Top PDF Model selection, identification and robust control for dynamical systems

Model selection, identification and robust control for dynamical systems

Model selection, identification and robust control for dynamical systems

Proceeding., of the Work.ohop on Struc- t'Uml Safety Eval'Uation Ba.,ed on Sy.,tern Ident'(fimtion Approache.,.. Vieweg and Sons. Technical report, Ph.D. thesis, California [r]

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Frequency Domain Subspace Identification of Multivariable Dynamical Systems for Robust Control Design

Frequency Domain Subspace Identification of Multivariable Dynamical Systems for Robust Control Design

** Engineering Department, Lancaster University, Lancaster LA1 4YW, UK (a.montazeri@lancaster.ac.uk). Abstract: Black-box system identification is subjected to the modelling uncertainties that are propagated from the non-parametric model of the system in time/frequency-domain. Unlike classical H 1 /H 2 spectral analysis, in the recent robust Local Polynomial Method (LPM), the modelling variances are separated to noise contribution and nonlinear contribution while suppressing the transient noise. On the other hand, without an appropriate weighting on the objective function in the system identification methods, the acquired model is subjected to bias. Consequently, in this paper the weighted regression problem in subspace frequency-domain system identification is revisited in order to have an unbiased estimate of the frequency response matrix of a flexible manipulator as a multi-input multi-output lightly-damped system.
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Frequency Domain Subspace Identification of Multivariable Dynamical Systems for Robust Control Design

Frequency Domain Subspace Identification of Multivariable Dynamical Systems for Robust Control Design

** Engineering Department, Lancaster University, Lancaster LA1 4YW, UK (a.montazeri@lancaster.ac.uk). Abstract: Black-box system identification is subjected to the modelling uncertainties that are propagated from the non-parametric model of the system in time/frequency-domain. Unlike classical H 1 /H 2 spectral analysis, in the recent robust Local Polynomial Method (LPM), the modelling variances are separated to noise contribution and nonlinear contribution while suppressing the transient noise. On the other hand, without an appropriate weighting on the objective function in the system identification methods, the acquired model is subjected to bias. Consequently, in this paper the weighted regression problem in subspace frequency-domain system identification is revisited in order to have an unbiased estimate of the frequency response matrix of a flexible manipulator as a multi-input multi-output lightly-damped system.
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Efficient parameter identification and model selection in nonlinear dynamical systems via sparse Bayesian learning

Efficient parameter identification and model selection in nonlinear dynamical systems via sparse Bayesian learning

The results are presented in Figure 2 for systems one to five excited with a single sine wave of 10Hz at an amplitude of 100N. The output data were corrupted with white Gaussian noise with a variance of 0.4%, relative to the standard deviation of the observations. Note that this noise propagates through the numerical differentiation and leads to a higher variance in ˙ x. The first column in Figure 2 shows the phase-space representation in terms of x 1 and x 2 . The second column shows the measured and predicted responses in the time domain (for one excitation cycle), where the shaded area illustrates the predictive uncertainty through the 3σ confidence interval. The third column shows the coefficient vector β resulting from sparse Bayesian inference. For clarity, only coefficients that yielded non-zero values are shown. Also, the absolute values of the coefficients are plotted so as to enable visualisation in the logarithmic domain. The posterior variances and optimised prior variance hyperparameters are shown alongside the coefficient, on the right axis. The posterior variance quantifies the posterior uncertainty around each coefficient vector. The optimised hyper-prior variance, α i for each term is also called a “sparsity factor” as this quantifies the degree to which any given column in the dictionary contributes to sparsifying the solution. If α is low, this means that the prior assumption is that the solution will be concentrated tightly around that vector and thus deeming it “relevant”. If α is high, this implies that the vector does not contribute to a sparse solution.
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Identification of nonlinear dynamical systems with time delay

