| 1. |
- Axehill, Daniel, 1978-, et al.
(författare)
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Improved complexity analysis of branch and bound for hybrid MPC
- 2010
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Ingår i: Proceedings of the 49th IEEE Conference on Decision and Control (CDC). - 9781424477463 ; , s. 4216-4222
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Konferensbidrag (refereegranskat)abstract
- In this work, the computational effort of Mixed Integer Quadratic Programming solvers based on branch and bound is studied. The origin of this interest is that hybrid MPC problems for Mixed Logical Dynamical systems can be formulated as optimization problems in this form and since these have to be solved in real-time, it is interesting to be able to compute a good bound on the computational complexity. Classically, the bound on the worst case computational complexity is given by the case when it is necessary to expand all nodes in the entire tree. The usefulness of branch and bound relies on the fact that this worst case scenario is very rare in practice. The objective in this work is to reduce the gap between the conservative worst case bound on the number of nodes and the number of nodes actually necessary to explore on-line in the optimization routine. Approaches to compute this bound are presented and motivated theoretically and the performance of the analysis is evaluated in numerical examples.
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| 2. |
- Briat, Corentin, et al.
(författare)
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Nonlinear state-dependent delay modeling and stability analysis of internet congestion control
- 2010
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Ingår i: 49TH IEEE CONFERENCE ON DECISION AND CONTROL (CDC). - 9781424477463 ; , s. 1484-1491
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Konferensbidrag (refereegranskat)abstract
- It is shown that the queuing delay involved in the congestion control algorithm is state-dependent and does not depend on the current time. Then, using an accurate formulation for buffers, networks with arbitrary topologies can be built. At equilibrium, our model reduces to the widely used setup by Paganini et al. Using this model, the delay-derivative is analyzed and it is proved that the delay time-derivative does not exceed one for the considered topologies. It is then shown that the considered congestion control algorithm globally stabilizes a delay-free single buffer network. Finally, using a specific linearization result for systems with state-dependent delays from Cooke and Huang, we show the local stability of the single bottleneck network.
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| 3. |
- Fuchs, Alexander, et al.
(författare)
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On the choice of the linear decision functions for point location in polytopic data sets - Application to Explicit MPC
- 2010
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Ingår i: Proceedings of the 49th IEEE Conference on Decision and Control (CDC). - 9781424477463 ; , s. 5283-5288
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Konferensbidrag (refereegranskat)abstract
- This paper deals with efficient point location in large polytopic data sets, as required for the implementation of Explicit Model Predictive Control laws. The focus is on linear decision functions (LDF) which performs scalar product evaluations and an interval search to return the index set of candidate polytopes possibly containing the query point. We generalize a special LDF which uses the euclidean directions of the state space and the projection of the polytopes bounding boxes onto these directions to identify the candidate polytopes. Our generalized LDF may use any vector of the state space as direction and the projection of any points contained in the polytopes. We prove that there is a finite number of LDFs returning different index sets and show how to find the one returning the lowest worst-case number of candidate polytopes, a number that can be seen as a performance measure. Based on the results from an exhaustive study of low complexity problems, heuristics for the choice of the LDF are derived, involving the mean shift algorithm from pattern recognition. The result of extensive simulations on a larger problem attest the generalized LDF a 40% gain in performance, mainly through adjusted directions, at a small additional storage cost.
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| 4. |
- Larsson, Christian A., et al.
(författare)
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Identification of nonlinear systems using misspecified predictors
- 2010
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Ingår i: 49TH IEEE CONFERENCE ON DECISION AND CONTROL (CDC). - 9781424477463 ; , s. 7214-7219
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Konferensbidrag (refereegranskat)abstract
- Identification of nonlinear systems is an important albeit difficult task. This work considers parameter estimation, using the prediction error method, of the class of models that fit into a nonlinear state space formulation. Finding the optimal predictor for such nonlinear models, if at all possible, often requires significant effort. As an alternative, techniques from indirect inference are used to circumvent this problem. A misspecified predictor, parameterized by a new set of parameters, is used in lieu of the optimal predictor. These new parameters are found numerically by using simulations of the model to be identified. The proposed method is applied to simulation examples and real process data with encouraging results.
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| 5. |
- Larsson, Christian A., et al.
