| 1. |
- Abdalmoaty, Mohamed R., 1986-, et al.
(författare)
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Identification of a Class of Nonlinear Dynamical Networks⁎
- 2018
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Ingår i: IFAC-PapersOnLine. - : Elsevier B.V.. - 2405-8963. ; 51:15, s. 868-873
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Tidskriftsartikel (refereegranskat)abstract
- Identification of dynamic networks has attracted considerable interest recently. So far the main focus has been on linear time-invariant networks. Meanwhile, most real-life systems exhibit nonlinear behaviors; consider, for example, two stochastic linear time-invariant systems connected in series, each of which has a nonlinearity at its output. The estimation problem in this case is recognized to be challenging, due to the analytical intractability of both the likelihood function and the optimal one-step ahead predictors of the measured nodes. In this contribution, we introduce a relatively simple prediction error method that may be used for the estimation of nonlinear dynamical networks. The estimator is defined using a deterministic predictor that is nonlinear in the known signals. The estimation problem can be defined using closed-form analytical expressions in several non-trivial cases, and Monte Carlo approximations are not necessarily required. We show, that this is the case for some block-oriented networks with no feedback loops and where all the nonlinear modules are polynomials. Consequently, the proposed method can be applied in situations considered challenging by current approaches. The performance of the estimation method is illustrated on a numerical simulation example.
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| 2. |
- Agüero, Juan C., et al.
(författare)
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Accuracy of linear multiple-input multiple-output (MIMO) models obtained by maximum likelihood estimation
- 2012
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Ingår i: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 48:4, s. 632-637
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we study the accuracy of linear multiple-input multiple-output (MIMO) models obtained by maximum likelihood estimation. We present a frequency-domain representation for the information matrix for general linear MIMO models. We show that the variance of estimated parametric models for linear MIMO systems satisfies a fundamental integral trade-off. This trade-off is expressed as a multivariable 'water-bed' effect. An extension to spectral estimation is also discussed.
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| 3. |
- Ebadat, Afrooz, et al.
(författare)
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Applications Oriented Input Design for Closed-Loop System Identification : a Graph-Theory Approach
- 2014
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Ingår i: 2014 IEEE 53RD ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC). - : IEEE. - 9781467360906 ; , s. 4125-4130
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Konferensbidrag (refereegranskat)abstract
- A new approach to experimental design for identification of closed-loop models is presented. The method considers the design of an experiment by minimizing experimental cost, subject to probabilistic bounds on the input and output signals, and quality constraints on the identified model. The input and output bounds are common in many industrial processes due to physical limitations of actuators. The aforementioned constraints make the problem non-convex. By assuming that the experiment is a realization of a stationary process with finite memory and finite alphabet, we use results from graph-theory to relax the problem. The key feature of this approach is that the problem becomes convex even for non-linear feedback systems. A numerical example shows that the proposed technique is an attractive alternative for closed-loop system identification.
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| 4. |
- Eckhard, Diego, et al.
(författare)
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Mean-squared error experiment design for linear regression models
- 2012
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Ingår i: 16th IFAC Symposium on System Identification. - : IFAC. - 9783902823069 ; , s. 1629-1634
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Konferensbidrag (refereegranskat)abstract
- This work solves an experiment design problem for a linear regression problem using a reduced order model. The quality of the model is assessed using a mean square error measure that depends linearly on the parameters. The designed input signal ensures a predefined quality of the model while minimizing the input energy.
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| 5. |
- Eckhard, Diego, et al.
(författare)
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On the convergence of the Prediction Error Method to its global minimum
- 2012
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Ingår i: 16th IFAC Symposium on System Identification. - : IFAC. - 9783902823069 ; , s. 698-703
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Konferensbidrag (refereegranskat)abstract
- The Prediction Error Method (PEM) is related to an optimization problem built on input/output data collected from the system to be identified. It is often hard to find the global solution of this optimization problem because the corresponding objective function presents local minima and/or the search space is constrained to a nonconvex set. The existence of local minima, and hence the difficulty in solving the optimization, depends mainly on the experimental conditions, more specifically on the spectrum of the input/output data collected from the system. It is therefore possible to avoid the existence of local minima by properly choosing the spectrum of the input; in this paper we show how to perform this choice. We present sufficient conditions for the convergence of PEM to the global minimum and from these conditions we derive two approaches to avoid the existence of nonglobal minima. We present the application of one of these two approaches to a case study where standard identification toolboxes tend to get trapped in nonglobal minima.
