This paper proposes a nonlinear estimator for the robust reconstruction of process and sensor faults for a class of uncertain nonlinear systems. The proposed fault estimation method augments the system dynamics with an ultra-local (in time) internal state–space representation (a finite chain of integrators) of the fault vector. Next, a nonlinear state observer is designed based on the known parts of the augmented dynamics. This nonlinear filter (observer) reconstructs the fault signal as well as the states of the augmented system. We provide sufficient conditions that guarantee stability of the estimation error dynamics: firstly, asymptotic stability (i.e., exact fault estimation) in the absence of perturbations induced by the fault model mismatch (mismatch between internal ultra-local model for the fault and the actual fault dynamics), uncertainty, external disturbances, and measurement noise and, secondly, Input-to-State Stability (ISS) of the estimation error dynamics is guaranteed in the presence of these perturbations. In addition, to support performance-based estimator design, we provide Linear Matrix Inequality (LMI) conditions for L₂-gain and L₂−L_∞ induced norm and cast the synthesis of the estimator gains as a semi-definite program where the effect of model mismatch and external disturbances on the fault estimation error is minimized in the sense of L₂-gain, for an acceptable L₂−L_∞ induced norm with respect to measurement noise. The latter result facilitates a design that explicitly addresses the performance trade-off between noise sensitivity and robustness against model mismatch and external disturbances. Finally, numerical results for a benchmark system illustrate the performance of the proposed methodologies.

@en

Ground fault detection in inverter-based microgrid (IBM) systems is challenging, particularly in a real-time setting, as the fault current deviates slightly from the nominal value. This difficulty is reinforced when there are partially decoupled disturbances and modeling uncertainties. The conventional solution of installing more relays to obtain additional measurements is costly and also increases the complexity of the system. In this brief, we propose a data-assisted diagnosis scheme based on an optimization-based fault detection filter with the output current as the only measurement. Modeling the microgrid dynamics and the diagnosis filter, we formulate the filter design as a quadratic programming (QP) problem that accounts for decoupling partial disturbances, robustness to nondecoupled disturbances and modeling uncertainties by training with data, and ensuring fault sensitivity simultaneously. To ease the computational effort, we also provide an approximate but analytical solution to this QP. Additionally, we use classical statistical results to provide a thresholding mechanism that enjoys probabilistic false-alarm guarantees. Finally, we implement the IBM system with Simulink and real-time digital simulator (RTDS) to verify the effectiveness of the proposed method through simulations.

@en

We study the problem of identifying a linear time-varying output map from measurements and linear time-varying system states, which are perturbed with Gaussian observation noise and process uncertainty, respectively. Employing a stochastic model as prior knowledge for the parameters of the unknown output map, we reconstruct their estimates from input/output pairs via a Bayesian approach to optimize the posterior probability density of the output map parameters. The resulting problem is a non-convex optimization, for which we propose a tractable linear matrix inequalities approximation to warm-start a first-order subsequent method. The efficacy of our algorithm is shown experimentally against classical Expectation Maximization and Dual Kalman Smoother approaches.

@en

This paper considers the problem of fault estimation in linear time-invariant systems when actuators are subject to unknown additive faults. A data-driven approach is proposed to design an inverse-system-based filter for reconstructing fault signals when the underlying fault subsystem can be either a minimum phase or non-minimum phase system. Unlike traditional two-step data-driven methods in the literature, the proposed method directly computes the filter parameters from input-output data to avoid the propagation of identification errors through an inverse operation into the fault estimates, which is the case in state-of-the-art filter designs. Furthermore, regarding out-of-sample performance of the filter, a kernel-based regularization is exploited to not only reduce the model complexity but also enable the design scheme to take advantage of available prior knowledge on the underlying system behavior. This knowledge can be incorporated into basis functions, promoting the desired solution to the optimization problem. To validate the effectiveness of the proposed method, a simulation study is conducted, demonstrating a notable reduction in estimation error compared to state-of-the-art methods.

