Every linear system can be naturally identified with a rational curve in a Grassmann variety. The associated curve is often referred to as Hermann-Martin curve of the system. This article explains this crucial link be...
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ISBN:
(纸本)3540239537
Every linear system can be naturally identified with a rational curve in a Grassmann variety. The associated curve is often referred to as Hermann-Martin curve of the system. This article explains this crucial link between systems theory and geometry. The geometric translation also provides important tools when studying control design problems. In a second part of the article it is shown how it is possible to tackle some important control design problems by geometric means.
In this paper we study the attitude estimation problem for an accelerated rigid body using gyros and accelerometers. The application in mind is that of a walking robot and particular attention is paid to the large and...
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ISBN:
(纸本)3540239537
In this paper we study the attitude estimation problem for an accelerated rigid body using gyros and accelerometers. The application in mind is that of a walking robot and particular attention is paid to the large and abrupt changes in accelerations that can be expected in such an environment. We propose a state estimation algorithm that fuses data from rate gyros and accelerometers to give long-term drift free attitude estimates. The algorithm does not use any local parameterization of the rigid body kinematics and can thus be used for a rigid body performing any kind of rotations. The algorithm is a combination of two non-standard, but in a sense linear, Kalman filters between which a trigger based switching takes place. The kinematics representation used makes it possible to construct a linear algorithm that can be shown to give convergent estimates for this nonlinear problem. The state estimator is evaluated in simulations demonstrating how the estimates are long term stable even in the presence of gyrodrift.
A coordinate-free approach to the tracking problem for simple mechanical systems on Lie groups highlights the exploitation of geometrical and topological structure in controller design. First, the algebraic structure ...
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ISBN:
(纸本)3540239537
A coordinate-free approach to the tracking problem for simple mechanical systems on Lie groups highlights the exploitation of geometrical and topological structure in controller design. First, the algebraic structure of the Lie group is used to construct an intrinsic and coordinate-free notion of configuration error. This construction leads through geometric ideas to a state feedback "inner" controller that gives the error dynamics the structure of a simple mechanical system on the original Lie group. This structure in turn allows the stability properties of the identity element of the error system to be characterized in terms of a potential energy-like error function, through implicit definition of a locally exponentially stabilizing state feedback "outer" controller. Stabilization of the identity element of the error system is equivalent to the original system tracking a smooth and bounded, but otherwise arbitrary, reference trajectory. Finally, suitable choices for the error function may be identified based on purely topological considerations. This means that a class of error functions may be defined for any simple mechanical system on the configuration space, greatly simplifying the design task. As an example of the power of this result, it is known that error functions corresponding to almost-global tracking may be found on any compact connected Lie group, and such functions have been explicitly constructed for many important special cases. The intrinsic, coordinate-free, structure-based approach is used to show a separation principle for this tracking problem, namely that the system velocities in the tracking controller may be replaced by their estimates, obtained from any locally exponentially convergent observer, without affecting the convergence properties of the closed-loop system.
This paper is concerned with problems of set point regulation of a boundary controlled viscous Burgers' equation. The methodology for obtaining the desired controls for solving these problems is based on the recen...
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ISBN:
(纸本)3540239537
This paper is concerned with problems of set point regulation of a boundary controlled viscous Burgers' equation. The methodology for obtaining the desired controls for solving these problems is based on the recent nonequilibrium theorem which has been applied successfully for finite dimensional nonlinear systems. In particular a dynamic control law is obtained, in each case, from outputs of the associated augmented zero dynamics. Our proofs rely on the authors earlier work in which there is established a generalized root locus methodology via convergence of trajectories for the boundary controlled viscous Burgers' equation.
This paper presents a nonsmooth output feedback framework for local and/or global stabilization of a class of inherently nonlinear systems, which may not be achieved by any smooth feedback controller. A systematic des...
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ISBN:
(纸本)3540239537
This paper presents a nonsmooth output feedback framework for local and/or global stabilization of a class of inherently nonlinear systems, which may not be achieved by any smooth feedback controller. A systematic design algorithm is presented for the construction of stabilizing, dynamic output compensators that are nonsmooth but Holder continuous. A new ingredient of the proposed output feedback control scheme is the introduction of a recursive observer design procedure, making it possible to construct a reduced-order observer step-by-step, in a naturally augmented fashion. Such nonsmooth design leads to a number of new results on output feedback stabilization of nonlinear systems with unstabilizable/undetectable linearization. One of them is the global stabilizability of a chain of odd power integrators by Holder continuous output feedback. The other one is the local stabilization using nonsmooth output feedback for a class of nonlinear systems studied in [14], where global stabilizability by nonsmooth state feedback was proved to be possible.
James Hampton was a quiet and secretive man who left behind a monumental work of visionary art, along with a strange handwritten script. Hampton's script, or Hamptonese, bears no significant resemblance to any kno...
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ISBN:
(纸本)3540239537
James Hampton was a quiet and secretive man who left behind a monumental work of visionary art, along with a strange handwritten script. Hampton's script, or Hamptonese, bears no significant resemblance to any known written language. In this paper we analyze Hamptonese using hidden Markov models. This analysis shows that Hamptonese is not a simple substitution for English and provides some evidence that Hamptonese may be the written equivalent of "speaking in tongues".
The focus of this work is on certain geometric aspects of the classification problems for invariant and conditioned invariant subspaces. In this paper, we make an attempt to illustrate the interplay between geometry a...
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ISBN:
(纸本)3540239537
The focus of this work is on certain geometric aspects of the classification problems for invariant and conditioned invariant subspaces. In this paper, we make an attempt to illustrate the interplay between geometry and control, by focussing on the connections between partial state observers, spaces of invariant and conditioned invariant subspaces, and nilpotent matrices.
Firstly this paper summarizes some of the the relations between control theory and coalgebra and Hopf algebra theory, particularly the fact that the cofree coalgebra over a finite rank free module consists precisely o...
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ISBN:
(纸本)3540239537
Firstly this paper summarizes some of the the relations between control theory and coalgebra and Hopf algebra theory, particularly the fact that the cofree coalgebra over a finite rank free module consists precisely of the realizable power series in noncommuting variables. The second half of the paper concerns generalizations of the Hopf algebra of permutations which in turn generalizes the Hopf algebras of noncommutative symmetric functions and the Hopf algebra of quasisymmetric functions.
In this paper we introduce the semi-tensor product of matrices, which is a generalization of conventional matrix product. Three of its applications will be discussed: Numerical solution to Morgan's problem, Estima...
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ISBN:
(纸本)3540239537
In this paper we introduce the semi-tensor product of matrices, which is a generalization of conventional matrix product. Three of its applications will be discussed: Numerical solution to Morgan's problem, Estimation of region of attraction of a stable equilibrium, and Non-regular linearization.
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