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A popular technique used to obtain linear representations of nonlinear systems is the so-called Koopman approach, where the nonlinear dynamics are lifted to a (possibly infinite dimensional) linear space through nonlinear functions called observables. In the lifted space, the dynamics are linear and represented by a so-called Koopman operator. While the Koopman theory was originally introduced for autonomous systems, it has been widely used to derive linear time-invariant (LTI) models for nonlinear systems with inputs through various approximation schemes such as the extended dynamics mode decomposition (EDMD). However, recent extensions of the Koopman theory show that the lifting process for such systems results in a linear parameter-varying (LPV) model instead of an LTI form. As LTI Koopman model based control has been successfully used in practice and it is generally temping to use such LTI descriptions of nonlinear systems, due to the simplicity of the associated control tool chain, a systematic approach is needed to synthesise optimal LTI approximations of LPV Koopman models compared to the ad-hoc schemes such as EDMD, which is based on least-squares regression. In this work, we introduce optimal LTI Koopman approximations of exact Koopman models of nonlinear systems with inputs by using l2-gain and generalized H2 norm performance measures. We demonstrate the advantages of the proposed Koopman modelling procedure compared to EDMD., Comment: Preprint submitted to the joint IFAC conference: SSSC-TDS-LPVS, 2022

The ever increasing need for performance results in increasingly rigorous demands on throughput and positioning accuracy of high-precision motion systems, which often suffer from position dependent effects that originate from relative actuation and sensing of the moving-body. Due to the highly stiff mechanical design, such systems are typically controlled using rigid body control design approaches. Nonetheless, the presence of position dependent flexible dynamics severely limits attainable position tracking performance. This paper presents two extensions of the conventional rigid body control framework towards active control of position dependent flexible dynamics. Additionally, a novel control design approach is presented, which allows for shaping of the full closed-loop system by means of structured $H_\infty$ co-design. The effectiveness of the approach is validated through simulation using a high-fidelity model of a state-of-the-art moving-magnet planar actuator., Comment: 6 pages, 7 figures

We present a variational Bayesian identification procedure for polynomial NARMAX models based on message passing on a factor graph. Message passing allows us to obtain full posterior distributions for regression coefficients, precision parameters and noise instances by means of local computations distributed according to the factorization of the dynamic model. The posterior distributions are important to shaping the predictive distribution for outputs, and ultimately lead to superior model performance during 1-step ahead prediction and simulation.

This work presents a novel regularization method for the identification of Nonlinear Autoregressive eXogenous (NARX) models. The regularization method promotes the exponential decay of the influence of past input samples on the current model output. This is done by penalizing the sensitivity of the NARX model simulated output with respect to the past inputs. This promotes the stability of the estimated models and improves the obtained model quality. The effectiveness of the approach is demonstrated through a simulation example, where a neural network NARX model is identified with this novel method. Moreover, it is shown that the proposed regularization approach improves the model accuracy in terms of simulation error performance compared to that of other regularization methods and model classes., Accepted for presentation at the 61st IEEE Conference on Decision and Control

Increasingly stringent throughput requirements in the industry necessitate the need for lightweight design of high-precision motion systems to allow for high accelerations, while still achieving accurate positioning of the moving-body. The presence of position dependent dynamics in such motion systems severely limits achievable position tracking performance using conventional sequential loop closing (SLC) control design strategies. This paper presents a novel extension of the conventional SLC design framework towards linear-parameter-varying systems, which allows to circumvent limitations that are introduced by position dependent effects in high-precision motion systems. Advantages of the proposed control design approach are demonstrated in simulation using a high-fidelity model of a moving-magnet planar actuator system, which exhibits position dependency in both actuation and sensing., 6 pages

We propose a variational Bayesian inference procedure for online nonlinear system identification. For each output observation, a set of parameter posterior distributions is updated, which is then used to form a posterior predictive distribution for future outputs. We focus on the class of polynomial NARMAX models, which we cast into probabilistic form and represent in terms of a Forney-style factor graph. Inference in this graph is efficiently performed by a variational message passing algorithm. We show empirically that our variational Bayesian estimator outperforms an online recursive least-squares estimator, most notably in small sample size settings and low noise regimes, and performs on par with an iterative least-squares estimator trained offline., 6 pages, 4 figures. Accepted to the American Control Conference 2022

