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A dual adaptive model predictive control (MPC) algorithm is presented for linear, time-invariant systems subject to bounded disturbances and parametric uncertainty in the state-space matrices. Online set-membership identification is performed to reduce the uncertainty and thus control affects both the informativity of identification and the system’s performance. The main contribution of the paper is to include this dual effect in the MPC optimization problem using a predicted worst-case cost in the objective function. This allows the controller to perform active exploration, that is, the control input reduces the uncertainty in the regions of the parameter space that have most influence on the performance. Additionally, the MPC algorithm ensures robust constraint satisfaction of state and input constraints. Advantages of the proposed algorithm are shown by comparing it to a passive adaptive MPC algorithm from the literature., IEEE Transactions on Automatic Control, 68 (5), ISSN:0018-9286, ISSN:1558-2523

Recently, various algorithms for data-driven simulation and control have been proposed based on the Willems' fundamental lemma. However, when collected data are noisy, these methods lead to ill-conditioned data-driven model structures. In this work, we present a maximum likelihood framework to obtain an optimal data-driven model, the signal matrix model, in the presence of output noise. Data compression and noise level estimation schemes are also proposed to apply the algorithm efficiently to large datasets and unknown noise level scenarios. Two approaches in system identification and receding horizon control are developed based on the derived optimal estimator. The first one identifies a finite impulse response model. This approach improves the least-squares estimator with less restrictive assumptions. The second one applies the signal matrix model as the predictor in predictive control. The control performance is shown to be better than existing data-driven predictive control algorithms, especially under high noise levels. Both approaches demonstrate that the derived estimator provides a promising framework to apply data-driven algorithms to noisy data., IEEE Transactions on Automatic Control, 68 (1), ISSN:0018-9286, ISSN:1558-2523

Flexible wings pose a considerable modeling challenge, as they involve highly coupled and nonlinear interactions between the aerodynamic and structural dynamics. In this work, we provide an open source code framework, unifying recent data-driven modeling methods that extend the dynamic mode decomposition with control (DMDc) to model the nonlinear aeroelasticity of flexible wings. Our framework consists of (1) a fully parametrized flexible wing model; (2) a fluid-structure interaction (FSI) solver that couples a detailed finite element model of the wing structure with a 3D unsteady aerodynamic panel method; and (3) three different data-driven reduced-order aeroelastic modeling methods. We demonstrate our framework on two flexible wings and provide tutorials to compare the different data-driven methods. The code is widely applicable and useful for generating accurate and efficient data-driven reduced-order models, and it provides a benchmark for future developments of aeroelastic reduced-order modeling methods.

This paper investigates the effect of model uncertainty on the nonlinear dynamics of a generic aeroelastic system. Among the most dangerous phenomena to which these systems are prone, Limit Cycle Oscillations are periodic isolated responses triggered by the nonlinear interactions among elastic deformations, inertial forces, and aerodynamic actions. In a dynamical systems setting, these responses typically emanate from Hopf bifurcation points, and thus a recently proposed framework, which address the problem of robustness from a nonlinear dynamics viewpoint, is employed. Briefly, the notion of robust bifurcation margin extends the concept of μ analysis technique from the robust control theory. The main contribution of this article is a systematic investigation of the numerous scenarios arising in the study of nonlinear flutter when uncertainties in the model are accounted for in the analyses. The advantages of adopting this framework include the possibility to: quantify relevant information for the determination of the nonlinear stability envelope; gain a more in-depth understanding of the physical mechanisms triggering subcritical and supercritical Hopf bifurcations; and reveal properties of the nominal system by identifying isolated branches not straightforward to detect with conventional numerical approaches., Nonlinear Dynamics, 103 (2), ISSN:0924-090X, ISSN:1573-269X

This letter proposes a dual control finite horizon LQR synthesis procedure for unknown systems characterized by mean and covariance estimates. The optimized policy comprises time-varying state-feedback and dithering components, and the control problem is framed as a multiobjective synthesis which seeks a balance between exploitation and exploration costs. It is shown that classic experiment design problems can be recast in this framework by replacing the exploitation cost with an information reward. Numerical examples demonstrate the different dual control trade-offs on plants with different properties.

