| 1. |
- Ferizbegovic, Mina, et al.
(författare)
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Learning Robust LQ-Controllers Using Application Oriented Exploration
- 2020
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Ingår i: IEEE Control Systems Letters. - : Institute of Electrical and Electronics Engineers (IEEE). - 2475-1456. ; 4:1, s. 19-24
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Tidskriftsartikel (refereegranskat)abstract
- This letter concerns the problem of learning robust LQ-controllers, when the dynamics of the linear system are unknown. First, we propose a robust control synthesis method to minimize the worst-case LQ cost, with probability 1-δ , given empirical observations of the system. Next, we propose an approximate dual controller that simultaneously regulates the system and reduces model uncertainty. The objective of the dual controller is to minimize the worst-case cost attained by a new robust controller, synthesized with the reduced model uncertainty. The dual controller is subject to an exploration budget in the sense that it has constraints on its worst-case cost with respect to the current model uncertainty. In our numerical experiments, we observe better performance of the proposed robust LQ regulator over the existing methods. Moreover, the dual control strategy gives promising results in comparison with the common greedy random exploration strategies.
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| 2. |
- Grussler, Christian, et al.
(författare)
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Identification of externally positive systems
- 2018
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Ingår i: 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017. - 9781509028733 ; 2018-January, s. 6549-6554
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Konferensbidrag (refereegranskat)abstract
- We consider identification of externally positive linear discrete-time systems from input/output data. The proposed method is formulated as a semidefinite program, and is guaranteed to identify models that are ellipsoidal cone-invariant and, consequently, externally positive. We demonstrate empirically that this cone-invariance approach can significantly reduce the conservatism associated with methods that enforce internal positivity as a sufficient condition for external positivity.
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| 3. |
- Horta Ribeiro, Antônio, et al.
(författare)
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On the smoothness of nonlinear system identification
- 2020
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Ingår i: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 121
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Tidskriftsartikel (refereegranskat)abstract
- We shed new light on the smoothness of optimization problems arising in prediction error parameter estimation of linear and nonlinear systems. We show that for regions of the parameter space where the model is not contractive, the Lipschitz constant and β-smoothness of the objective function might blow up exponentially with the simulation length, making it hard to numerically find minima within those regions or, even, to escape from them. In addition to providing theoretical understanding of this problem, this paper also proposes the use of multiple shooting as a viable solution. The proposed method minimizes the error between a prediction model and the observed values. Rather than running the prediction model over the entire dataset, multiple shooting splits the data into smaller subsets and runs the prediction model over each subset, making the simulation length a design parameter and making it possible to solve problems that would be infeasible using a standard approach. The equivalence to the original problem is obtained by including constraints in the optimization. The new method is illustrated by estimating the parameters of nonlinear systems with chaotic or unstable behavior, as well as neural networks. We also present a comparative analysis of the proposed method with multi-step-ahead prediction error minimization.
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| 4. |
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| 5. |
- 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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| 6. |
- 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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| 7. |
- Umenberger, Jack, et al.
(författare)
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Learning convex bounds for linear quadratic control policy synthesis
- 2018
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Ingår i: Neural Information Processing Systems 2018.
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Konferensbidrag (refereegranskat)abstract
- Learning to make decisions from observed data in dynamic environments remains a problem of fundamental importance in a numbers of fields, from artificial intelligence and robotics, to medicine and finance. This paper concerns the problem of learning control policies for unknown linear dynamical systems so as to maximize a quadratic reward function. We present a method to optimize the expected value of the reward over the posterior distribution of the unknown system parameters, given data. The algorithm involves sequential convex programing, and enjoys reliable local convergence and robust stability guarantees. Numerical simulations and stabilization of a real-world inverted pendulum are used to demonstrate the approach, with strong performance and robustness properties observed in both.
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| 8. |
- Umenberger, Jack, et al.
(författare)
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Maximum likelihood identification of stable linear dynamical systems
- 2018
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Ingår i: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 96, s. 280-292
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Tidskriftsartikel (refereegranskat)abstract
- This paper concerns maximum likelihood identification of linear time invariant state space models, subject to model stability constraints. We combine Expectation Maximization (EM) and Lagrangian relaxation to build tight bounds on the likelihood that can be optimized over a convex parametrization of all stable linear models using semidefinite programming. In particular, we propose two new algorithms: EM with latent States & Lagrangian relaxation (EMSL), and EM with latent Disturbances & Lagrangian relaxation (EMDL). We show that EMSL provides tighter bounds on the likelihood when the effect of disturbances is more significant than the effect of measurement noise, and EMDL provides tighter bounds when the situation is reversed. We also show that EMDL gives the most broadly applicable formulation of EM for identification of models with singular disturbance covariance. The two new algorithms are validated with extensive numerical simulations.
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| 9. |
- Umenberger, Jack, et al.
(författare)
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Nonlinear Input Design as Optimal Control of a Hamiltonian System
- 2020
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Ingår i: IEEE Control Systems Letters. - : IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC. - 2475-1456. ; 4:1, s. 85-90
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Tidskriftsartikel (refereegranskat)abstract
- We propose an input design method for a general class of parametric probabilistic models, including nonlinear dynamical systems with process noise. The goal of the procedure is to select inputs such that the parameter posterior distribution concentrates about the true value of the parameters; however, exact computation of the posterior is intractable. By representing (samples from) the posterior as trajectories from a certain Hamiltonian system, we transform the input design task into an optimal control problem. The method is illustrated via numerical examples, including magnetic resonance imaging pulse sequence design.
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| 10. |
- Umenberger, Jack, et al.
(författare)
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On Identification via EM with Latent Disturbances and Lagrangian Relaxation
- 2015
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Ingår i: IFAC-PapersOnLine. - : Elsevier BV. - 2405-8963.
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Konferensbidrag (refereegranskat)abstract
- In the application of the Expectation Maximization (EM) algorithm to identification of dynamical systems, latent variables are typically taken as system states, for simplicity. In this work, we propose a different choice of latent variables, namely, system disturbances. Such a formulation is shown, under certain circumstances, to improve the fidelity of bounds on the likelihood, and circumvent difficulties related to intractable model transition densities. To access these benefits, we propose a Lagrangian relaxation of the challenging optimization problem that arises when formulating over latent disturbances, and fully develop the method for linear models.
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