Efficiently computable stability and performance analysis of nonlinear systems becomes increasingly more important in practical applications. Dissipativity can express stability and performance jointly, but existing results are limited to the regions around the equilibrium points of these nonlinear systems. The incremental framework, based on the convergence of the system trajectories, removes this limitation. We investigate how stability and performance characterizations of nonlinear systems in the incremental framework are linked to dissipativity, and how general performance characterization beyond the L2-gain concept can be understood in this framework. This paper presents a matrix inequalities-based convex incremental dissipativity analysis for nonlinear systems via quadratic storage and supply functions. The proposed dissipativity analysis links the notions of incremental, differential, and general dissipativity. We show that through differential dissipativity, incremental and general dissipativity of the nonlinear system can be guaranteed. These results also lead to the incremental extensions of the L2-gain, the generalized H2-norm, the L∞-gain, and passivity of nonlinear systems.

Identifying systems with high-dimensional inputs and outputs, such as systems measured by video streams, is a challenging problem with numerous applications in robotics, autonomous vehicles and medical imaging. In this paper, we propose a novel non-linear state-space identification method starting from high-dimensional input and output data. Multiple computational and conceptual advances are combined to handle the high-dimensional nature of the data. An encoder function, represented by a neural network, is introduced to learn a reconstructability map to estimate the model states from past inputs and outputs. This encoder function is jointly learned with the dynamics. Furthermore, multiple computational improvements, such as an improved reformulation of multiple shooting and batch optimization, are proposed to keep the computational time under control when dealing with high-dimensional and large datasets. We apply the proposed method to a video stream of a simulated environment of a controllable ball in a unit box. The study shows low simulation error with excellent long term prediction capability of the model obtained using the proposed method., Comment: Accepted to SYSID 2021 (revised with reviewer feedback)

Thermal convection is ubiquitous in nature as well as in many industrial applications. The identification of effective control strategies to, e.g., suppress or enhance the convective heat exchange under fixed external thermal gradients is an outstanding fundamental and technological issue. In this work, we explore a novel approach, based on a state-of-the-art Reinforcement Learning (RL) algorithm, which is capable of significantly reducing the heat transport in a two-dimensional Rayleigh-B\'enard system by applying small temperature fluctuations to the lower boundary of the system. By using numerical simulations, we show that our RL-based control is able to stabilize the conductive regime and bring the onset of convection up to a Rayleigh number $Ra_c \approx 3 \cdot 10^4$, whereas in the uncontrolled case it holds $Ra_{c}=1708$. Additionally, for $Ra > 3 \cdot 10^4$, our approach outperforms other state-of-the-art control algorithms reducing the heat flux by a factor of about $2.5$. In the last part of the manuscript, we address theoretical limits connected to controlling an unstable and chaotic dynamics as the one considered here. We show that controllability is hindered by observability and/or capabilities of actuating actions, which can be quantified in terms of characteristic time delays. When these delays become comparable with the Lyapunov time of the system, control becomes impossible., Comment: 24 pages, 10 figures

This paper describes a method for the active control of the deformations on a magnetically-levitated moving-magnet planar motor. The motor under consideration is comprised of a stator on a double coil array configuration and a mover with permanent magnets, and it is designed to perform positioning tasks with nanometer level of accuracy. Due to the spatially asymmetric, non-uniform force distribution on the magnet plate, mechanical deformations are induced to the mover, which can severely hinder the desired positioning accuracy. The proposed method overcomes this challenge by properly shaping the force distribution on the moving magnet plate, which is enabled by the presence of multiple coils interacting with the mover, corresponding to an ‘`overactuation’' scheme. As a consequence, the independent control of elementary deformation shapes (modes) is achieved. The proposed overactuation scheme is experimentally validated on a planar motor prototype, proving the efficiency of the proposed method during both standstill and motion.

In recent years, there has been a growing interest in the development of global linear embeddings of nonlinear dynamical systems. A possible solution is given by the Koopman framework. The main idea is to lift the nonlinear system to a possibly infinite dimensional, but linear, space where the dynamics are governed by a so-called Koopman operator. In practice, only a limited number of lifting functions (called observables) can be used. However, as the choice is generally ad-hoc, there is no guarantee on the approximation capability. Furthermore, in its original formulation, the Koopman framework only addresses autonomous systems. In the present work, we aim to address these shortcomings.

The linear parameter-varying framework enables systematic control design approaches to meet increasing performance requirements and complexity of systems. The aim of this letter is to develop local frequency response data-based analysis and synthesis conditions for multiple-input multiple-output linear parameter-varying systems to facilitate fast tuning. Key advantages are local stability and performance guarantees and a global controller parameterization. The effectiveness of the proposed methods are evaluated based on a simulation example.