@en

We present a framework for learning of modeling uncertainties in Linear Time Invariant (LTI) systems to improve the predictive capacity of system models in the input-output sense. First, we propose a methodology to extend the LTI model with an uncertainty model. The proposed framework guarantees stability of the extended model. To achieve this, two semi-definite programs are provided that allow obtaining optimal uncertainty model parameters, given state and uncertainty data. Second, to obtain this data from available input-output trajectory data, we introduce a filter in which an internal model of the uncertainty is proposed. This filter is also designed via a semi-definite program with guaranteed robustness with respect to uncertainty model mismatches, disturbances, and noise. Numerical simulations are presented to illustrate the effectiveness and practicality of the proposed methodology in improving model accuracy, while guaranteeing model stability.

@en

We consider the extension of the adaptive Golden RAtio ALgorithm (aGRAAL) for variational inequalities. We show that by selecting the momentum parameter beyond the golden ratio the convergence speed can be improved, which motivates us to study the switching between small and large momentum parameters to accelerate convergence. We validate the performance of our proposed algorithms on several classes of variational inequality problems studied in the machine learning literature, including Nash equilibrium, feasibility problem, composite minimization, Markov decision processes, and zero-sum games, and compare them to existing methods.@en

We study the data-driven finite-horizon linear quadratic regularization (LQR) problem reformulated as a semidefinite program (SDP). Our contribution is to propose two novel accelerated first-order methods for solving the resulting SDP. Our methods enjoy adaptive stepsize and adaptive smoothing parameters that speed up convergence and in turn, enhance scalability. Finally, we compare our accelerated first-order methods and show their benefits via numerical simulations on a benchmark LQR example.

@en

We study a diagnosis scheme to reliably detect the active mode of discrete-time, switched affine systems in the presence of measurement noise and asynchronous switching. The proposed scheme consists of two parts: (i) the construction of a bank of filters, and (ii) the introduction of a residual/threshold-based diagnosis rule. We develop an exact finite optimization-based framework to numerically solve an optimal bank of filters in which the contribution of measurement noise to the residual is minimized. The design problem is safely approximated through linear matrix inequalities and thus becomes tractable. We further propose a thresholding policy along with probabilistic false-alarm guarantees to estimate the active system mode in real-time. In comparison with the existing results, the guarantees improve from a polynomial dependency in the probability of false alarm to a logarithmic form. This improvement is achieved under the additional assumption of sub-Gaussianity, which is expected in many applications. The performance of the proposed approach is validated through a numerical example and an application of the building radiant system.

@en

This paper addresses the problem of robust process and sensor fault reconstruction for nonlinear systems. The proposed method augments the system dynamics with an approximated internal linear model of the combined contribution of known nonlinearities and unknown faults - leading to an approximated linear model in the augmented state. We exploit the broad modeling power of ultra-local models to characterize this internal dynamics. We use a linear filter to reconstruct the augmented state (simultaneously estimating the state of the original system and the sum of nonlinearities and faults). Having this combined estimate, we can simply subtract the analytic expression of nonlinearities from that of the corresponding estimate to reconstruct the fault vector. Because the nonlinearity does not play a role in the filter dynamics (it is only used as a static nonlinear output to estimate the fault), we can avoid standard restrictive assumptions like globally (one-sided) Lipschitz nonlinearities and/or the need for Lipschitz constants to carry out the filter design. The filter synthesis is posed as a mixed H₂/H_∞ optimization problem where the effect of disturbances and model mismatches is minimized in the H_∞ sense, for an acceptable H₂ performance with respect to measurement noise.

@en

We propose two novel numerical schemes for the approximate implementation of the dynamic programming (DP) operation concerned with finite-horizon optimal control of discrete-time systems with input-affine dynamics. The proposed algorithms involve discretization of the state and input spaces and are based on an alternative path that solves the dual problem corresponding to the DP operation. We provide error bounds for the proposed algorithms, along with a detailed analysis of their computational complexity. In particular, for a specific class of problems with separable data in the state and input variables, the proposed approach can reduce the typical time complexity of the DP operation from O(XU) to O(X+U) , where X and U denote the size of the discrete state and input spaces, respectively. This reduction in complexity is achieved by an algorithmic transformation of the minimization in DP operation to an addition via discrete conjugation.@en

