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387
A Survey of Computational Complexity Results in Systems and Control
, 2000
"... The purpose of this paper is twofold: (a) to provide a tutorial introduction to some key concepts from the theory of computational complexity, highlighting their relevance to systems and control theory, and (b) to survey the relatively recent research activity lying at the interface between these fi ..."
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Cited by 133 (20 self)
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The purpose of this paper is twofold: (a) to provide a tutorial introduction to some key concepts from the theory of computational complexity, highlighting their relevance to systems and control theory, and (b) to survey the relatively recent research activity lying at the interface between these fields. We begin with a brief introduction to models of computation, the concepts of undecidability, polynomial time algorithms, NPcompleteness, and the implications of intractability results. We then survey a number of problems that arise in systems and control theory, some of them classical, some of them related to current research. We discuss them from the point of view of computational complexity and also point out many open problems. In particular, we consider problems related to stability or stabilizability of linear systems with parametric uncertainty, robust control, timevarying linear systems, nonlinear and hybrid systems, and stochastic optimal control.
Transfer functions of regular linear systems Part III: Inversions And Duality
 Trans. Amer. Math. Soc
, 2000
"... We study four transformations which lead from one wellposed linear system to another: timeinversion, flowinversion, timeflowinversion and duality. Timeinversion means reversing the direction of time, flowinversion means interchanging inputs with outputs, while timeflowinversion means doing ..."
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Cited by 95 (16 self)
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We study four transformations which lead from one wellposed linear system to another: timeinversion, flowinversion, timeflowinversion and duality. Timeinversion means reversing the direction of time, flowinversion means interchanging inputs with outputs, while timeflowinversion means doing both of the inversions mentioned before. A wellposed linear system is timeinvertible if and only if its operator semigroup extends to a group. The system is flowinvertible if and only if its inputoutput map has a bounded inverse on some (hence, on every) finite time interval [0; ] ( > 0). This is true if and only if the transfer function of has a uniformly bounded inverse on some right halfplane. The system is timeflowinvertible if and only if on some (hence, on every) finite time interval [0; ], the combined operator from the initial state and the input function to the final state and the output function is invertible. This is the case, for example, if the system is conservative, since then is unitary. Timeowinversion can sometimes, but not always, be reduced to a combination of time and flowinversion. We derive a surprising necessary and sucient condition for to be timeflowinvertible: its system operator must have a uniformly bounded inverse on some left halfplane.
Pn learning: Bootstrapping binary classifiers by structural constraints
 In IEEE Conference on Computer Vision and Pattern Recognition
, 2010
"... This paper shows that the performance of a binary classifier can be significantly improved by the processing of structured unlabeled data, i.e. data are structured if knowing the label of one example restricts the labeling of the others. We propose a novel paradigm for training a binary classifier f ..."
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Cited by 60 (4 self)
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This paper shows that the performance of a binary classifier can be significantly improved by the processing of structured unlabeled data, i.e. data are structured if knowing the label of one example restricts the labeling of the others. We propose a novel paradigm for training a binary classifier from labeled and unlabeled examples that we call PN learning. The learning process is guided by positive (P) and negative (N) constraints which restrict the labeling of the unlabeled set. PN learning evaluates the classifier on the unlabeled data, identifies examples that have been classified in contradiction with structural constraints and augments the training set with the corrected samples in an iterative process. We propose a theory that formulates the conditions under which PN learning guarantees improvement of the initial classifier and validate it on synthetic and real data. PN learning is applied to the problem of online learning of object detector during tracking. We show that an accurate object detector can be learned from a single example and an unlabeled video sequence where the object may occur. The algorithm is compared with related approaches and stateoftheart is achieved on a variety of objects (faces, pedestrians, cars, motorbikes and animals). 1.
Minimax differential dynamic programming: An application to robust bipedwalking
 in Advances in Neural Information Processing Systems 14
, 2002
"... We have developed a robust control policy design method for highdimensional state spaces by using differential dynamic programming with a minimax criterion. As an example, we applied our method to a simulated five link biped robot. The results show lower joint torques using the optimal control poli ..."
