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| 2. |
- Umenberger, Jack, et al.
(författare)
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Bayesian identification of state-space models via adaptive thermostats
- 2019
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Ingår i: 2019 IEEE 58th conference on decision and control (CDC). - : IEEE. - 9781728113982 ; , s. 7382-7388
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Konferensbidrag (refereegranskat)abstract
- Bayesian modeling has been recognized as a powerful approach to system identification, not least due to its intrinsic uncertainty quantification. However, despite many recent developments, Bayesian identification of nonlinear state space models still poses major computational challenges. We propose a new method to tackle this problem. The technique is based on simulating a so-called thermostat, a stochastic differential equation constructed to have the posterior parameter distribution as its limiting distribution. Simulating the thermostat requires access to unbiased estimates of the gradient of the log-posterior. To handle this, we make use of a recent method for debiasing particle-filter-based smoothing estimates. Numerical results show a clear benefit of this approach compared to a direct application of (biased) particle-filter-based gradient estimates within the thermostat.
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| 3. |
- Umenberger, Jack, et al.
(författare)
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Convex Bounds for Equation Error in Stable Nonlinear Identification
- 2019
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Ingår i: IEEE Control Systems Letters. - : Institute of Electrical and Electronics Engineers (IEEE). - 2475-1456. ; 3:1, s. 73-78
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Tidskriftsartikel (refereegranskat)abstract
- Equation error, also known as one-step-ahead prediction error, is a common quality-of-fit metric in dynamical system identification and learning. In this letter, we use Lagrangian relaxation to construct a convex upper bound on equation error that can be optimized over a convex set of nonlinear models that are guaranteed to be contracting, a strong form of nonlinear stability. We provide theoretical results on the tightness of the relaxation, and show that the method compares favorably to established methods on a variety of case studies.
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| 4. |
- Umenberger, Jack, et al.
(författare)
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Robust exploration in linear quadratic reinforcement learning
- 2019
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Ingår i: Advances in neural information processing systems 32 (NIPS 2019). - : Neural Information Processing Systems (NIPS). ; , s. 15310-15320
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Konferensbidrag (refereegranskat)abstract
- This paper concerns the problem of learning control policies for an unknown linear dynamical system to minimize a quadratic cost function. We present a method, based on convex optimization, that accomplishes this task robustly: i.e., we minimize the worst-case cost, accounting for system uncertainty given the observed data. The method balances exploitation and exploration, exciting the system in such a way so as to reduce uncertainty in the model parameters to which the worst-case cost is most sensitive. Numerical simulations and application to a hardware-in-the-loop servo-mechanism demonstrate the approach, with appreciable performance and robustness gains over alternative methods observed in both.
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| 5. |
- Umenberger, Jack, et al.
(författare)
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Specialized Interior-Point Algorithm for Stable Nonlinear System Identification
- 2019
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Ingår i: IEEE Transactions on Automatic Control. - : IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC. - 0018-9286 .- 1558-2523. ; 64:6, s. 2442-2456
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Tidskriftsartikel (refereegranskat)abstract
- Estimation of nonlinear dynamic models from data poses many challenges, including model instability and nonconvexity of long-term simulation fidelity. Recently Lagrangian relaxation has been proposed as a method to approximate simulation fidelity and guarantee stability via semidefinite programming (SDP); however, the resulting SDPs have large dimension, limiting their utility in practical problems. In this paper, we develop a path-following interior-point algorithm that takes advantage of special structure in the problem and reduces computational complexity from cubic to linear growth with the length of the dataset. The new algorithm enables empirical comparisons to established methods including nonlinear autoregressive models with exogenous inputs, and we demonstrate superior generalization to new data. We also explore the "regularizing" effect of stability constraints as an alternative to regressor subset selection.
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| 6. |
- Zhang, Han, et al.
(författare)
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Inverse optimal control for discrete-time finite-horizon Linear Quadratic Regulators
- 2019
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Ingår i: Automatica. - : Elsevier Ltd. - 0005-1098 .- 1873-2836. ; 110
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we consider the inverse optimal control problem for discrete-time Linear Quadratic Regulators (LQR), over finite-time horizons. Given observations of the optimal trajectories, or optimal control inputs, to a linear time-invariant system, the goal is to infer the parameters that define the quadratic cost function. The well-posedness of the inverse optimal control problem is first justified. In the noiseless case, when these observations are exact, we analyze the identifiability of the problem and provide sufficient conditions for uniqueness of the solution. In the noisy case, when the observations are corrupted by additive zero-mean noise, we formulate the problem as an optimization problem and prove that the solution to this problem is statistically consistent. The performance of the proposed method is illustrated through numerical examples.
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