Identification of nonlinear dynamical systems with time delay

© The Author(s) 2021 Abstract This paper proposes a technique to identify nonlinear dynamical systems with time delay. The sparse optimization algorithm is extended to nonlinear systems with time delay. The proposed algorithm combines cross-validation techniques from machine learning for automatic model selection and an algebraic operation for preprocessing signals to filter the noise and for removing the dependence on initial conditions. We further integrate the bootstrapping resampling technique with the sparse regression to obtain the statistical properties of estimation. We use Taylor expansion to parameterize time delay. The proposed algorithm in this paper is computationally efficient and robust to noise. A nonlinear Duffing oscillator is simulated to demonstrate the efficiency and accuracy of the proposed technique. An experimental example of a nonlinear rotary flexible joint is presented to further validate the proposed method.
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Model-based robust and stochastic control, and statistical inference for uncertain dynamical systems

Model-based robust and stochastic control, and statistical inference for uncertain dynamical systems

Most parameter estimation algorithms generate models with probabilistic descriptions of the uncertain- ties. For such models, robustness characterizations are intrinsically stochastic and can be written in terms of a probability distribution or a level of confidence in estimates with probabilistic risk of incorrectness. Contrary to deterministic robust MPC, stochastic robust MPC incorporates such probabilistic uncertainties and probabilistic violations of constraints, and allows for specified levels of risk during operation. Commonly used probabilistic analysis approaches are Monte Carlo (MC) methods, in which many simulations are run with sampled random variables or random sequences. The effects of uncertainty on the closed-loop system are quantified by simulating a large number of individual deterministic model realizations. While such MC approaches are applicable to most systems, the computational cost can be prohibitively expensive, especially in real-time optimal control algorithms such as MPC. Apart from simulation-based methods, convex approx- imations for a receding horizon method of the constrained discrete-time stochastic control are considered in [55], in which convexity of the resultant optimization is carried out in the basis of robust optimiza- tion [22, 27] that includes robust linear programs and more generally robust convex programs (see [21] for details of robust convex optimization). However, such robust optimization formulations of chance constraints are not applicable to the cases when the stochastic dynamical system has nonlinear parametric uncertainties, whereas this paper can manage the system model that is linear parameter-varying Gaussian, for which the system matrices have nonlinear dependence of random variables and there are additive Gaussian random processes corresponding to external disturbance and measurement noise.
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Fault Detection and Model Identification in Linear Dynamical Systems

Fault Detection and Model Identification in Linear Dynamical Systems

lems with more than one fault model? What if the problem must be formulated more in terms of the original system matrices? What happens when a control is already present in the model? Could alternative cost functions be minimized? Does knowl- edge of initial conditions impact the theory? This section will address these questions

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Structured Feature Selection of Continuous Dynamical Systems for Aircraft Dynamics Identification

Structured Feature Selection of Continuous Dynamical Systems for Aircraft Dynamics Identification

The remaining of the article is organized as follows. In Section 2 we present with more details the model-based approach which motivates the need for ac- curate system identification techniques, while Section 3 is a brief summary of the existing well-established methods. We define in Section 4 the broad class of dynamical systems said to be structured, and explain in Section 5 how the identification of most of these systems can be cast as linear regression problems. Section 6 is devoted to motivating and describing a first multi-task structured feature selection technique suited for this type of problem, which we call block- sparse lasso. Because of the undesirable behaviors of this algorithm when the model features are strongly correlated, two adaptations making use of bootstrap stabilization and generalized Tikhonov regularization are proposed in Section 7. All statistical models suggested are shown to be equivalent to surrogate lasso problems, which can be efficiently solved by well-known existing optimization algorithm. After presenting an application to aircraft trajectory optimization in Section 8, experiments using a real data set of 10 471 recorded flights are carried out in Section 9 to evaluate the performance of our approach and compare it to other existing techniques.
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Robust and Model Predictive Control for Boundary Control Systems

Robust and Model Predictive Control for Boundary Control Systems

1 1. INTRODUCTION Mathematical control theory is the area of application-oriented mathematics that is concerned with the analysis and design of control systems. In this context, controlling a system means forcing it to behave in a desired way. The behavior of the system is usually assessed by measuring some observable properties (outputs) of the system, and the system should then be manipulated such that these measurements have desired values. This control objective is called output regulation. A simple example of output regulation would be cruise control in cars, where the velocity of the vehicle is kept at a constant value by a servomechanism controlling the throttle of the car. The controlled systems are often modeled by ordinary differential equations (ODEs) or partial differential equations (PDEs). Many technological systems can be modeled by ODEs, but there are many important processes such as those involving diffusion, vibrations, and elasticity that are described by PDEs. In this thesis, control of PDEs is considered in the case that the control enters and the measurement is taken through the boundary of the system. Such approach is essentially relevant to systems that can be accessed solely via their boundaries.
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Approximate Bayesian Computation by Subset Simulation for model selection in dynamical systems