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Cited by 56 (11 self)
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We have developed a robust control policy design method for highdimensional state spaces by using differential dynamic programming with a minimax criterion. As an example, we applied our method to a simulated five link biped robot. The results show lower joint torques using the optimal control policy compared to torques generated by a handtuned PD servo controller. Results also show that the simulated biped robot can successfully walk with unknown disturbances that cause controllers generated by standard differential dynamic programming and the handtuned PD servo to fail. Learning to compensate for modeling error and previously unknown disturbances in conjunction with robust control design is also demonstrated. We also applied proposed method to a real biped robot for optimizing swing leg trajectories. 1
Multirate Simulation for High Fidelity Haptic Interaction with Deformable Objects in Virtual Environments
, 2000
"... Haptic interaction is an increasingly common form of interaction in virtual environment (VE) simulations. This medium introduces some new challenges. In this paper we study the problem arising from the difference between the sampling rate requirements of haptic interfaces and the significantly lower ..."
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Cited by 39 (5 self)
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Haptic interaction is an increasingly common form of interaction in virtual environment (VE) simulations. This medium introduces some new challenges. In this paper we study the problem arising from the difference between the sampling rate requirements of haptic interfaces and the significantly lower update rates of the physical models being manipulated. We propose a multirate simulation approach which uses a local linear approximation. The treatment includes a detailed analysis and experimental verification of the approach. The proposed method is also shown to improve the stability of the haptic interaction.
Nonparametric Representation of Policies and Value Functions: A TrajectoryBased Approach
 In NIPS 15
, 2003
"... A longstanding goal of reinforcement learning is to develop nonparametric representations of policies and value functions that support rapid learning without suffering from interference or the curse of dimensionality. ..."
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Cited by 31 (6 self)
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A longstanding goal of reinforcement learning is to develop nonparametric representations of policies and value functions that support rapid learning without suffering from interference or the curse of dimensionality.
Positive Polynomials and Robust Stabilization with FixedOrder Controllers
 IEEE Transactions on Automatic Control
, 2002
"... Recent results on positive polynomials are used to obtain a convex inner approximation of the stability domain in the space of coe#cients of a polynomial. An application to the design of fixedorder controllers robustly stabilizing a linear system subject to polytopic uncertainty is then proposed ..."
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Cited by 28 (14 self)
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Recent results on positive polynomials are used to obtain a convex inner approximation of the stability domain in the space of coe#cients of a polynomial. An application to the design of fixedorder controllers robustly stabilizing a linear system subject to polytopic uncertainty is then proposed, based on LMI optimization.
Iterative Learning Control  Analysis, Design, and Experiments
, 2000
"... In many industrial robot applications it is a fact that the robot is programmed to do the same task repeatedly. By observing the control error in the di#erent iterations of the same task it becomes clear that it is actually highly repetitive. Iterative Learning Control (ILC) allows to iteratively co ..."
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Cited by 25 (4 self)
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In many industrial robot applications it is a fact that the robot is programmed to do the same task repeatedly. By observing the control error in the di#erent iterations of the same task it becomes clear that it is actually highly repetitive. Iterative Learning Control (ILC) allows to iteratively compensate for and, hence, remove this repetitive error. In the thesis
Robust control/scheduling codesign: application to robot control
 in "RTAS’05 IEEE RealTime and Embedded Technology and Applications Symposium
, 2005
"... Control systems running on a computer are subject to timing disturbances coming from implementation constraints. Fortunately closedloop systems behave robustly w.r.t. modelling errors and disturbances, and the controller design can be performed to explicitly enhance robustness against specific unce ..."
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Cited by 23 (10 self)
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Control systems running on a computer are subject to timing disturbances coming from implementation constraints. Fortunately closedloop systems behave robustly w.r.t. modelling errors and disturbances, and the controller design can be performed to explicitly enhance robustness against specific uncertainties. On one hand robustness in process controllers can be used to comply with weakly modelled timing uncertainties. On the other hand the principle of robust closedloop control can also be applied to the realtime scheduler to provide online adaption of some scheduling parameters, with the objective of controlling the computing resource allocation. The control performance specification may be set according to both control and implementation constraints. The approach is illustrated through several examples using simulation and an experimental feedback scheduler is briefly described.