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This paper proposes an adaptive output‐feedback boundary control scheme to stabilize the vibrations of the moving cage in the dual‐cable mining elevator system assuming the damping coefficients of the cage axial and roll motions are unknown. The mathematical formulation of the system in the Riemann coordinates is described by a 4×4 $ 4\\times 4$hyperbolic partial differential equation (PDE) on a time‐varying domain coupled with an ordinary differential equation (ODE) anti‐collocated with the control input. At first, the nominal non‐adaptive output feedback scheme is formulated by composing a state‐feedback controller with the PDE state observer, utilizing the infinite‐dimensional backstepping technique. Specifically, we apply two backstepping transformations to design the nominal state‐feedback controller. This significantly facilitates the adaptive solutions of the backstepping kernel equations, when unknown parameters are replaced by their time‐varying estimates. Then, a Lyapunov‐based approach is followed to design the update laws for the unknown damping coefficients and to prove the closed‐loop stability. It is shown that all states in the closed‐loop system are uniformly bounded and the cage dynamics is asymptotically stable. A numerical simulation is presented to demonstrate the performance of the proposed controller. This paper proposes an observer‐based adaptive output‐feedback boundary control to stabilize the vibrations of the moving cage of a dual‐cable mining elevator. This system is comprised of two mechanically jointed winding drums that drive the two cables through the floating sheaves to lift the cage. Due to the compliance property of the cables, the system is prone to imbalance problems, including the axial and roll vibrations of the cage. Therefore, besides the motion control force, the vibration control forces are also applied at the floating sheaves, to balance the cage roll and suppress the axial vibrations of the moving cage. The vibration dynamics of the system is described by the time‐dependent moving boundary wave PDE‐ODE model.

Doubly robust estimators are widely used to draw inference about the average effect of a treatment. Such estimators are consistent for the effect of interest if either one of two nuisance parameters is consistently estimated. However, if flexible, data-adaptive estimators of these nuisance parameters are used, double robustness does not readily extend to inference. We present a general theoretical study of the behaviour of doubly robust estimators of an average treatment effect when one of the nuisance parameters is inconsistently estimated. We contrast different methods for constructing such estimators and investigate the extent to which they may be modified to also allow doubly robust inference. We find that while targeted minimum loss-based estimation can be used to solve this problem very naturally, common alternative frameworks appear to be inappropriate for this purpose. We provide a theoretical study and a numerical evaluation of the alternatives considered. Our simulations highlight the need for and usefulness of these approaches in practice, while our theoretical developments have broad implications for the construction of estimators that permit doubly robust inference in other problems.

A robust interacting multiple model approach is proposed to address the problem of accuracy and non‐Gaussian measurement noise in manoeuvering target tracking. The proposed approach introduces multiple fading factors into the prediction covariance matrix and adjusts each channel of the gain matrix in real time to improve the accuracy caused by model mismatch and enhance state transition capability. Considering the non‐Gaussian noise, an improved IMM filter is constructed to further improve the robustness using the maximum correntropy criterion. The simulation results show that the proposed approach can effectively suppress the non‐Gaussian noise and improve the accuracy with adaptability and robustness. The multiple fading factors are constructed for adjusting prediction covariance matrix in the IMM prediction process, and a cost function based on the maximum correntropy criterion is designed in the IMM update step to obtain an iterative state estimation solution by maximizing this function.

In cognitive radio networks, conventional power control algorithms (PCAs) based on instantaneous perfect channel gain may lead to performance degradation in practical systems, since channel uncertainties are inevitable because of quantisation errors and estimation errors. As a result, robustness of the algorithms becomes an important issue. However, traditional robust PCAs with probabilistic models require to perfectly know the distribution information of the estimation error (e.g. Gaussian distribution) which is difficult to obtain. Moreover, the distribution function of the actual error may not be Gaussian distribution. In this study, instead of using deterministic distribution model, a robust PCA based on a distribution‐free method is designed to minimise total transmit power of secondary users subject to probabilistic interference and signal to interference plus noise ratio constraints. Based on the minimax probability machine, the original problem is reformulated as a second order cone programming problem solved by interior‐point method. An adaptive estimation scheme is proposed to estimate the actual mean and covariance matrix of uncertain parameters. Simulation results demonstrate the effectiveness and robustness of the proposed algorithm by comparing with the robust algorithms under worst‐case constraints and probabilistic constraints, respectively.

This article presents a novel approach for adaptive nonlinear state estimation in a modified autoregressive time series with fixed coefficients, leveraging an adaptive polynomial Kalman filter (APKF). The proposed APKF dynamically adjusts the evolving system dynamics by selecting an appropriate autoregressive time‐series model corresponding to the optimal polynomial order, based on the minimum residual error. This dynamic selection enhances the robustness of the state estimation process, ensuring accurate predictions, even in the presence of varying system complexities and noise. The proposed methodology involves predicting the next state using polynomial extrapolation. Extensive simulations were conducted to validate the performance of the APKF, demonstrating its superiority in accurately estimating the true system state compared with traditional Kalman filtering methods. The root‐mean‐square error was evaluated for various combinations of standard deviations of sensor noise and process noise for different sample sizes. On average, the root‐mean‐square error value, which represents the disparity between the true sensor reading and estimate derived from the adaptive Kalman filter, was 35.31% more accurate than that of the traditional Kalman filter. The comparative analysis highlights the efficacy of the APKF, showing significant improvements in state estimation accuracy and noise resilience. The article presents a novel state estimation method for a modified autoregressive time series, utilizing an adaptive polynomial Kalman filter. This approach dynamically adjusts to changing system dynamics by predicting future states through polynomial extrapolation.