This book describes a user-friendly, evolutionary algorithms-based framework for estimating data-driven models for a wide class of dynamical systems, including linear and nonlinear ones. The methodology addresses the problem of automating the process of estimating data-driven models from a user’s perspective. By combining elementary building blocks, it learns the dynamic relations governing the system from data, giving model estimates with various trade-offs, e.g. between complexity and accuracy. The evaluation of the method on a set of academic, benchmark and real-word problems is reported in detail. Overall, the book offers a state-of-the-art review on the problem of nonlinear model estimation and automated model selection for dynamical systems, reporting on a significant scientific advance that will pave the way to increasing automation in system identification.

The feedforward control design problem for a single-axis dual-stage actuator system with piezoelectric ac- tuator at the short-stroke is analyzed in this paper. With such actuator layout, the main question is how to balance the contribution of the individual actuators in a efficient manner, while complying to actuators limitations. A control configuration and a sequential design methodology are proposed to take into account interactions between actuators. In addition, various feedforward controller design strategies that conform to the configuration proposed are presented, such as inversion based feedforward, mass feedforward and standard compli- ance compensation. Based on observed shortcomings of each feedforward design, a novel mixed compliance compensation feedforward controller is presented. Results are analyzed in terms of their physical interpretations and simulation studies.

Unlike for Linear Time-Invariant (LTI) systems, for nonlinear systems, there exists no general framework for systematic convex controller design which incorporates performance shaping. The Linear Parameter-Varying (LPV) framework sought to bridge this gap by extending convex LTI synthesis results such that they could be applied to nonlinear systems. However, recent literature has shown that naive application of the LPV framework can fail to guarantee the desired asymptotic stability guarantees for nonlinear systems. Incremental dissipativity theory has been successfully used in the literature to overcome these issues for Continuous-Time (CT) systems. However, so far no solution has been proposed for output-feedback based incremental control for the Discrete-Time (DT) case. Using recent results on convex analysis of incremental dissipativity for DT nonlinear systems, in this paper, we propose a convex output-feedback controller synthesis method to ensure closed-loop incremental dissipativity of DT nonlinear systems via the LPV framework. The proposed method is applied on a simulation example, demonstrating improved stability and performance properties compared to a standard LPV controller design., Accepted to 60th Conference on Decision and Control, Austin, 2021

Growing demands in the semiconductor industry result in the need for enhanced performance of lithographic equipment. However, position tracking accuracy of high precision mechatronics is often limited by the presence of disturbance sources, which originate from unmodelled or unforeseen deterministic environmental effects. To negate the effects of these disturbances, a learning based feedforward controller is employed, where the underlying control policy is estimated from experimental data based on Gaussian Process regression. The proposed approach exploits the property of including prior knowledge on the expected steady state behaviour of residual dynamics in terms of kernel selection. Corresponding hyper-parameters are optimized using the maximization of the marginalized likelihood. Consequently, the learned function is employed as augmentation of the currently employed rigid body feedforward controller. The effectiveness of the augmentation is experimentally validated on a magnetically levitated planar motor stage. The results of this paper demonstrate the benefits and possibilities of machine-learning based approaches for compensation of static effects, which originate from residual dynamics, such that position tracking performance for moving-magnet planar motor actuators is improved., This paper is to be published in Proceedings of Machine Learning Research vol 144

In general, most dynamical systems exhibit some sort of nonlinear behavior. However, most control and identification applications rely on LTI models, which are only valid locally. In recent years, the Koopman framework has gained popularity within the control and identification communities, proposing a global linear representation of nonlinear systems. This is achieved through the embedding of the nonlinear state-space into a possibly infinite-dimensional lifted space where the dynamics are linear and governed by the Koopman operator. In practice, only a finite number of lifting functions is used and, while the choice of the dictionary heavily impacts the representation quality of the resulted linear model, there are little to no systematic methods for the selection. We address this by combining a Least Squares Support Vector Machine (LS-SVM) regression, to estimate the nonlinear state transition map, with the linearity condition of the Koopman form.

