Model error bounds for identification of stochastic models for control design
First Claim
1. A computer-implemented method for computing model error bounds of stochastic models for control design, said method comprising:
- computing a high order model estimate, wherein said model represents an auto-regressive with exogenous inputs model; and
computing an estimate of the model error bounds, wherein said estimated model error bounds are represented by a singular value, and wherein said computing an estimate of said model error bounds comprises computing the largest singular value of said model error bounds.
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Abstract
A method for computing model error bounds for system identification of stochastic systems is disclosed. The model error bounds take the form of additive frequency-weighted singular value bounds such that they are directly used in H∞ and μ-synthesis robust control design methods. The largest singular value of the additive uncertainty bound is determined by performing a high number of simulations for the model uncertainty. Simulated values of the uncertainty are computed for a large data population, such that each candidate entry of simulated value lies on the 3-sigma ellipsoids defined by the covariance functions. For each simulated value of uncertainty, the maximum singular values are then determined. In order to determine the scalar uncertainty function needed for robust control design, the maximum over the population of the maximum singular values of uncertainty simulated values is then computed.
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Citations
41 Claims
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1. A computer-implemented method for computing model error bounds of stochastic models for control design, said method comprising:
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computing a high order model estimate, wherein said model represents an auto-regressive with exogenous inputs model; and
computing an estimate of the model error bounds, wherein said estimated model error bounds are represented by a singular value, and wherein said computing an estimate of said model error bounds comprises computing the largest singular value of said model error bounds. - View Dependent Claims (2)
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3. A computer-implemented method for computing singular values of model error bounds for a stochastic control system, said method comprising:
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computing a plurality of simulated values of said model error for a data population;
determining a plurality of maximum singular values of said plurality of simulated values of said model error; and
determining a scalar uncertainty function such that said model error is bounded by said scalar uncertainty function, wherein said determining a scalar uncertainty function comprises computing, for said data population, a maximum value of said plurality of maximum singular values. - View Dependent Claims (4, 5, 6, 7, 8)
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9. A method for computing model error bounds of stochastic models for control design, said method comprising:
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computing a high order model estimate, wherein said model represents an auto-regressive with exogenous inputs model; and
computing an estimate of said model error bounds, wherein said estimated model error bounds are represented by a singular value, and wherein said computing an estimate of said model error bounds comprises;
computing a plurality of simulated values of said model error for a data population;
determining a plurality of maximum singular values of said plurality of simulated values of said model error; and
determining a scalar uncertainty function such that said model error is bounded by said scalar uncertainty function, wherein said determining a scalar uncertainty function comprises computing, for said data population, a maximum value of said plurality of maximum singular values. - View Dependent Claims (10, 11, 12, 13, 14)
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15. A computer readable medium having stored thereon instructions for computing model error bounds of stochastic models for control design, wherein said instructions, when executed, cause the computer to:
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compute a high order model estimate, wherein the model represents an auto-regressive with exogenous inputs model;
compute an estimate of the model error bounds, wherein the estimated model error bounds are represented by a singular value, and wherein said compute an estimate of the model error bounds comprises;
computing a plurality of simulated values of said model error for a data population;
determining a plurality of maximum singular values of said plurality of simulated values of said model error; and
determining a scalar uncertainty function such that said model error is bounded by said scalar uncertainty function, wherein said determining a scalar uncertainty function comprises computing, for said data population, a maximum value of said plurality of maximum singular values. - View Dependent Claims (16, 17, 18, 19, 20)
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21. A computer-implemented method for computing model error bounds of a stochastic model for control design, said method comprising:
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determining a closed-loop representation of said stochastic model;
performing a closed-loop simulation of said stochastic model to generate input and output data for said stochastic model; and
computing an estimate of the model error bounds, wherein said estimated model error bounds are represented by a singular value. - View Dependent Claims (22, 23, 26)
computing a high order model estimate using said input and output data, wherein said model represents an auto-regressive with exogenous inputs model, and wherein said computing an estimate of said model error bounds comprises computing the largest singular value of said model error bounds.