For a material efficient construction process of lightweight concrete shells, tensioned cablenets can be used as a supporting formwork. In order to guarantee the mechanical stability of the shells,tight tolerances in their form need to be met. To this end, methods have recently been proposed to readjustthe form of the cable net on the construction site. This paperproposes a novel view on the cable netmodel as a dynamical system and derives robust control approaches based onH∞andμsynthesis. Bothapproaches can account for input uncertainties and external disturbances. Theμcontroller additionallyis robust against the uncertain model parameters, which makes their precise identification unnecessary.Theμsynthesis also provides a priori bounds on the allowable fabrication tolerances of the cable net inorder to guarantee robust performance of the closed-loop system. The resulting LTI controllers can beapplied to the system without expert knowledge about the system model or the underlying optimization.The effectiveness of the controllers is demonstrated in numerical experiments., IFAC-PapersOnLine, 53 (2), ISSN:2405-8963, 21th IFAC World Congress. Proceedings

This work proposes a novel robust model predictive control (MPC) algorithm for linear systems affected by dynamic model uncertainty and exogenous disturbances. The uncertainty is modeled using a linear fractional perturbation structure with a time-varying perturbation matrix, enabling the algorithm to be applied to a large model class. The MPC controller constructs a state tube as a sequence of parameterized ellipsoidal sets to bound the state trajectories of the system. The proposed approach results in a semidefinite program to be solved online, whose size scales linearly with the order of the system. The design of the state tube is formulated as an offline optimization problem, which offers flexibility to impose desirable features such as robust invariance on the terminal set. This contrasts with most existing tube MPC strategies using polytopic sets in the state tube, which are difficult to design and whose complexity grows combinatorially with the system order. The algorithm guarantees constraint satisfaction, recursive feasibility, and stability of the closed loop. The advantages of the algorithm are demonstrated using two simulation studies., International Journal of Robust and Nonlinear Control, ISSN:1049-8923, ISSN:1099-1239

A novel approach to reduced-order modeling of high-dimensional systems with time-varying properties is proposed. It combines the problem formulation of the Dynamic Mode Decomposition method with the concept of balanced realization. It is assumed that the only information available on the system comes from input, state, and output trajectories, thus the approach is fully data-driven. The goal is to obtain an input-output low dimensional linear model which approximates the system across its operating range. Time-varying features of the system are retained by means of a Linear Parameter-Varying representation made of a collection of state-consistent linear time-invariant reduced-order models. The algorithm formulation hinges on the idea of replacing the orthogonal projection onto the Proper Orthogonal Decomposition modes, used in Dynamic Mode Decomposition-based approaches, with a balancing oblique projection constructed from data. As a consequence, the input-output information captured in the lower-dimensional representation is increased compared to other projections onto subspaces of same or lower size. Moreover, a parameter-varying projection is possible while also achieving state-consistency. The validity of the proposed approach is demonstrated on a morphing wing for airborne wind energy applications by comparing the performance against two recent algorithms. Analyses account for both prediction accuracy and closed-loop performance in model predictive control applications., Aerospace Science and Technology, 115, ISSN:1270-9638

The paper investigates the selection of state sequences in data-driven projection-based model reduction methods that compute parsimonious models by forming regression problems featuring low-order fictitious states. Specifically, subspace identification and dynamic mode decomposition techniques are considered. It is shown that, while sharing a seemingly equivalent structure, they differ profoundly in the way these states are selected. A theoretical characterization of the differences is given, including a parametrization of a new class of state transformations implicitly used in both approaches and a balanced transformation obtained directly from data. Numerical examples are proposed to show the impact of these differences on the accuracy of the extracted low-order representations.