The identification of black-box nonlinear state-space models requires a flexible representation of the state and output equation. Artificial neural networks have proven to provide such a representation. However, as in many identification problems, a nonlinear optimization problem needs to be solved to obtain the model parameters (layer weights and biases). A well-thought initialization of these model parameters can often avoid that the nonlinear optimization algorithm converges to a poorly performing local minimum of the considered cost function. This paper introduces an improved initialization approach for nonlinear state-space models represented as a recurrent artificial neural network and emphasizes the importance of including an explicit linear term in the model structure. Some of the neural network weights are initialized starting from a linear approximation of the nonlinear system, while others are initialized using random values or zeros. The effectiveness of the proposed initialization approach over previously proposed methods is illustrated on two benchmark examples., Comment: Accepted for presentation at the European Control Conference 2021, Rotterdam, The Netherlands

This document contains the supplementary material for the contribution "On Automated Multi-objective Identification Using Grammar-based Genetic Programming".

Nonlinear state-space identification for dynamical systems is most often performed by minimizing the simulation error to reduce the effect of model errors. This optimization problem becomes computationally expensive for large datasets. Moreover, the problem is also strongly non-convex, often leading to sub-optimal parameter estimates. This paper introduces a method that approximates the simulation loss by splitting the data set into multiple independent sections similar to the multiple shooting method. This splitting operation allows for the use of stochastic gradient optimization methods which scale well with data set size and has a smoothing effect on the non-convex cost function. The main contribution of this paper is the introduction of an encoder function to estimate the initial state at the start of each section. The encoder function estimates the initial states using a feed-forward neural network starting from historical input and output samples. The efficiency and performance of the proposed state-space encoder method is illustrated on two well-known benchmarks where, for instance, the method achieves the lowest known simulation error on the Wiener--Hammerstein benchmark.

After sixty years of quantitative biophysical modeling of neurons, the identification of neuronal dynamics from input-output data remains a challenging problem, primarily due to the inherently nonlinear nature of excitable behaviors. By reformulating the problem in terms of the identification of an operator with fading memory, we explore a simple approach based on a parametrization given by a series interconnection of Generalized Orthonormal Basis Functions (GOBFs) and static Artificial Neural Networks. We show that GOBFs are particularly well-suited to tackle the identification problem, and provide a heuristic for selecting GOBF poles which addresses the ultra-sensitivity of neuronal behaviors. The method is illustrated on the identification of a bursting model from the crab stomatogastric ganglion., Slightly extended pre-print of the paper to be presented at the 59th Conference on Decision and Control, held remotely between December 14-18, 2020

This paper applies the classical prediction error method (PEM) to the estimation of nonlinear discrete-time models of neuronal systems subject to input-additive noise. While the nonlinear system exhibits excitability, bifurcations, and limit-cycle oscillations, we prove consistency of the parameter estimation procedure under output feedback. Hence, this paper provides a rigorous framework for the application of conventional nonlinear system identification methods to discrete-time stochastic neuronal systems. The main result exploits the elementary property that conductance-based models of neurons have an exponentially contracting inverse dynamics. This property is implied by the voltage-clamp experiment, which has been the fundamental modeling experiment of neurons ever since the pioneering work of Hodgkin and Huxley., ERC

Model structure and complexity selection remains a challenging problem in system identification, especially for parametric non-linear models. Many Evolutionary Algorithm (EA) based methods have been proposed in the literature for estimating model structure and complexity. In most cases, the proposed methods are devised for estimating structure and complexity within a specified model class and hence these methods do not extend to other model structures without significant changes. In this paper, we propose a Tree Adjoining Grammar (TAG) for stochastic parametric models. TAGs can be used to generate models in an EA framework while imposing desirable structural constraints and incorporating prior knowledge. In this paper, we propose a TAG that can systematically generate models ranging from FIRs to polynomial NARMAX models. Furthermore, we demonstrate that TAGs can be easily extended to more general model classes, such as the non-linear Box-Jenkins model class, enabling the realization of flexible and automatic model structure and complexity selection via EA., Comment: Accepted as brief paper by Automatica

Recently, a number of counter examples have surfaced where Linear Parameter-Varying (LPV) control synthesis applied to achieve asymptotic output tracking and disturbance rejection for a nonlinear system, fails to achieve the desired asymptotic tracking and rejection behavior even when the scheduling variations remain in the bounded region considered during design. It has been observed that the controlled system may exhibit an oscillatory motion around the equilibrium point in the presence of a bounded constant input disturbance even if integral action is present. This work aims at investigating how and why the baseline Lyapunov stability notion, currently widely used in the LPV framework, fails to guarantee the desired system behavior. Specifically, it is shown why the quadratic Lyapunov concept is insufficient to always guarantee asymptotic stability under reference tracking and disturbance rejection scenarios, and why an equilibrium independent stability notion is required for LPV stability analysis and synthesis of controllers. The introduced concepts and the apparent pitfalls are demonstrated via a simulation example., Accepted to European Control Conference (ECC) 2020, Saint Petersburg