Principal component analysis (PCA) is one of the most commonly used statistical procedures with a wide range of applications. This paper considers both minimax and adaptive estimation of the principal subspace in the high dimensional setting. Under mild technical conditions, we first establish the optimal rates of convergence for estimating the principal subspace which are sharp with respect to all the parameters, thus providing a complete characterization of the difficulty of the estimation problem in term of the convergence rate. The lower bound is obtained by calculating the local metric entropy and an application of Fano's lemma. The rate optimal estimator is constructed using aggregation, which, however, might not be computationally feasible. We then introduce an adaptive procedure for estimating the principal subspace which is fully data driven and can be computed efficiently. It is shown that the estimator attains the optimal rates of convergence simultaneously over a large collection of the parameter spaces. A key idea in our construction is a reduction scheme which reduces the sparse PCA problem to a high-dimensional multivariate regression problem. This method is potentially also useful for other related problems.

This paper proposes a new secure distributed estimation for cyber‐physical systems against adversarial attacks with noisy input. To mitigate the effect of attacks, a novel distributed attack detection based on a reliable reference estimation obtained by temporal convex combination is proposed. Furthermore, for more effective and robust performance, an adaptation rule to adjust convex combination weights is presented, in which the generalized correntropy method with nonlinear loss function and stochastic gradient descent are utilized. Besides, to eliminate input noise, a bias‐compensation method in local adaptation of the secure distributed estimation is proposed. Simulations show superior dynamic and real‐time adaptability of the proposed algorithm under complex attacking scenarios. This letter proposes a new secure distributed estimation for cyber‐physical systems against adversarial attacks with noisy input. To mitigate the effect of attacks, a novel adversarial detection method is proposed based on a reliable reference estimation obtained by temporal convex combination and a generalized correntropy based adaptation rule is presented to adjust convex combination weights. Besides, to eliminate input noise, a bias‐compensation method in local adaptation of the secure distributed estimation is proposed.

For the sparse vector model, we consider estimation of the target vector, of its ℓ2-norm and of the noise variance. We construct adaptive estimators and establish the optimal rates of adaptive estimation when adaptation is considered with respect to the triplet “noise level—noise distribution—sparsity.” We consider classes of noise distributions with polynomially and exponentially decreasing tails as well as the case of Gaussian noise. The obtained rates turn out to be different from the minimax nonadaptive rates when the triplet is known. A crucial issue is the ignorance of the noise variance. Moreover, knowing or not knowing the noise distribution can also influence the rate. For example, the rates of estimation of the noise variance can differ depending on whether the noise is Gaussian or sub-Gaussian without a precise knowledge of the distribution. Estimation of noise variance in our setting can be viewed as an adaptive variant of robust estimation of scale in the contamination model, where instead of fixing the “nominal” distribution in advance we assume that it belongs to some class of distributions.

We consider the linear regression problem under semi-supervised settings wherein the available data typically consists of: (i) a small or moderate sized “labeled” data, and (ii) a much larger sized “unlabeled” data. Such data arises naturally from settings where the outcome, unlike the covariates, is expensive to obtain, a frequent scenario in modern studies involving large databases like electronic medical records (EMR). Supervised estimators like the ordinary least squares (OLS) estimator utilize only the labeled data. It is often of interest to investigate if and when the unlabeled data can be exploited to improve estimation of the regression parameter in the adopted linear model. In this paper, we propose a class of “Efficient and Adaptive Semi-Supervised Estimators” (EASE) to improve estimation efficiency. The EASE are two-step estimators adaptive to model mis-specification, leading to improved (optimal in some cases) efficiency under model mis-specification, and equal (optimal) efficiency under a linear model. This adaptive property, often unaddressed in the existing literature, is crucial for advocating “safe” use of the unlabeled data. The construction of EASE primarily involves a flexible “semi-nonparametric” imputation, including a smoothing step that works well even when the number of covariates is not small; and a follow up “refitting” step along with a cross-validation (CV) strategy both of which have useful practical as well as theoretical implications towards addressing two important issues: under-smoothing and over-fitting. We establish asymptotic results including consistency, asymptotic normality and the adaptive properties of EASE. We also provide influence function expansions and a “double” CV strategy for inference. The results are further validated through extensive simulations, followed by application to an EMR study on auto-immunity.

We study the nonparametric maximum likelihood estimator (NPMLE) for estimating Gaussian location mixture densities in d-dimensions from independent observations. Unlike usual likelihood-based methods for fitting mixtures, NPMLEs are based on convex optimization. We prove finite sample results on the Hellinger accuracy of every NPMLE. Our results imply, in particular, that every NPMLE achieves near parametric risk (up to logarithmic multiplicative factors) when the true density is a discrete Gaussian mixture without any prior information on the number of mixture components. NPMLEs can naturally be used to yield empirical Bayes estimates of the oracle Bayes estimator in the Gaussian denoising problem. We prove bounds for the accuracy of the empirical Bayes estimate as an approximation to the oracle Bayes estimator. Here our results imply that the empirical Bayes estimator performs at nearly the optimal level (up to logarithmic factors) for denoising in clustering situations without any prior knowledge of the number of clusters.