The paper proposes a novel approach to data-driven reduced-order modeling which combines the Dynamic Mode Decomposition technique with the concept of balanced realization. The information on the system comes from input, state, and output trajectories, and the goal is to derive a linear low-dimensional input-output model approximation. % of the system around a given trim point. Since the dynamics of aerospace systems markedly changes when some parameters are varied, it is desirable to capture this feature in the system's description. Therefore, a Linear Parameter-Varying representation made of a collection of state-consistent linear time-invariant reduced-order models is sought. The main technical novelty of the proposed algorithm consists of replacing the orthogonal projection onto the POD modes, typical of Dynamic Mode Decomposition techniques, with a balancing oblique projection. The advantages are that the input-output information in the lower-dimensional representation is maximized, and that a parameter-varying projection is possible while also achieving state-consistency. The validity of the proposed approach is demonstrated on a morphing wing for airborne wind energy applications by comparing its prediction capabilities with those of a recent algorithm from the literature., AIAA Scitech 2021 Forum, ISBN:978-1-62410-609-5

The paper proposes a multi-step identification approach to classify a nonlinear system into qualitatively different regimes and then estimate a low-dimensional subspace where predictions of the original state at future times can be obtained by simulation of low-order dynamics. Proper Orthogonal Decomposition is used to build a library of characteristic modes from training data and is combined with regularization techniques for both the classification and estimation problems. Group Lasso is proposed to more effectively perform the former task. Moreover, l(1) and l(2) regularization problems with singular values weighting of the dynamic modes are suggested to handle the estimation problem in complex scenarios where limited measurement points are available or sensors are noisy. Results obtained on the Rijke tube system, a nonlinear thermoacoustic benchmark problem, demonstrate better classification accuracy and lower prediction error compared with a method from the literature. Copyright (C) 2021 The Authors., IFAC-PapersOnLine, 54 (14), ISSN:2405-8963

Autonomous exploration is an application of growing importance in robotics. A promising strategy is ergodic trajectory planning, whereby an agent spends in each area a fraction of time which is proportional to its probability information density function. In this paper, a decentralized ergodic multi-agent trajectory planning algorithm featuring limited communication constraints is proposed. The agents' trajectories are designed by optimizing a weighted cost encompassing ergodicity, control energy and close-distance operation objectives. To solve the underlying optimal control problem, a second-order descent iterative method coupled with a projection operator in the form of an optimal feedback controller is used. Exhaustive numerical analyses show that the multi-agent solution allows a much more efficient exploration in terms of completion task time and control energy distribution by leveraging collaboration among agents., IEEE Robotics and Automation Letters, 6 (4), ISSN:2377-3766

This paper formulates an input design approach for truncated infinite impulse response identification in the context of implicit model representations recently used as basis for data-driven simulation and control approaches. Precisely, the considered model consists of a linear combination of the columns of a data (or signal) matrix. An optimal combination for the case of noisy data was recently proposed using a maximum likelihood approach, and the objective here is to optimize the input entries of the data matrix such that the mean-square error matrix of the estimate is minimized. A least-norm problem is derived in terms of the optimality criteria typically considered in the experiment design literature. Numerical results showcase the improved estimation fit achieved with the optimized input. Copyright (C) 2021 The Authors., IFAC-PapersOnLine, 54 (7), ISSN:2405-8963, 19th IFAC Symposium on System Identification, SYSID 2021

This paper presents a novel kernel-based system identification method, which promotes low complexity of the model in terms of the McMillan degree of the system. The regularization matrix is characterized as a linear combination of pre-selected rank-one matrices with unknown hyperparameter coefficients, and the hyperparameters are derived using a maximum a posteriori estimation approach. Each basis matrix is the optimal regularization matrix for a first-order system. With this basis matrix selection, the McMillan degree of the identified model is upper-bounded by the rank of the regularization matrix, which in turn is equal to the cardinality of the hyperparameters. For this reason, a sparsity-promoting prior is chosen for hyperparameter tuning. The resulting optimization problem has a difference of convex program form which can be efficiently solved. The advantages of the proposed method are that the identified model has a low-complexity structure and that an improved bias-variance trade-off is achieved. Numerical results confirm that the proposed method achieves a better bias-variance trade-off as well as a better fit to the model compared to both the empirical Bayes method and the atomic-norm regularization., IFAC-PapersOnLine, 53 (2), ISSN:2405-8963, 21th IFAC World Congress. Proceedings