Thermal convection is ubiquitous in nature as well as in many industrial applications. The identification of effective control strategies to, e.g., suppress or enhance the convective heat exchange under fixed external thermal gradients is an outstanding fundamental and technological issue. In this work, we explore a novel approach, based on a state-of-the-art Reinforcement Learning (RL) algorithm, which is capable of significantly reducing the heat transport in a two-dimensional Rayleigh-B��nard system by applying small temperature fluctuations to the lower boundary of the system. By using numerical simulations, we show that our RL-based control is able to stabilize the conductive regime and bring the onset of convection up to a Rayleigh number $Ra_c \approx 3 \cdot 10^4$, whereas in the uncontrolled case it holds $Ra_{c}=1708$. Additionally, for $Ra > 3 \cdot 10^4$, our approach outperforms other state-of-the-art control algorithms reducing the heat flux by a factor of about $2.5$. In the last part of the manuscript, we address theoretical limits connected to controlling an unstable and chaotic dynamics as the one considered here. We show that controllability is hindered by observability and/or capabilities of actuating actions, which can be quantified in terms of characteristic time delays. When these delays become comparable with the Lyapunov time of the system, control becomes impossible., 24 pages, 10 figures

Linear parameter-varying (LPV) models have been introduced to describe nonlinear (NL) and time-varying (TV) systems and make use of powerful results of linear control theory. LPV systems extend the notion of linear time invariant (LTI) systems, with the difference that the input/output relations change depending on a scheduling parameter. The goal is to efficiently convert a nonlinear model to an LPV representation with minimal complexity and conservativeness and preserving the system properties. A novel approach for modeling nonlinear systems in terms of a quasi-linear representation is based on the Koopman operator theory. Typically, an infinite-dimensional operator is obtained that requires an approximation for practical applications. Based on the resulting model, an LPV description can be obtained using a velocity-based linearization, which is valid at every operating point.

The Best Linear Approximation (BLA) framework has already proven to be a valuable tool to analyze nonlinear systems and to start the nonlinear modeling process. The existing BLA framework is limited to systems with additive (colored) noise at the output. Such a noise framework is a simplified representation of reality. Process noise can play an important role in many real-life applications. This paper generalizes the Best Linear Approximation framework to account also for the process noise, both for the open-loop and the closed-loop setting, and shows that the most important properties of the existing BLA framework remain valid. The impact of the process noise contributions on the robust BLA estimation method is also analyzed.

Motivated by neuronal models from neuroscience, we consider the system identification of simple feedback structures whose behaviors include nonlinear phenomena such as excitability, limit-cycles and chaos. We show that output feedback is sufficient to solve the identification problem in a two-step procedure. First, the nonlinear static characteristic of the system is extracted, and second, using a feedback linearizing law, a mildly nonlinear system with an approximately-finite memory is identified. In an ideal setting, the second step boils down to the identification of a LTI system. To illustrate the method in a realistic setting, we present numerical simulations of the identification of two classical systems that fit the assumed model structure., Comment: 18th European Control Conference (ECC), Napoli, Italy, June 25-28 2019

In many engineering applications the level of nonlinear distortions in frequency response function (FRF) measurements is quantified using specially designed periodic excitation signals called random phase multisines and periodic noise. The technique is based on the concept of the best linear approximation (BLA) and it allows one to check the validity of the linear framework with a simple experiment. Although the classical BLA theory can handle measurement noise only, in most applications the noise generated by the system -- called process noise -- is the dominant noise source. Therefore, there is a need to extend the existing BLA theory to the process noise case. In this paper we study in detail the impact of the process noise on the BLA of nonlinear continuous-time systems operating in a closed loop. It is shown that the existing nonparametric estimation methods for detecting and quantifying the level of nonlinear distortions in FRF measurements are still applicable in the presence of process noise. All results are also valid for discrete-time systems and systems operating in open loop., Comment: Accepted for publication in IEEE Transactions on Instrumentation & Measurement

