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]

154 Read more

** 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.

Show more
** 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.

Show more
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.

Show more
14 Read more

© 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.

Show more
12 Read more

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.

Show more
255 Read more

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

176 Read more

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.

Show more
29 Read more

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.

Show more
100 Read more

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.

Show more
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.

Show more
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.

Show more
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.

Show more
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.

Show more
37 Read more

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.

Show more
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.

Show more
56 Read more

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”

Show more
17 Read more

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.

Show more
15 Read more

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.

Show more
45 Read more

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.

Show more
22 Read more