Approximate Bayesian Computation by Subset Simulation for model selection in dynamical systems

a Department of Applied Mechanics, Chalmers University of Technology, Gothenburg, Sweden b Division of Engineering and Applied Science, California Institute of Technology, CA, USA Abstract Approximate Bayesian Computation (ABC) methods are originally conceived to expand the horizon of Bayesian inference methods to the range of models for which only forward simulation is available. However, there are well- known limitations of the ABC approach to the Bayesian model selection problem, mainly due to lack of a sufficient summary statistics that work across models. In this paper, we show that formulating the standard ABC posterior distribution as the exact posterior PDF for a hierarchical state-space model class allows us to independently estimate the evidence for each alternative candidate model. We also show that the model evidence is a simple by-product of the ABC-SubSim algorithm. The validity of the proposed approach to ABC model selection is illustrated using simulated data from a three-story shear building with Masing hysteresis.
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Robust design optimisation of dynamical space systems

Robust design optimisation of dynamical space systems

Figure 1. Belief, nominal solution and margin for the first approach described in paragraph 6.1 8. CONCLUSIONS In this paper we described a new approach to do design for resilience by taking into account both robustness and reliability. The method is the Evidence Network Model that is able to model complex systems varying in time and affected by epistemic uncertainty. The approach has been validated with a realistic test case regarding the ​ resource allocation problem in a spacecraft and finally compared with the classical approach of margins.
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Robust design optimisation of dynamical space systems

Robust design optimisation of dynamical space systems

Figure 1. Belief, nominal solution and margin for the first approach described in paragraph 6.1 8. CONCLUSIONS In this paper we described a new approach to do design for resilience by taking into account both robustness and reliability. The method is the Evidence Network Model that is able to model complex systems varying in time and affected by epistemic uncertainty. The approach has been validated with a realistic test case regarding the ​resource allocation problem in a spacecraft and finally compared with the classical approach of margins.
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Robust design optimisation of dynamical space systems

Robust design optimisation of dynamical space systems

Figure 1. Belief, nominal solution and margin for the first approach described in paragraph 6.1 8. CONCLUSIONS In this paper we described a new approach to do design for resilience by taking into account both robustness and reliability. The method is the Evidence Network Model that is able to model complex systems varying in time and affected by epistemic uncertainty. The approach has been validated with a realistic test case regarding the ​resource allocation problem in a spacecraft and finally compared with the classical approach of margins.
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Robust Adaptive Model Predictive Control of Nonlinear Systems

Robust Adaptive Model Predictive Control of Nonlinear Systems

For systems whose true dynamics can only be approximated to within a large margin of un- certainty, it becomes necessary to directly account for the plant-model mismatch. To date, the most general and rigourous means for doing this involves explicitly accounting for the error in the online calculation, using the robust-MPC approaches discussed in Section 10.1. While the theoretical foundations and guarantees of stability for these tools are well established, it remains problematic in most cases to find an appropriate approach yielding a satisfactory balance between computational complexity, and conservatism of the error calculations. For example, the framework of min-max feedback-MPC Magni et al. (2003); Scokaert & Mayne (1998) provides the least-conservative control by accounting for the effects of future feedback actions, but is in most cases computationally intractable. In contrast, computationally simple approaches such as the openloop method of Marruedo et al. (2002) yield such conservatively- large error estimates, that a feasible solution to the optimal control problem often fails to exist.
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Robust Distributed Model Predictive Control of Linear Systems

Robust Distributed Model Predictive Control of Linear Systems

for a non-iterative parallel, and in [12] for a non-iterative sequential setup. In contrast, this paper considers tube techniques tailored for iterative distributed MPC based on distributed opti- mization. The paper highlights computational issues, which arise if existing tube MPC controllers are synthesized and computed on a distributed system. As a first contribution of the paper, it is shown how structured versions of these con- trollers can be synthesized in a distributed manner. The main synthesis steps include constraint tightening and distributed computation of robust positive invariant sets. As a second contribution, it is to shown that the resulting structured controllers can be operated using distributed optimization in closed-loop.
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Aspects on Robust Control and Identification

