Minimality of dynamic input-output decoupling for nonlinear systems

In this note we study the strong dynamic input-output decoupling problem for nonlinear systems. Using an algebraic theory for nonlinear control systems, we obtain for a dynamic input-output decouplable nonlinear system a compensator of minimal dimension that solves the decoupling problem

Quantum Internal Model Principle: Decoherence Control

In this article, we study the problem of designing a Decoherence Control for quantum systems with the help of a scalable ancillary quantum control and techniques from geometric control theory, in order to successfully and completely decouple an open quantum system from its environment. We re-formulate the problem of decoherence control as a disturbance rejection scheme which also leads us to the idea of Internal Model Principle for quantum control systems which is first of its kind in the literature. It is shown that decoupling a quantum disturbance from an open quantum system, is possible only with the help of a quantum controller which takes into account the model of the environmental interaction. This is demonstrated for a simple 2-qubit system wherein the effects of decoherence are completely eliminated. The theory provides conditions to be imposed on the controller to ensure perfect decoupling. Hence the problem of decoherence control naturally gives rise to the quantum internal model principle which relates the disturbance rejecting control to the model of the environmental interaction. Classical internal model principle and disturbance decoupling focus on different aspects viz. perfect output tracking and complete decoupling of output from external disturbances respectively. However for quantum systems, the two problems come together and merge in order to produce an effective platform for decoherence control. In this article we introduce a seminal connection between disturbance decoupling and the corresponding analog for internal model principle for quantum systems.Comment: Submitted to IEEE Transactions on Automatic Control, Mar 15 2010. A basic introduction appeared in 46th IEEE CDC 2007. Acknowledgements: The authors would like to thank the Center for Quantum Information Science and Technology at Tsinghua University, R.-B. Wu, J. Zhang, J.-W. Wu, M. Jiang, C.-W. Li and G.-L. Long for their valuable comments and suggestion

Robust H2/H∞-state estimation for discrete-time systems with error variance constraints

Copyright [1997] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This paper studies the problem of an H∞-norm and variance-constrained state estimator design for uncertain linear discrete-time systems. The system under consideration is subjected to time-invariant norm-bounded parameter uncertainties in both the state and measurement matrices. The problem addressed is the design of a gain-scheduled linear state estimator such that, for all admissible measurable uncertainties, the variance of the estimation error of each state is not more than the individual prespecified value, and the transfer function from disturbances to error state outputs satisfies the prespecified H∞-norm upper bound constraint, simultaneously. The conditions for the existence of desired estimators are obtained in terms of matrix inequalities, and the explicit expression of these estimators is also derived. A numerical example is provided to demonstrate various aspects of theoretical results

A Tractable Fault Detection and Isolation Approach for Nonlinear Systems with Probabilistic Performance

This article presents a novel perspective along with a scalable methodology to design a fault detection and isolation (FDI) filter for high dimensional nonlinear systems. Previous approaches on FDI problems are either confined to linear systems or they are only applicable to low dimensional dynamics with specific structures. In contrast, shifting attention from the system dynamics to the disturbance inputs, we propose a relaxed design perspective to train a linear residual generator given some statistical information about the disturbance patterns. That is, we propose an optimization-based approach to robustify the filter with respect to finitely many signatures of the nonlinearity. We then invoke recent results in randomized optimization to provide theoretical guarantees for the performance of the proposed filer. Finally, motivated by a cyber-physical attack emanating from the vulnerabilities introduced by the interaction between IT infrastructure and power system, we deploy the developed theoretical results to detect such an intrusion before the functionality of the power system is disrupted

Decoherence Control in Open Quantum System via Classical Feedback

In this work we propose a novel strategy using techniques from systems theory to completely eliminate decoherence and also provide conditions under which it can be done so. A novel construction employing an auxiliary system, the bait, which is instrumental to decoupling the system from the environment is presented. Our approach to decoherence control in contrast to other approaches in the literature involves the bilinear input affine model of quantum control system which lends itself to various techniques from classical control theory, but with non-trivial modifications to the quantum regime. The elegance of this approach yields interesting results on open loop decouplability and Decoherence Free Subspaces(DFS). Additionally, the feedback control of decoherence may be related to disturbance decoupling for classical input affine systems, which entails careful application of the methods by avoiding all the quantum mechanical pitfalls. In the process of calculating a suitable feedback the system has to be restructured due to its tensorial nature of interaction with the environment, which is unique to quantum systems. The results are qualitatively different and superior to the ones obtained via master equations. Finally, a methodology to synthesize feedback parameters itself is given, that technology permitting, could be implemented for practical 2-qubit systems to perform decoherence free Quantum Computing.Comment: 17 pages, 4 Fig

Active actuator fault-tolerant control of a wind turbine benchmark model

This paper describes the design of an active fault-tolerant control scheme that is applied to the actuator of a wind turbine benchmark. The methodology is based on adaptive filters obtained via the nonlinear geometric approach, which allows to obtain interesting decoupling property with respect to uncertainty affecting the wind turbine system. The controller accommodation scheme exploits the on-line estimate of the actuator fault signal generated by the adaptive filters. The nonlinearity of the wind turbine model is described by the mapping to the power conversion ratio from tip-speed ratio and blade pitch angles. This mapping represents the aerodynamic uncertainty, and usually is not known in analytical form, but in general represented by approximated two-dimensional maps (i.e. look-up tables). Therefore, this paper suggests a scheme to estimate this power conversion ratio in an analytical form by means of a two-dimensional polynomial, which is subsequently used for designing the active fault-tolerant control scheme. The wind turbine power generating unit of a grid is considered as a benchmark to show the design procedure, including the aspects of the nonlinear disturbance decoupling method, as well as the viability of the proposed approach. Extensive simulations of the benchmark process are practical tools for assessing experimentally the features of the developed actuator fault-tolerant control scheme, in the presence of modelling and measurement errors. Comparisons with different fault-tolerant schemes serve to highlight the advantages and drawbacks of the proposed methodology

Nonlinear stability analysis of plane Poiseuille flow by normal forms

In the subcritical interval of the Reynolds number 4320\leq R\leq R_c\equiv 5772, the Navier--Stokes equations of the two--dimensional plane Poiseuille flow are approximated by a 22--dimensional Galerkin representation formed from eigenfunctions of the Orr--Sommerfeld equation. The resulting dynamical system is brought into a generalized normal form which is characterized by a disposable parameter controlling the magnitude of denominators of the normal form transformation. As rigorously proved, the generalized normal form decouples into a low--dimensional dominant and a slaved subsystem. {}From the dominant system the critical amplitude is calculated as a function of the Reynolds number. As compared with the Landau method, which works down to R=5300, the phase velocity of the critical mode agrees within 1 per cent; the critical amplitude is reproduced similarly well except close to the critical point, where the maximal error is about 16 per cent. We also examine boundary conditions which partly differ from the usual ones.Comment: latex file; 4 Figures will be sent, on request, by airmail or by fax (e-mail address: rauh at beta.physik.uni-oldenburg.de