This paper deals with the certification problem for robust quadratic stability, robust state convergence, and robust quadratic performance of linear systems that exhibit bounded rates of variation in their parameters. We consider both continuous-time (CT) and discrete-time (DT) parameter-varying systems. In this paper, we provide a uniform method for this certification problem in both cases and we show that, contrary to what was claimed previously, the DT case requires a significantly different treatment compared to the existing CT results. In the established uniform approach, quadratic Lyapunov functions, that are affine in the parameter, are used to certify robust stability, robust convergence rates, and robust performance in terms of linear matrix inequality feasibility tests. To exemplify the procedure, we solve the certification problem for $\mathscr{L}_2$-gain performance both in the CT and the DT cases. A numerical example is given to show that the proposed approach is less conservative than a method with slack variables., 8 pages, 3 figures

Linearity is a common assumption for many real-life systems, but in many cases the nonlinear behavior of systems cannot be ignored and must be modeled and estimated. Among the various existing classes of nonlinear models, Parallel Hammerstein Models (PHM) are interesting as they are at the same time easy to interpret as well as to estimate. One way to estimate PHM relies on the fact that the estimation problem is linear in the parameters and thus that classical least squares (LS) estimation algorithms can be used. In that area, this article introduces a regularized LS estimation algorithm inspired on some of the recently developed regularized impulse response estimation techniques. Another mean to estimate PHM consists in using parametric or non-parametric exponential sine sweeps (ESS) based methods. These methods (LS and ESS) are founded on radically different mathematical backgrounds but are expected to tackle the same issue. A methodology is proposed here to compare them with respect to (i) their accuracy, (ii) their computational cost, and (iii) their robustness to noise. Tests are performed on simulated systems for several values of methods respective parameters and of signal to noise ratio. Results show that, for a given set of data points, the ESS method is less demanding in computational resources than the LS method but that it is also less accurate. Furthermore, the LS method needs parameters to be set in advance whereas the ESS method is not subject to conditioning issues and can be fully non-parametric. In summary, for a given set of data points, ESS method can provide a first, automatic, and quick overview of a nonlinear system than can guide more computationally demanding and precise methods, such as the regularized LS one proposed here.