Aspects on Robust Control and Identification

Chapter 6 Conclusions Since most of the controllers in the process industry are of PID-type, it is still today important to develop user friendly tuning methods for fixed structure linear controllers. Frequency loop shaping methods are inherently iterative procedures. In Paper I, a new approach for designing a fixed-structure linear controller is presented that is more straightforward to use compared to traditional methods. By using this method the designer does not need to specify any weight filters and a more satisfactory design is achieved in every iteration step. In order to productify this method, a fancy user interface can be developed by quite a small effort that can visualize all the interactive design parameters existing in this method as well as contemporary iteration results of controllers with different structures. It would further improve and clarify the iteration results to the designer. A drawback with this tuning method is that it can only be used offline and needs a model of the system to be tuned as an input.
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Adaptive control of nonlinear dynamical systems using a model reference approach

Adaptive control of nonlinear dynamical systems using a model reference approach

May 3, 2013 Keywords: Nonlinear dynamics; adaptive control; model reference 1. Introduction Control of systems which exhibit nonlinear dynamical behavior, par- ticularly chaos, has been an active area of interest in recent years following the work of Ott, Grebogi, & Yorke (1990). In addition to this approach, nonlinear systems which exhibit chaotic dynamics have also been controlled using a more standard control engineering approach including techniques such as feedback linearization and adaptive con- trol (Di Benardo, 1996). Of these approaches, adaptive control is often most useful in a practical engineering environment, as it requires only a limited knowledge of the plant structure and parameters. When a reference model is used, adaptive controllers can also be applied to systems where the details of the plant cannot be fully known a priori or vary with time. Using these type of algorithms without knowledge of plant parameters, such that we assume zero initial conditions for the controller gains, has become known as the “minimal control synthesis”
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Identification of N-state spatio-temporal dynamical
systems using a polynomial model

Identification of N-state spatio-temporal dynamical systems using a polynomial model

Binary cellular automata however can only be applied to systems with two states o and 1. But there are many processes that exhibit more than two states one famous example is excitable media in which any cell can take on three states: quiescent, excited and refractory. However there are very few studies on the identification of n- state spatio-temporal systems. In this paper a polynomial model of n-state spatio- temporal system is given for the first time, and a completely new approach for the identification of n-state spatio-temporal systems is proposed including neighbourhood detection and rule determination.
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A Simple Model of Robust Portfolio Selection

A Simple Model of Robust Portfolio Selection

A second class of models makes use of some tools borrowed from the ro- bust control literature: Maenhout (2004) adapts a framework developed by Anderson, Hansen and Sargent (2003) to derive a portfolio selection model set in continuous time, where the decision maker has got a preference for robustness; Maenhout’s (2004) model, which extends the classical Merton’s (1990) model, assumes that the decision maker has got a reference probabil- ity measure over asset returns, but she considers also alternative probability measures, equivalent to the reference measure (in the probabilistic sense of equivalence), and she chooses among these measures according to a penalty function based on the relative entropy between the probability measures. Uppal and Wang (2003) extend Maenhout’s model to take into account mul- tiple sources of uncertainty and shed some light on real world phenomena such as underdiversi…cation and the home bias. Both Maenhout and Uppal and Wang provide closed formulas for the optimal portfolios.
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A class of robust adaptive controllers for infinite dimensional dynamical systems

A class of robust adaptive controllers for infinite dimensional dynamical systems

An adaptive controller for a perturbed innite dimensional plant is developed to force the state of the plant track the state of a reference model. The reference model is based on the nom- inal plant that has a physical similarity with the plant. Using a Lyapunov stability argument, which is based on the H 1 -Riccati equation of the nominal plant, an adaptive law is developed for the adjustment of the feedback gain. It is proved that the closed-loop system is stable with the tracking error remaining bounded, and converging to zero provided that the norm of the structured perturbation is less than a specied attenuation bound. Results of numerical studies regarding a heat equation and a beam equation are presented to demonstrate the applicability of the proposed control algorithm.
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