This article proposes a framework which allows the study of stability robustness of equilibria of a nonlinear system in the face of parametric uncertainties from the point of view of bifurcation theory. In this context, a branch of equilibria is stable if bifurcations (i.e., qualitative changes of the steady-state solutions) do not occur as one or more bifurcation parameters are varied. The work focuses specifically on Hopf bifurcations, where a stable branch of equilibria meets a branch of periodic solutions. It is of practical interest to evaluate how the presence of uncertain parameters in the system alters the result of analyses performed with respect to a nominal vector field. Note that in this article bifurcation parameters have a different meaning than uncertain parameters. To answer the question, the concept of robust bifurcation margins is proposed based on the idea of describing the uncertain system in a Linear Fractional Transformation fashion. The robust bifurcation margins can be interpreted as nonlinear analogues of the structural singular value, or $\mu$, which provides robust stability margins for linear time invariant systems. Their computation is formulated as a nonlinear program aided by a continuation-based multistart strategy to mitigate the issue of local minima. Application of the framework is demonstrated on two case studies from the power system and aerospace literature., SIAM Journal on Applied Dynamical Systems, 19 (3), ISSN:1536-0040

This paper proposes a new methodology in linear time-periodic (LTP) system identification. In contrast to previous methods that totally separate dynamics at different tag times for identification, the method focuses on imposing appropriate structural constraints on the linear time-invariant (LTI) reformulation of LTP systems. This method adopts a periodically-switched truncated infinite impulse response model for LTP systems, where the structural constraints are interpreted as the requirement to place the poles of the non-truncated models at the same locations for all sub-models. This constraint is imposed by combining the atomic norm regularization framework for LTI systems with the group lasso technique in regression. As a result, the estimated system is both uniform and low-order, which is hard to achieve with other existing estimators. Monte Carlo simulation shows that the grouped atomic norm method does not only show better results compared to other regularized methods, but also outperforms the subspace identification method under high noise levels in terms of model fitting. ISSN:2405-8963

The paper discusses an extension of μ (or structured singular value), a well-established technique from robust control for the study of linear systems subject to structured uncertainty, to nonlinear polynomial problems. Robustness is a multifaceted concept in the nonlinear context, and in this work the point of view of bifurcation theory is assumed. The latter is concerned with the study of qualitative changes of the steady-state solutions of a nonlinear system, so-called bifurcations. The practical goal motivating the work is to assess the effect of modeling uncertainties on flutter, a dynamic instability prompted by an adverse coupling between aerodynamic, elastic, and inertial forces, when considering the system as nonlinear. Specifically, the onset of flutter in nonlinear systems is generally associated with limit cycle oscillations emanating from a Hopf bifurcation point. Leveraging μ and its complementary modeling paradigm, namely linear fractional transformation, this work proposes an approach to compute margins to the occurrence of Hopf bifurcations for uncertain nonlinear systems. An application to the typical section case study with linear unsteady aerodynamic and hardening nonlinearities in the structural parameters will be presented to demonstrate the applicability of the approach., CEAS Aeronautical Journal, 11 (4)

In this paper, the hierarchical Bayesian method for regularized system identification is introduced. To this end, a hyperprior distribution is considered for the regularization matrix and then, the impulse response and the regularization matrix are jointly estimated based on a maximum a posteriori (MAP) approach. Toward introducing a suitable hyperprior, we decompose the regularization matrix using Cholesky decomposition and reduce the estimation problem to the cone of upper triangular matrices with positive diagonal entries. Following this, the hyperprior is introduced on a designed sub-cone of this set. The method differs from the current trend in regularized system identification from various aspect, e.g., the estimation is performed by solving a single stage problem. The MAP estimation problem reduces to a multi-convex optimization problem and a sequential convex programming algorithm is introduced for solving this problem. Consequently, the proposed method is a computationally efficient strategy specially when the regularization matrix has a large size. The method is numerically verified on benchmark examples. Owing to the employed full Bayesian approach, the estimation method shows a satisfactory bias-variance trade-off., IFAC-PapersOnLine, 53 (2), ISSN:2405-8963, 21th IFAC World Congress. Proceedings