In the past few years, online convex optimization (OCO) has received notable attention in the control literature thanks to its flexible real-time nature and powerful performance guarantees. In this article, we propose new step-size rules and OCO algorithms that simultaneously exploit gradient predictions, function predictions and dynamics, features particularly pertinent to control applications. The proposed algorithms enjoy static and dynamic regret bounds in terms of the dynamics of the reference action sequence, gradient prediction error, and function prediction error, which are generalizations of known regularity measures from the literature. We present results for both convex and strongly convex costs. We validate the performance of the proposed algorithms in a trajectory tracking case study, as well as portfolio optimization using real-world datasets.

@en

We introduce a distributionally robust minimium mean square error estimation model with a Wasserstein ambiguity set to recover an unknown signal from a noisy observation. The proposed model can be viewed as a zero-sum game between a statistician choosing an estimator—that is, a measurable function of the observation—and a fictitious adversary choosing a prior—that is, a pair of signal and noise distributions ranging over independent Wasserstein balls—with the goal to minimize and maximize the expected squared estimation error, respectively. We show that, if the Wasserstein balls are centered at normal distributions, then the zero-sum game admits a Nash equilibrium, by which the players’ optimal strategies are given by an affine estimator and a normal prior, respectively. We further prove that this Nash equilibrium can be computed by solving a tractable convex program. Finally, we develop a Frank–Wolfe algorithm that can solve this convex program orders of magnitude faster than state-of-the-art general-purpose solvers. We show that this algorithm enjoys a linear convergence rate and that its direction-finding subproblems can be solved in quasi-closed form.

@en

In this article, we propose a tractable nonlinear fault estimation filter along with explicit performance bounds for a class of linear dynamical systems in the presence of both additive and nonlinear multiplicative faults. We consider the case, where both faults may occur simultaneously and through an identical dynamical relationship, a setting that is relevant to several application domains, including automotive driving, aviation, and chemical plants. The proposed filter architecture combines tools from model-based approaches in the control literature and regression techniques from machine learning. To this end, we view the regression operator through a system-theoretic perspective to develop operator bounds that are then utilized to derive performance bounds for the proposed estimation filter. In the case of constant, simultaneously, and identically acting additive and multiplicative faults, it can be shown that the estimation error converges to zero with an exponential rate. The performance of the proposed estimation filter in the presence of incipient faults is validated through an application on the lateral safety systems of SAE level 4 automated vehicles. The numerical results show that the theoretical bounds of this study are indeed close to the actual estimation error.

@en

We present a learning method to learn the mapping from an input space to an action space, which is particularly suitable when the action is an optimal decision with respect to a certain unknown cost function. We use an inverse optimization approach to retrieve the cost function by introducing a new loss function and a new hypothesis class of mappings. A tractable convex reformulation of the learning problem is also presented. The method is effective for learning input-action mapping in continuous input-action space with input-output constraints, typically present in control systems. The learning approach can be effectively transformed to learn a Model Predictive Control (MPC) behaviour and a case study to mimic an MPC is presented, which is a rather computationally heavy control strategy. Simulation and experimental results show the effectiveness of the proposed approach.

@en

Multi-sensor networks are becoming more and more popular in order to assess the post-occupancy performance of smart buildings, since they enable continuous monitoring with a high spatial resolution of the occupancy, thermal comfort and indoor air quality. An urgent, but poorly attended topic in this field is the automated detection of sensor anomalies. For example, CO2-sensors can perform auto-calibration, during which the data is not reliable. Without identifying the poor reliability of this data, any analysis based on it may be misleading. Automated detection and diagnosis of multi-sensor anomalies is a challenging task due to the complex characteristics of each data point, the variety of data points and the sheer number of data points. As a result, rule-based algorithms require an extensive expert-based set of rules, which makes them sensitive to threshold values and case specific exceptions. Machine learning algorithms can overcome these issues, but they require datasets with labelled sensor anomalies to do diagnosis. Acquiring such labelled datasets is labour intensive and therefore expensive. In this paper we show the potential of a transition from an unsupervised to a supervised machine learning approach. The unsupervised algorithm is used to detect anomalies and to identify anomaly classes of interest. This enables for labelling such classes efficiently in order to train classifiers for multiple classes of anomalies. The unsupervised and supervised algorithms are employed in parallel during the transition, allowing for the simultaneous detection of unknown anomaly classes and diagnosis of known anomaly classes. The improved performance of the combined classifier compared to unsupervised detection is shown by the precision-recall curve. Though the presented approach is rather generic, it does have some limitations. Because a window-based approach is used, only time windows can be detected as being anomalous, not the exact time. Also, we focus on the detection of sudden anomalies and the approach does not allow for detecting stationary or trend anomalies.@en