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| 6. |
- Everitt, Niklas, 1987-, et al.
(författare)
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A Geometric Approach to Variance Analysis of Cascaded Systems
- 2013
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Ingår i: Proceedings of the 52nd Conference On Decision And Control. - : IEEE conference proceedings. - 9781467357173 ; , s. 6496-6501
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Konferensbidrag (refereegranskat)abstract
- Modeling complex and interconnected systems is a key issue in system identification. When estimating individual subsystems of a network of interconnected system, it is of interest to know the improvement of model-accuracy in using different sensors and actuators. In this paper, using a geometric approach, we quantify the accuracy improvement from additional sensors when estimating the first of a set of subsystems connected in a cascade structure. We present results on how the zeros of the first subsystem affect the accuracy of the corresponding model. Additionally we shed some light on how structural properties and experimental conditions determine the accuracy. The results are particularized to FIR systems, for which the results are illustrated by numerical simulations. A surprising special case occurs when the first subsystem contains a zero on the unit circle; as the model orders grows large, thevariance of the frequency function estimate, evaluated at thecorresponding frequency of the unit-circle zero, is shown to be the same as if the other subsystems were completely known.
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| 7. |
- Everitt, Niklas, 1987-, et al.
(författare)
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Variance Analysis of Linear SIMO Models with Spatially Correlated Noise
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- Substantial improvement in accuracy of identied linear time-invariant single-input multi-output (SIMO) dynamical models ispossible when the disturbances aecting the output measurements are spatially correlated. Using an orthogonal representation for the modules composing the SIMO structure, in this paper we show that the variance of a parameter estimate of a module is dependent on the model structure of the other modules, and the correlation structure of the disturbances. In addition, we quantify the variance-error for the parameter estimates for finite model orders, where the effect of noise correlation structure, model structure and signal spectra are visible. From these results, we derive the noise correlation structure under which the mentioned model parameterization gives the lowest variance, when one module is identied using less parameters than the other modules.
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| 8. |
- Everitt, Niklas, 1987-, et al.
(författare)
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Variance Results for Parallel Cascade Serial Systems
- 2014
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Ingår i: Proceedings of 19th IFAC World Congress. - : Elsevier BV.
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Konferensbidrag (refereegranskat)abstract
- Modelling dynamic networks is important in different fields of science. At present, little is known about how different inputs and sensors contribute to the statistical properties concerning an estimate of a specific dynamic system in a network. We consider two forms of parallel serial structures, one multiple-input-multiple-output structure and one single-input multiple-output structure. The quality of the estimated models is analysed by means of the asymptotic covariance matrix, with respect to input signal characteristics, noise characteristics, sensor locations and previous knowledge about the remaining systems in the network. It is shown that an additive property applies to the information matrix for the considered structures. The impact of input signal selection, sensor locations and incorporation of previous knowledge isillustrated by simple examples.
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| 9. |
- Ferizbegovic, Mina
(författare)
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Dual control concepts for linear dynamical systems
- 2022
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- We study simultaneous learning and control of linear dynamical systems. In such a setting, control policies are derived with respect to two objectives: i) to control the system as well as possible, given the current knowledge of system dynamics (exploitation), and ii) to gather as much information as possible about the unknown system that can improve control (exploration).These two objectives are often in conflict, and this phenomenon is known as the exploration-exploitation trade-off.More specifically, in the context of simultaneous learning and control, we consider: linear quadratic regulation (LQR) problem, model reference control, and data-driven control based on Willems \textit{et al.}'s fundamental lemma. First, we consider the LQR problem with unknown dynamics. We present robust and certainty equivalence (CE) model-based control methods that balance exploration and exploitation. We focus on control policies that can be iteratively updated after sequentially collecting data.We propose robust (with respect to parameter uncertainty) LQR design methods. To quantify uncertainty, we derive a methodbased on Bayesian inference, which is directly applicable to robust control synthesis. To begin, we derive a robust controller to minimize the worst-case cost, with high probability, given the empirical observation of the system. This robust controller synthesis is then used to derive a robust dual controller, which updates its control policy after collecting data. An episode in which data is collected is called exploration, and the episode using an updated control policy called exploitation. The objective is to minimize the worst-case cost of the updated control policy, requiring that a given exploration budget constrains the worst-case cost during exploration. Additionally, we derive methods that balance exploration and exploitation to minimize the cumulative worst-case cost for a fixed number