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23. The method of claim 22, wherein said the estimated model error bounds are represented by an additive, frequency-weighted singular value.
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26. The method of claim 21, wherein said computing an estimate of the model error bounds comprises:
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computing a plurality of simulated values of said model error for said input and output data;
determining a plurality of maximum singular values of said plurality of simulated values of said model error; and
determining a scalar uncertainty function such that said model error is bounded by said scalar uncertainty function, wherein said determining a scalar uncertainty function comprises computing, for said data population, a maximum value of said plurality of maximum singular values.
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- 24. The method of 23 further comprises refining an identification trajectory corresponding to said stochastic model using said estimated model error bounds.
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27. A computer-implemented method for computing model error bounds of a stochastic model for control design, said method comprising:
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determining a closed-loop representation of said stochastic model;
performing an identification trajectory refinement corresponding to said stochastic model;
performing a closed-loop simulation of said stochastic model using said refined identification trajectory to generate input and output data for said stochastic model; and
computing an estimate of the model error bounds, wherein said estimated model error bounds are represented by a singular value. - View Dependent Claims (28, 29, 30, 31)
computing a high order model estimate using said input and output data, wherein said model represents an auto-regressive with exogenous inputs model, and wherein said computing an estimate of said model error bounds comprises computing the largest singular value of said model error bounds.
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29. The method of claim 28, wherein said the estimated model error bounds are represented by an additive, frequency-weighted singular value.
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30. The method of claim 29, wherein said refining said identification trajectory comprises increasing a spectral energy in a plurality of selected frequency regions.
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31. The method of claim 28, wherein said computing an estimate of the model error bounds comprises:
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computing a plurality of simulated values of said model error for said input and output data;
determining a plurality of maximum singular values of said plurality of simulated values of said model error; and
determining a scalar uncertainty function such that said model error is bounded by said scalar uncertainty function, wherein said determining a scalar uncertainty function comprises computing, for said data population, a maximum value of said plurality of maximum singular values.
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32. A computer-implemented method comprising:
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computing a model error bound for a stochastic model of a control system, wherein said computing a model error bounds comprises computing a singular value of said model error bound; and
performing an identification trajectory refinement of said stochastic model using said model error bound. - View Dependent Claims (33, 34, 35, 36, 37, 38, 39, 40, 41)
computing a high order model estimate, wherein the model represents an auto-regressive with exogenous inputs model; and
computing an estimate of the model error bounds, wherein the estimated model error bounds are represented by a singular value, and wherein said compute an estimate of the model error bounds comprises;
computing a plurality of simulated values of said model error for a data population;
determining a plurality of maximum singular values of said plurality of simulated values of said model error;
determining a scalar uncertainty function such that said model error is bounded by said scalar uncertainty function, wherein said determining a scalar uncertainty function comprises computing, for said data population, a maximum value of said plurality of maximum singular values.
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35. The method of claim 34, wherein said scalar uncertainty function determines the largest singular value of said model error bounds.
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36. The method of claim 34, wherein said largest singular value of said model error bounds is a frequency-weighted singular value bound.
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37. The method of claim 34, wherein each of said plurality of simulated values of said model error lies on a curve defined by a computed covariance of multivariable transfer functions, wherein said multivariable transfer functions describe said stochastic control system.
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38. The method of claim 37, wherein said model error lies on 3-sigma ellipsoids curve.
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39. The method of claim 34, wherein performing said identification trajectory refinement comprises an iterative trajectory refinement operation based on said estimated model error bound.
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40. The method of claim 32, wherein said performing said identification trajectory refinement comprises increasing a spectral energy in a plurality of selected frequency regions.
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41. The method of claim 32, wherein said model error bounds are additive model error bounds.
Specification