiao Zhang,Feng Ding +1 more
TL;DR: The interaction estimation theory is introduced to study an on-line algorithm for joint state-parameter estimation and a bilinear state observer based recursive least squares algorithm is developed using the least squares method.
Journal ArticleDOI
Algebraic approaches for fault identification in discrete-event systems
TL;DR: Algebraic approaches for fault identification in discrete-event systems that are described by Petri nets are developed and a redundant Petri net embedding is explored that uses 2k additional places and enables the simultaneous identification of 2k-1 transition faults and k place faults.
Journal ArticleDOI
Polynomial extended Kalman filter
TL;DR: A polynomial version of the well-known extended Kalman filter (EKF) for the state estimation of nonlinear discrete-time stochastic systems is presented, showing significant improvements.
Journal ArticleDOI
Recursive parameter estimation and its convergence for bilinear systems
Xiao Zhang,Feng Ding,Feng Ding +2 more
TL;DR: In this paper, an adaptive filtering-based recursive identification algorithm for joint estimation of states and parameters of bilinear state-space systems with an autoregressive moving average noise was developed.
Journal ArticleDOI
Discretization of nonlinear control systems via the Carleman linearization
TL;DR: The proposed Carleman discretization does not deteriorate rapidly as the sampling period increases, and examples of open-loop and deadbeat closed-loop responses of an isothermal continuous stirred tank reactor reveal the advantages of the proposed discretized scheme.
References
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Journal ArticleDOI
Bilinear systems: An appealing class of "nearly linear" systems in theory and applications
C. Bruni,G. DiPillo,G. Koch +2 more
TL;DR: This work is intended to motivate the interest of bilinear systems and to present the current state of research in its various aspects.
Journal ArticleDOI
Natural Bilinear Control Processes
TL;DR: It is shown that these so-called bilinear systems have a variable dynamical structure that makes them quite controllable and may utilize appropriately controlled unstable modes of response to enhance controllability.
Journal ArticleDOI
Realization and Structure Theory of Bilinear Dynamical Systems
TL;DR: It is shown that the condition of realizability corresponds to that of the factorizability of the kernels of this expansion of the zero-state response and there exists a canonical form of the equations and the results of the realization theory are interpreted on this basis.
Book ChapterDOI
Lie Algebras and Lie Groups in Control Theory
TL;DR: The theory of differential equations and control have been linked very closely because most of the early applications of control theory were to engineering problems of the type which are most naturally described by ordinary differential equations as discussed by the authors.
Journal ArticleDOI
Paper: Observation of bilinear systems with application to biological control
TL;DR: A system of bilinear equations is derived which under appropriate conditions model the microbial cellgrowth and product formation of various waste treatment and fermentation systems and are significant for the on-line control of these biological processes.
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