| 1. |
- Byrnes, Christopher I., et al.
(author)
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Interior point solutions of variational problems and global inverse function theorems
- 2007
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In: International Journal of Robust and Nonlinear Control. - : Wiley. - 1049-8923 .- 1099-1239. ; 17:5-6, s. 463-481
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Journal article (peer-reviewed)abstract
- Variational problems and the solvability of certain nonlinear equations have a long and rich history beginning with calculus and extending through the calculus of variations. In this paper, we are interested in 'well-connected' pairs of such problems which are not necessarily related by critical point considerations. We also study constrained problems of the kind which arise in mathematical programming. We are also interested in interior minimizing points for the variational problem and in the well-posedness (in the sense of Hadamard) of solvability of the related systems of equations. We first prove a general result which implies the existence of interior points and which also leads to the development of certain generalization of the Hadamard-type global inverse function theorem, along the theme that uniqueness quite often implies existence. This result is illustrated by proving the non-existence of shock waves for certain initial data for the vector Burgers' equation. The global inverse function theorem is also illustrated by a derivation of the existence of positive definite solutions of matrix Riccati equations without first analysing the nonlinear matrix Riccati differential equation. The main results on the existence of solutions to geometrically constrained well-connected pairs are then presented and illustrated by a geometric analysis of the existence of interior points for linear programming problems.
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| 2. |
- Dankowicz, Harry, et al.
(author)
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On the stabilizability of near-grazing dynamics in impact oscillators
- 2007
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In: International Journal of Robust and Nonlinear Control. - : Wiley. - 1049-8923 .- 1099-1239. ; 17:15, s. 1405-1429
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Journal article (peer-reviewed)abstract
- A constructive proof is presented for the existence of event-driven control strategies that guarantee the local persistence of system attractors with at most low-velocity contact in vibro-impacting oscillators. In particular, sufficient conditions are formulated on the linearization of the control strategies along a grazing periodic trajectory, i.e. an oscillating motion that achieves zero-relative-velocity contact with a mechanical obstacle, to ensure the asymptotic stability of the grazing trajectory and, consequently, sustained dynamics in the vicinity of the grazing trajectory even under small changes in system parameters. The implications of the methodology are illustrated with linear and nonlinear, single- and multiple-degree-of-freedom examples of vibro-impact oscillators.
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| 3. |
- Falcone, Paolo, 1977, et al.
(author)
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Linear Time Varying Model Predictive Control and its Application to Active Steering Systems: Stability Analysis and Experimental Validation
- 2008
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In: International Journal of Robust and Nonlinear Control. - : Wiley. - 1099-1239 .- 1049-8923. ; 18:8, s. 862-875
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Journal article (peer-reviewed)abstract
- A Model Predictive Control (MPC) approach for controlling an Active Front Steering (AFS) system in an autonomous vehicle is presented. At each time step a trajectory is assumed to be known over a finite horizon, and an MPC controller computes the front steering angle in order to best follow the desired trajectory on slippery roads at the highest possible entry speed. We start from the results presented in [2], [6] and formulate the MPC problem based on successive on-line linearization of the nonlinear vehicle model (LTV MPC). We present a sufficient stability conditions for such LTV MPC scheme. The condition is derived for a general class of nonlinear discrete time systems and results into an additional convex constraint to be included in the LTV MPC design. For the AFS control problem, we compare the proposed LTV MPC scheme against the LTV MPC scheme in [6] where stability has been enforced with an ad-hoc constraint. Simulation and experimental tests up to 21 m/s on icy roads show the effectiveness of the LTV MPC formulation.
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| 4. |
- Johansson, Rolf, et al.
(author)
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The Yakubovich-Kalman-Popov Lemma and Stability Analysis of Dynamic Output Feedback Systems
- 2006
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In: International Journal of Robust and Nonlinear Control. - : Wiley. - 1099-1239 .- 1049-8923. ; 16:2, s. 45-69
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Journal article (peer-reviewed)abstract
- This paper presents theory related to stability analysis and stability criteria relevant for observer-based feedback control systems. To this purpose, a special formulation of the Yakubovich-Kalman-Popov (YKP) lemma is provided. We exploit that controllability is not necessary for existence of Lur'e-Lyaptinov functions as used in stability criteria. Constructive means for dynamic output feedback stabilization, positivity, factorization and passivity are provided. Copyright (c) 2005 John Wiley & Sons, Ltd.
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| 5. |
- Jönsson, Ulf T.
(author)
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Robustness of transitions in switched linear systems
- 2005
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In: International Journal of Robust and Nonlinear Control. - : Wiley. - 1049-8923 .- 1099-1239. ; 15:7, s. 293-314
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Journal article (peer-reviewed)abstract
- A robustness problem for transitions in switched linear systems is considered in this paper. The specific problem is to estimate the size of the image when a subset of an affine subspace is mapped by an uncertain system to another affine subspace. It is assumed that the system dynamics is linear and that the uncertainty and the disturbances are characterized by integral quadratic constraints (IQC). The estimates can be obtained by solving a special affinely parameterized linear quadratic optimal control problem. The results are applied to the problem of verifying robustness of oscillations in a switched linear system. In particular, sufficient conditions are given, which ensure that there remains a periodic solution when the system is perturbed by a Lipschitz continuous nonlinearity.
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| 6. |
- Ng, Kok Yew, et al.
(author)
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New results in robust actuator fault reconstruction for linear uncertain systems using sliding mode observers
- 2007
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In: International Journal of Robust and Nonlinear Control. - : Wiley Online Library. - 1049-8923 .- 1099-1239. ; 17:14, s. 1294-1319
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Journal article (peer-reviewed)abstract
- This paper presents a robust actuator fault reconstruction scheme for linear uncertain systems using sliding mode observers. In existing work, fault reconstruction via sliding mode observers is limited to either linear certain systems subject to unknown inputs, relative degree one systems or a specific class of relative degree two systems. This paper presents a new method that is applicable to a wider class of systems with relative degree higher than one, and can also be used for systems with more unknown inputs than outputs. The method uses two sliding mode observers in cascade. Signals from the first observer are processed and used to drive the second observer. Overall, this results in actuator fault reconstruction being feasible for a wider class of systems than using existing methods. A simulation example verifies the claims made in this paper.
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| 7. |
- Sandberg, Henrik, et al.
(author)
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Model approximation using magnitude and phase criteria : Implications for model reduction and system identification
- 2007
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In: International Journal of Robust and Nonlinear Control. - : Wiley. - 1049-8923 .- 1099-1239. ; 17:05-6, s. 435-461
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Journal article (peer-reviewed)abstract
- In this paper, we use convex optimization for model reduction and identification of transfer functions. Two different approximation criteria are studied. When the first criterion is used, magnitude functions are matched, and when the second criterion is used, phase functions are matched. The weighted error bounds have direct interpretation in a Bode diagram, and are suitable to engineers working with frequency-domain data. We also show that transfer functions that have similar magnitude or phase functions have a small relative H-infinity error, under certain stability and minimum phase assumptions. The error bounds come from bounds associated with the Hilbert transform operator restricted in its application to rational transfer functions. Furthermore, it is shown how the approximation procedures can be implemented with linear matrix inequalities, and four examples are included to illustrate the results.
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