(författare)
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On optimal input design for nonlinear FIR-type systems
- 2010
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Ingår i: 49TH IEEE CONFERENCE ON DECISION AND CONTROL (CDC). - New York : IEEE. - 9781424477463 ; , s. 7220-7225
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Konferensbidrag (refereegranskat)abstract
- We consider optimal input design for system identification of nonlinear FIR-type systems in the prediction error (PEM) framework. The input sequences are designed in terms of their statistical properties and not directly in time domain. The starting point is the asymptotic properties of PEM estimates. The fact that the inverse covariance matrix of the estimated parameters is linear in the input probability density function is exploited to formulate convex optimization problems. The main issues considered are the parameterization of the input pdf, reduction of the number of free variables in the optimization and to some extent signal generation. Two special model classes where tractable problems are obtainable are studied in detail. Convex formulations of the input design problem are presented for the static nonlinear and nonlinear FIR cases. Numerical examples of the discussed ideas are also presented.
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| 6. |
- Möller, Anders, et al.
(författare)
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Input-Output Analysis of Power Controlin Wireless Networks
- 2010
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Ingår i: Proceedings of the IEEE Conference on Decision and Control. - 9781424477463 ; , s. 6451-6456
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Konferensbidrag (refereegranskat)abstract
- In a wireless communication network different users share a common resource. An objective of radio resource management is to assign the resources in an effective way between the users. Power control is an important component in this setting that has been extensively studied over the last two decades. In many real networks there are inherent time delays due to filtering of signals and control signaling. Time delays can affect stability and convergence properties of the power control algorithms. We therefore consider power control laws of higher order to include models with delays and delay compensation. The main contribution of this paper is to prove less conservative conditions for system stability. Our primary tool to reduce conservativeness is to use scalings in an input-output framework for stability analysis.
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| 7. |
- Sturk, Christopher, et al.
(författare)
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Tuning a synthetic in vitro oscillator using control-theoretic tools
- 2010
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Ingår i: Proceedings of the IEEE Conference on Decision and Control. - NEW YORK : IEEE. - 9781424477463 ; , s. 2554-2559
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- This paper demonstrates the effectiveness of simple control-theoretic tools in generating simulation-guided experiments on a synthetic in vitro oscillator. A theoretical analysis of the behavior of such system is motivated by high cost, time consuming experiments, together with the excessive number of tuning parameters. A simplified model of the synthetic oscillator is chosen to capture only its essential features. The model is analyzed using the small gain theorem and the theory of describing functions. Such analysis reveals what are the parameters that primarily determine when the system can admit stable oscillations. Experimental verification of the theoretical and numerical findings is carried out and confirms the predicted results regarding the role of production and degradation rates.
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| 8. |
- Wahlberg, Bo, 1959-, et al.
(författare)
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On optimal input design in system identification for control
- 2010
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Ingår i: 49TH IEEE CONFERENCE ON DECISION AND CONTROL (CDC). - : IEEE. - 9781424477463 ; , s. 5548-5553
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Konferensbidrag (refereegranskat)abstract
- This paper considers a recently proposed framework for experiment design in system identification for control. We study model based control design methods, such as Model Predictive Control, where the model is obtained by means of a prediction error system identification method. The degradation in control performance due to uncertainty in the model estimate is specified by an application cost function. The objective is to find a minimum variance input signal, to be used in system identification experiment, such that the control application specification is guaranteed with a given probability when using the estimated model in the control design. We provide insight in the potentials of this approach by finite impulse response model examples, for which it is possible to analytically solve the optimal input problem. The examples show how the control specifications directly affect the excitation conditions in the system identification experiment.
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| 9. |
- Wahlberg, Bo, 1959-, et al.
(författare)
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On optimal input signal design for frequency response estimation
- 2010
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Ingår i: 49TH IEEE CONFERENCE ON DECISION AND CONTROL (CDC). - : IEEE. - 9781424477463 ; , s. 302-307
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Konferensbidrag (refereegranskat)abstract
- This paper studies optimal input excitation design for parametric frequency response estimation. The objective is to minimize the uncertainty of functions of the frequency response estimate at a specified frequency ω while limiting the power of the input signal. We focus on least-squares estimation of Finite Impulse Response (FIR) models and minimum variance input design. The optimal input problem is formulated as a convex optimization problem (semi-definite program) in the second order statistics of the input signal. We analytically characterize the optimal solution for first order FIR systems with two parameters, and perform a numerical study to obtain insights in the optimal solution for higher order models. The optimal solution is compared to the case when a sinusoidal input signal, with frequency ω and amplitude that gives the same accuracy as the optimal input, is used as excitation signal. For first order FIR models with two parameters the input signal power can be reduced at best by a factor of two by using the optimal input signal compared with such a sinusoidal input signal. Numerical studies show that less is in general gained for higher order systems, for which a sinusoidal input signal with frequency ω often is optimal. We consider estimation of the ℋ ∞-norm of a stable linear system, that is the maximum of the absolute value of the corresponding frequency response. An asymptotic error variance expression for ℋ∞-norm estimates is derived.
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