of episodes. In this thesis, we refer to such a problem as robust reinforcement learning. Essentially, it is a robust dual controller aiming to minimize the cumulative worst-case cost, and that updates its control policy in each episode.Numerical experiments show that the proposed methods perform better than existing state-of-the-art algorithms. Moreover, experiments also indicate that the exploration prioritizes the uncertainty reduction in the parameters that matter most for control.A control policy using the CE principle for LQR consists of a sum of an optimal controller calculated using estimated dynamics at time $t$, and an additive external excitation. It has been shown over the years that the optimal asymptotic rate of regret is in many instances $\mathcal{O}(\sqrt{T})$. In particular, this rate can be obtained by adding a white noise external excitation, with a variance decaying as $\gamma/\sqrt{T}$, where $\gamma$ is a predefined constant. As the amount of excitation is pre-determined, such approaches can be viewed as open-loop control of the external excitation. In this thesis, we approach the problem of designing the external excitation from a feedback perspective leveraging the well-known benefits of feedback control for decreasing sensitivity to external disturbances and system-model mismatch, as compared to open-loop strategies. The benefits of this approach over the open-loop approach can be seen in the case of unmodeled dynamics and disturbances. However, even when using the benefits of feedback control, we do not calculate the optimal amount of external excitation. To find the optimal amount of external excitation, we suggest exploration strategies that are based on a time-dependent scaling $\gamma_t$ and can attain cumulative regret similar to or lower than cumulative regret obtained for optimal scaling $\gamma^*$ according to numerical examples.Second, we consider the model reference control problem with the goal of proposing a data-driven robust control design method based on an average risk criterion, which we call Bayes control. We show that this approach has very close ties to the Bayesian kernel-based method, but the conceptual difference lies in the use of a deterministic respective stochastic setting for the system parameters. Finally, we consider data-driven control using Willems \textit{et al.}'s fundamental lemma. First, we propose variations of the fundamental lemma that, instead of a data trajectory, utilize correlation functions in the time domain, as well as power spectra of the input and the output in the frequency domain. Since data-driven control using the fundamental lemma can become a very expensive computation task for large datasets, the proposed variations are easy to computeeven for large datasets and can be efficient as a data compression technique. Second, we study connections of data informativity conditions between the results based on the fundamental lemma (finite time), and classical system identification. We show that finite time informativity conditions for state-space systems are closely linked to the identifiability conditions derived from the fundamental lemma. We prove that the obtained persistency of excitation conditions for infinite time are sufficient conditions for finite time informativity. Moreover, we reveal that the obtained conditions for a finite time in closed-loop are stricter than in classical system identification. This is a consequence of the noiseless data setting in the fundamental lemma that precludes the possibility of noise to excite the system in a feedback setting.
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| 10. |
- Ferizbegovic, Mina
(författare)
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Robust learning and control of linear dynamical systems
- 2020
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- We consider the linear quadratic regulation problem when the plant is an unknown linear dynamical system. We present robust model-based methods based on convex optimization, which minimize the worst-case cost with respect to uncertainty around model estimates. To quantify uncertainty, we derive a methodbased on Bayesian inference, which is directly applicable to robust control synthesis.We focus on control policies that can be iteratively updated after sequentially collecting data. More specifically, we seek to design control policies that balance exploration (reducing model uncertainty) and exploitation (control of the system) when exploration must be safe (robust).First, we derive a robust controller to minimize the worst-case cost, with high probability, given the empirical observation of the system. This robust controller synthesis is then used to derive a robust dual controller, which updates its control policy after collecting data. An episode in which data is collected is called exploration, and the episode using an updated control policy is exploitation. The objective is to minimize the worst-case cost of the updated control policy, requiring that a given exploration budget constrains the worst-case cost during exploration.We look into robust dual control in both finite and infinite horizon settings. The main difference between the finite and infinite horizon settings is that the latter does not consider the length of the exploration and exploitation phase, but it rather approximates the cost using the infinite horizon cost. In the finite horizon setting, we discuss how different exploration lengths affect the trade-off between exploration and exploitation.Additionally, we derive methods that balance exploration and exploitation to minimize the cumulative worst-case cost for a fixed number of episodes. In this thesis, we refer to such a problem as robust reinforcement learning. Essentially, it is a robust dual controller aiming to minimize the cumulative worst-case cost, and that updates its control policy in each episode.Numerical experiments show that the proposed methods have better performance compared to existing state-of-the-art algorithms. Moreover, experiments also indicate that the exploration prioritizes the uncertainty reduction in the parameters that matter most for control.
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