This paper presents a nonparametric method for identification of MIMO linear parameter-varying (LPV) models in state-space form. The states are first estimated up to a similarity transformation via a nonlinear canonical correlation analysis (CCA) operating in a reproducing kernel Hilbert space (RKHS). This enables to reconstruct a minimal-dimensional inference between past and future input, output and scheduling variables, making it possible to estimate a state sequence consistent with the data. Once the states are estimated, a least-squares support vector machine (LS-SVM)-based identification scheme is formulated, allowing to capture the dependency structure of the matrices of the estimated state-space model on the scheduling variables without requiring an explicit declaration of these often unknown dependencies; instead, it only requires the selection of nonlinear kernel functions and the tuning of the associated hyper-parameters. 2017 Elsevier Ltd This paper has presented a nonparametric method for identification of LPV-SS models. The proposed technique relies only on the inputs, outputs, and scheduling variables data. The states are estimated up to a similarity transformation by using correlation analysis between the past and future data. Once estimated, an LS-SVM-based non-parametric scheme is used to identify the underlying LPV model. The proposed scheme solves a convex optimization problem and provides encouraging results on a MIMO numerical example with challenging nonlinearities in the presence of noise. The proposed algorithm is further validated on the model of a continuous stirred tank reactor process, and results are compared with an earlier study that assumes complete knowledge of the states. We find that kernel CCA provides encouraging state reconstruction results, which can then be augmented with the measured data in order to build an LPV-SS model. The main contribution of this paper lies in formulating the kernel CCA and LS-SVM solution for this identification problem by preserving the linearity structure in parameter-dependent state-space models. The proposed method also does not impose any dependency structure on the matrix functions, affine or otherwise. Since LPV-SS models are important for LPV control synthesis purposes, we believe that this work has the potential to pave the way for efficient low-order LPV modeling for control synthesis. Syed Zeeshan Rizvi obtained his B.E. in Electronics Engineering from N.E.D. University of Engineering & Tech., Pakistan and his M.S. in Electrical Engineering from King Fahd University of Petroleum & Minerals, Saudi Arabia, in years 2006 and 2008, respectively. In January 2013, he joined the Complex Systems Control Laboratory at The University of Georgia in Athens, GA, where he focused on system identification, model reduction, and control synthesis methods for linear parameter-varying models. He obtained his Ph.D. focusing on LPV system identification and control in December 2016. He is currently working as a process control scientist with Corning Inc. in Corning, NY, focusing on data analytics and advanced process control solutions for specialty glass and ceramic manufacturing processes. Javad Mohammadpour Velni received B.S. and M.S. degrees in electrical engineering from Sharif University of Technology and University of Tehran, Iran, respectively, and Ph.D. degree in mechanical engineering from University of Houston, TX. He joined the University of Georgia as an assistant professor of electrical engineering in August 2012. Prior to that, he was with the University of Michigan, where he worked in the naval architecture & marine engineering department from October 2011 to July 2012. He was also a Research Assistant Professor of mechanical engineering at University of Houston from October 2008 to September 2011 and a Research Associate at the same institution from January 2008 to September 2008. He has published over 100 articles in international journals and conference proceedings, served in the editorial boards of ASME and IEEE conferences on control systems and edited two books on control of large-scale systems (published in 2010) and LPV systems modeling, control and applications (published in 2012). His current research interests are in secure control of cyber physical systems (and in particular, smart grids), coverage control of heterogeneous multi-agent systems, and data-driven approaches for model learning and control of complex distributed systems. Farshid Abbasi received his B.Sc. and M.Sc. degrees in Mechanical Engineering both from University of Tabriz in 2007 and 2010, respectively. In January 2013, he joined Complex Systems Controls Lab at the University of Georgia, where he received a Ph.D. in dynamic system and controls in December 2016. His research interests include multi-agent systems, cooperative control, machine learning and system identification methods focusing on complex nonlinear processes. He is currently with ASML as a controls and system identification research scientist where his research focuses on developing new control and data analysis techniques to enhance rapidly changing semiconductor technologies. Roland T?th was born in 1979 in Miskolc, Hungary. He received the B.Sc. degree in Electrical Engineering and the M.Sc. degree in Information Technology in parallel with distinction at the University of Pannonia, Veszpr�m, Hungary, in 2004, and the Ph.D. degree (cum laude) from the Delft Center for Systems and Control (DCSC), Delft University of Technology (TUDelft), Delft, The Netherlands, in 2008. He was a Post-Doctoral Research Fellow at DCSC, TUDelft, in 2009 and at the Berkeley Center for Control and Identification, University of California Berkeley, in 2010. He held a position at DCSC, TUDelft, in 2011�2012. Currently, he is an Assistant Professor at the Control Systems Group, Eindhoven University of Technology (TU/e). He is an Associate Editor of the IEEE Conference Editorial Board, the IEEE Transactions on Control Systems Technology and the International Journal of Robust and Nonlinear Control. His research interests are in linear parameter-varying (LPV) and nonlinear system identification, machine learning, process modeling and control, model predictive control and behavioral system theory. He received the TUDelft Young Researcher Fellowship Award in 2010, the VENI award of The Netherlands Organisation for Scientific Research in 2011 and the Starting Grant of the European Research Council in 2016. Nader Meskin received his B.Sc. from Sharif University of Technology, Tehran, Iran, in 1998, his M.Sc. from the University of Tehran, Iran in 2001, and obtained his Ph.D. in Electrical and Computer Engineering in 2008 from Concordia University, Montreal, Canada. He was a postdoctoral fellow at Texas A&M University at Qatar from January 2010 to December 2010. He is currently an Associate Professor at Qatar University and Adjunct Associate Professor at Concordia University, Montreal, Canada. His research interests include Fault Detection and Isolation (FDI), multi-agent systems, active control for clinical pharmacology, and linear parameter varying systems. He has published more than one hundred refereed journal and conference papers and he is a coauthor (with K. Khorasani) of the book Fault Detection and Isolation: Multi-Vehicle Unmanned Systems (Springer 2011). Scopus

In this note, novel linear matrix inequality (LMI) analysis conditions for the stability of linear parameter-varying (LPV) systems in input–output (IO) representation form are proposed together with bilinear matrix inequality (BMI) conditions for fixed-structure LPV-IO controller synthesis. Both the LPV-IO plant model and the controller are assumed to depend affinely and statically on the scheduling variables. By using an implicit representation of the plant and the controller interaction, an exact representation of the closed-loop behavior with affine dependence on the scheduling variables is achieved. This representation allows to apply Finsler’s Lemma for deriving exact stability as well as exact quadratic performance conditions. A DK-iteration based solution is carried out to synthesize the controller. The main results are illustrated by a numerical example.