In this paper, we present a methodology for actuator and sensor fault estimation in nonlinear systems. The method consists of augmenting the system dynamics with an approximated ultra-local model (a finite chain of integrators) for the fault vector and constructing a Nonlinear Unknown Input Observer (NUIO) for the augmented dynamics. Then, fault reconstruction is reformulated as a robust state estimation problem in the augmented state (true state plus fault-related state). We provide sufficient conditions that guarantee the existence of the observer and stability of the estimation error dynamics (asymptotic stability of the origin in the absence of faults and ISS guarantees in the faulty case). Then, we cast the synthesis of observer gains as a semidefinite program where we minimize the ℒ 2 -gain from the model mismatch induced by the approximated fault model to the fault estimation error. Finally, simulations are given to illustrate the performance of the proposed methodology.@en

The main objective of this article is to develop scalable dynamic anomaly detectors with high-fidelity simulators of power systems. On the one hand, models in high-fidelity simulators are typically 'intractable' if one opts to describe them in a mathematical formulation in order to apply existing model-based approaches from the anomaly detection literature. On the other hand, pure data-driven methods developed primarily in the machine learning literature neglect our knowledge about the underlying dynamics of power systems. In this study, we combine tools from these two mainstream approaches to develop a data-assisted model-based diagnosis filter utilizing both the knowledge from a picked abstract model and also the data of simulation results from high-fidelity simulators. The proposed diagnosis filter aims to achieve two desired features: (i) performance robustness with respect to model mismatch; (ii) high scalability. To this end, we propose a tractable (convex) optimization-based reformulation in which decisions are the filter parameters, the model-based information introduces feasible sets, and the data from the simulator forms the objective function to-be-minimized regarding the effect of model mismatch on the filter performance. To validate the theoretical results, we implement the developed diagnosis filter in DIgSILENT PowerFactory to detect false data injection attacks on the Automatic Generation Control measurements in the three-area IEEE 39-bus system.

@en

We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a p-dimensional Gaussian random vector from n independent samples. The proposed model minimizes the worst case (maximum) of Stein’s loss across all normal reference distributions within a prescribed Wasserstein distance from the normal distribution characterized by the sample mean and the sample covariance matrix. We prove that this estimation problem is equivalent to a semidefinite program that is tractable in theory but beyond the reach of general-purpose solvers for practically relevant problem dimensions p. In the absence of any prior structural information, the estimation problem has an analytical solution that is naturally interpreted as a nonlinear shrinkage estimator. Besides being invertible and well conditioned even for p > n, the new shrinkage estimator is rotation equivariant and preserves the order of the eigenvalues of the sample covariance matrix. These desirable properties are not imposed ad hoc but emerge naturally from the underlying distributionally robust optimization model. Finally, we develop a sequential quadratic approximation algorithm for efficiently solving the general estimation problem subject to conditional independence constraints typically encountered in Gaussian graphical models.

@en

In this article, we investigate the problem of practical output regulation, i.e., to design a controller that brings the system output in the vicinity of a desired target value while keeping the other variables bounded. We consider uncertain systems that are possibly nonlinear and the uncertainty of their linear parts is modeled element wise through a parametric family of matrix boxes. An optimization-based design procedure is proposed that delivers a continuous-time control and estimates the maximal regulation error. We also analyze an event-triggered emulation of this controller, which can be implemented on a digital platform, along with an explicit estimate of the regulation error.

@en