This letter proposes a new methodology for subspace identification of linear time-periodic (LTP) systems with periodic inputs. This method overcomes the issues related to the computation of frequency response of LTP systems by utilizing the frequency response of the time-lifted system with linear time-invariant structure instead. The response is estimated with an ensemble of input-output data with periodic inputs. This allows the frequency-domain subspace identification technique to be extended to LTP systems. The time-aliased periodic impulse response can then be estimated and the order-revealing decomposition of the block-Hankel matrix is formulated. The consistency of the proposed method is proved under mild noise assumptions. Numerical simulation shows that the proposed method performs better than multiple widely-used time-domain subspace identification methods when an ensemble of periodic data is available., IEEE Control Systems Letters, 5 (1), ISSN:2475-1456

A feedback control design is proposed for stochastic systems with finite second moment which aims at maximising the region of attraction of the equilibrium point. Polynomial Chaos (PC) expansions are employed to represent the stochastic closed loop system by a higher dimensional set of deterministic equations. By using the PC expanded system representation, the available information on the uncertainty affecting the system explicitly enters the control design problem. Further, this allows Lyapunov methods for deterministic systems to be used to formulate the stability criteria certifying the region of attraction. These criteria are parametrized by the feedback gain and formulated in a polynomial optimization program which is solved using sum-of-squares methods. This approach offers flexibility in the choice of the stochastic feedback law and accounts for input constraints. The application is demonstrated by two numerical examples., IFAC-PapersOnLine, 53 (2), ISSN:2405-8963, 21th IFAC World Congress. Proceedings

A method is presented to estimate the region of attraction (ROA) of stochastic systems with finite second moment and uncertainty-dependent equilibria. The approach employs Polynomial Chaos (PC) expansions to represent the stochastic system by a higher-dimensional set of deterministic equations. We first show how the equilibrium point of the deterministic formulation provides the stochastic moments of an uncertainty-dependent equilibrium point of the stochastic system. A connection between the boundedness of the moments of the stochastic system and the Lyapunov stability of its PC expansion is then derived. Defining corresponding notions of a ROA for both system representations, we show how this connection can be leveraged to recover an estimate of the ROA of the stochastic system from the ROA of the PC expanded system. Two optimization programs, obtained from sum-of-squares programming techniques, are provided to compute inner estimates of the ROA. The first optimization program uses the Lyapunov stability arguments to return an estimate of the ROA of the PC expansion. Based on this result and user specifications on the moments for the initial conditions, the second one employs the shown connection to provide the corresponding ROA of the stochastic system. The method is demonstrated by two examples. © 2020 Elsevier Ltd, Automatica, 122, ISSN:0005-1098

The newly-developed structured H∞ paradigm provides a powerful and versatile tool for multi-variable/multi-requirement control synthesis, with successful applications growing rapidly. However, due to its versatility, insights arising naturally from the standard (i.e., unstructured) H∞ framework as well as other design choices are easily overlooked. Hence, this paper shows how this type of information can be exploited to have better systematic understanding and control solutions. As application scenario, the design and analysis of a robust glide-slope approach controller is addressed. This controller is part of a complete automatic landing system developed under the scope of an aircraft landing challenge proposed by ONERA and AIRBUS.

In this article the problem of estimating the Region of Attraction (ROA) for polynomial nonlinear systems subject to modeling uncertainties is studied. Based on recent theoretical studies on the calculation of positively invariant sets, this article proposes an optimization problem which allows robust inner Estimates of the Region of Attraction (rERA) to be evaluated. The uncertainties, which can generically be time-invariant or time-varying, are described as semialgebraic sets, and the problem is solved numerically by means of Sum Of Squares relaxations, which allow set containment conditions to be enforced. The ensuing optimization entails non-convex constraints, and an iterative algorithm to enlarge the provable invariant level set is discussed. The proposed algorithm is applied to two study cases of increasing complexity. Further, in order to benchmark the proposed rERA algorithm, comparisons are shown with a class of well established algorithms based on Lyapunov functions level sets. The results showcase the prowess of the proposed approach and its advantages in terms of accuracy and computational time, particularly as the size of the system increases.