This study addresses a stochastic model predictive tracking problem for linear parameter-varying (LPV) systems described by affine parameter-dependent state-space representations and additive stochastic uncertainties. The reference trajectory is considered as a piecewise constant signal and assumed to be known at all time instants. To obtain prediction equations, the scheduling signal is usually assumed to be constant or its variation is assumed to belong to a convex set. In this study, the underlying scheduling signal is given a stochastic description during the prediction horizon, which aims to overcome the shortcomings of the two former characterisations, namely restrictiveness and conservativeness. Hence, the overall LPV system dynamics consists of additive and multiplicative noise terms up to second order. Due to the presence of stochastic disturbances, probabilistic state constraints are considered. Since the disturbances make the computation of prediction dynamics difficult, augmented state prediction dynamics are considered, by which, feasibility of probabilistic constraints and closed-loop stability are addressed. The overall approach is illustrated using a tank system model. 1 The Institution of Engineering and Technology 2017. Scopus

A novel estimator for the identification of continuous-time linear time-varying systems is presented in this paper. The estimator uses kernel-based regression to identify the time-varying coefficients of a linear ordinary differential equation, based on noisy samples of the input and output signals. The estimator adopts a mixed time- and frequency-domain formulation, which allows it to be formulated as the solution of a set of algebraic equations, without relying on finite differences to approximate the time derivatives. Since a kernel-based approach is used, the model complexity selection of the time-varying parameters is formulated as an optimisation problem with continuous variables. Variance and bias expressions of the estimate are derived and validated on a simulation example. Also, it is shown that, in highly noisy environments, the proposed kernel-based estimator provides more reliable results than an 'Oracle'-based estimator which is deprived of regularisation.

In this paper we propose a novel approach to identify dynamical systems. The method estimates the model structure and the parameters of the model simultaneously, automating the critical decisions involved in identification such as model structure and complexity selection. In order to solve the combined model structure and model parameter estimation problem, a new representation of dynamical systems is proposed. The proposed representation is based on Tree Adjoining Grammar, a formalism that was developed from linguistic considerations. Using the proposed representation, the identification problem can be interpreted as a multi-objective optimization problem and we propose a Evolutionary Algorithm-based approach to solve the problem. A benchmark example is used to demonstrate the proposed approach. The results were found to be comparable to that obtained by state-of-the-art non-linear system identification methods, without making use of knowledge of the system description., Submitted to European Control Conference (ECC) 2019

State-of-the-art methods for data-driven modelling of non-linear dynamical systems typically involve interactions with an expert user. In order to partially automate the process of modelling physical systems from data, many EA-based approaches have been proposed for model-structure selection, with special focus on non-linear systems. Recently, an approach for data-driven modelling of non-linear dynamical systems using Genetic Programming (GP) was proposed. The novelty of the method was the modelling of noise and the use of Tree Adjoining Grammar to shape the search-space explored by GP. In this paper, we report results achieved by the proposed method on three case studies. Each of the case studies considered here is based on real physical systems. The case studies pose a variety of challenges. In particular, these challenges range over varying amounts of prior knowledge of the true system, amount of data available, the complexity of the dynamics of the system, and the nature of non-linearities in the system. Based on the results achieved for the case studies, we critically analyse the performance of the proposed method., Comment: Paper accepted at IEEE CEC 2019

The paper describes a commutation method used for the active compensation of the deformation of the magnetically levitated mover of a planar motor. The single-stage double layer planar motor under consideration comprises a stator with two coil arrays and a mover with permanent magnets, and is designed to perform positioning tasks with high accuracy. To minimize the deformation of the light-weight moving structure, which is exposed to a large force during actuation, its flexible behavior is considered in the commutation of the machine. The commutation decouples the rigid-and flexible-body modes and calculates the required currents in the coils to produce a desired force and torque, as well as the modal force to control the flexible modes deformation. To decouple the flexible modes in the commutation, the relation from coil current to deformation is required, which is obtained by the coupling of a mechanical model and electromagnetic model of the motor. Using a 25-axis laser interferometer system, the deformation of the mover is measured and the relation from coil current to modal deformation is experimentally validated. In a second experiment, the deformation reduction of the magnetically levitated translator is demonstrated.

Though it is a crucial step for most identification methods in nonlinear structural dynamics, nonlinearity location is a sparsely addressed topic in the literature. In fact, locating nonlinearities in mechanical systems turns out to be a challenging problem when treated nonparametrically, that is, without fitting a model. The present contribution takes a new look at this problem by exploiting some recent developments in the identification of dynamic networks, originating from the systems and control community.