Jul 2026· Engineering Research Express· Vol 8, pp. 145212· 0 citations· 29 references
Physics
TL;DR
This paper presents an adaptive-gain AHD in which a network combining convolutional, recurrent, and attention layers is trained offline and deployed online to predict, from a short window of the raw noisy signal, the smallest gain that meets a prescribed velocity-accuracy target.
Abstract
Derivative estimation from noisy sensor measurements is a fundamental requirement in feedback control, and any such estimator is subject to an inherent trade-off between tracking speed and noise rejection. In the augmented homogeneous differentiator (AHD), this trade-off is governed by a single scalar gain. A large gain tracks fast transients but amplifies noise, whereas a small gain attenuates noise at the cost of a slower response, and no fixed value remains suitable when the signal statistics vary over time. This paper presents an adaptive-gain AHD in which a network combining convolutional, recurrent, and attention layers is trained offline and deployed online to predict, from a short window of the raw noisy signal, the smallest gain that meets a prescribed velocity-accuracy target. Using the raw noisy signal rather than the differentiator output as the network input avoids a direct feedback path from that output to the predictor. On a held-out window-level test set, the predictor attains R2=0.9834. In a frequency-sweep test, the adaptive scheme reduces the first-order velocity-estimation error by 99.3 % relative to a fixed gain tuned for the low-frequency regime. In a step test, it reduces the steady-state third-order derivative noise by 87.2 %. In closed-loop control of a variable-length pendulum, it reduces the control-input total variation by 32 % while preserving tracking accuracy.
This article addresses the problem of online estimation of the derivatives of a signal corrupted by measurement noise. The measured signal is modeled as the sum of a smooth nominal component and a uniformly bounded noise term. A key objective is to attenuate the effect of high‐frequency noise. A natural approach is to filter the measured signal before feeding it to the differentiator. However, this generally prevents exact estimation, even in the noise‐free case. Recently, filtering differentiators have been proposed to attenuate measurement noise while preserving exact derivative estimation in the absence of noise. This article extends existing filtering differentiator designs in several directions. First, we propose and analyze filtering differentiators based on homogeneity in the bi‐limit, which combine the robustness properties of bi‐limit homogeneous estimation with the noise‐attenuation capabilities provided by filtering. Second, we consider a broader class of filters, including general strongly observable LTI systems and nonlinear alternatives. We show that, in the absence of noise, the proposed differentiators recover the exact derivatives of the base signal. In addition, we provide a rigorous analysis of the effect of measurement noise and derive estimation‐error bounds for the corresponding bi‐homogeneous differentiators. The results are established through Lyapunov‐based arguments and illustrated by numerical examples.
Jaime A. Moreno, A. Levant· International Journal of Rob...· 0 citations
Actuator dead-zones are a common and troublesome nonlinearity in motion control: a band of commanded effort over which the plant does not respond, leaving a steady-state offset or a limit cycle. This paper proposes a data-driven architecture that compensates such mismatches without a model of the plant and without any parameterization of the dead-zone. The central idea is to identify, alongside the velocity-form predictor used for control, a second absolute subspace predictor. Because the absolute predictor carries no integral action, it behaves as a data-driven steady-state sensor, so a persistent actuator mismatch appears as a proportional prediction residual. Embedding this residual as a proxy in a behavioral Hankel matrix reduces the mismatch estimate to a single fixed orthogonal projection evaluated online, with no dynamic estimator, no injected probing signal, and no run-time prediction-error computation. Integrated into a subspace predictive controller, the framework is shown to be recursively feasible and practically input-to-state stable, and it recovers offset-free tracking once the dead-band traversal settles. The approach is validated in real time on a sixth-order, lightly damped Quanser multi-DOF torsion system, whose complex-conjugate poles give a lightly damped open-loop response, achieving offset-free tracking across a $\pm 0.18$\,V actuator dead-band. A second study on a high-precision power amplifier shows that the same architecture rejects dead-time-induced nonlinearities in fast-switching power electronics.
In adaptive control, parametric uncertainties in linear-in-parameter form consist of unknown parameters and known regressor signals. Convergence of the unknown parameters to their ideal values requires the regressor to satisfy a persistent excitation (PE) condition, which depends on future data and is therefore infeasible to guarantee online. Memory-based parameter update laws address this by enabling ideal parameter convergence under the online-verifiable finite excitation (FE) condition. In this paper, a new algorithm is proposed to construct a memory term via the Modified Gram-Schmidt orthogonalization procedure for a class of multi-input multi-output nonlinear systems with an unknown diagonal control effectiveness matrix and bounded nonparametric uncertainties. Under the finite excitation condition, the constructed memory term yields an identity coefficient matrix in the parameter estimation error dynamics. The identity coefficient matrix eliminates the need for time-varying adaptation gains, enables an explicit ultimate bound on the parameter estimation error, and preserves the structure of the nonparametric uncertainty bound under the memory term. Building on this, a combined adaptation law is developed for controller gain estimation under FE. The closed-loop tracking and estimation errors are shown to decay exponentially to a neighborhood of the origin, characterized by an explicit ultimate bound, with a decay rate that depends solely on user-defined gains and system constants, independent of the level of regressor excitation. This removes the dependence of the convergence rate on the level of regressor excitation, a key limitation of existing approaches such as concurrent learning, memory regressor extension, and DREM.
This paper studies a robust composite higher-order feedback iterative learning control method for affine nonlinear discrete-time systems. The considered system is subject to input saturation, randomly varying trial lengths, random initial state shifts, and external disturbances. In the controller formulation phase, a Bernoulli stochastic sequence is used to model the data dropout phenomenon caused by non-uniform trial lengths. To address information loss caused by varying trial lengths, a composite control law is developed by combining a higher-order feedforward learning term with a real-time feedback term. The proposed method uses input and error information from several previous trials to compensate for the loss of learning information caused by non-uniform trial lengths. Based on mathematical induction, it is shown that the mathematical expectation of the tracking error gradually converges towards a strictly bounded residual neighborhood. It can be clearly shown that the analytical limits of this area are related to the magnitude of external disturbances and the variations in the initial state. Moreover, in optimal circumstances, the suggested algorithm ensures the rigorous asymptotic convergence of the anticipated error to zero. Finally, numerical simulations support the theoretical analysis and show that the proposed method maintains satisfactory tracking performance under the considered nonideal factors.
Jinyi Chen, Hao Chen, Can Tian et al.· Mathematics· 0 citations
This paper addresses the prescribed-time (PT) tracking control problem for a class of nonlinear systems subjected to nonvanishing uncertain disturbances. To address the issue of discontinuous observation error derivatives caused by parameter constraints in conventional prescribed-time observer (PTO) designs, an improved PTO with a novel time-varying gain structure is proposed. The proposed observer removes the need for additional parameter conditions, ensures global continuity of the observation error derivatives, and enables smooth disturbance estimation and control input switching. To handle the inherent complexity explosion issue in backstepping design, a finite-time command filter (FTCF) is subsequently employed to approximate the virtual control signals. The continuity properties of the signals provided by the aforementioned observer naturally satisfy the requirement of the command filter that the input signal be continuous and possess a first-order derivative over the domain of definition. An adaptive compensation mechanism is further developed to correct the approximation errors introduced by the command filter in an online manner. Simulation results demonstrate that the proposed control scheme effectively achieves PT tracking control with prescribed performance for nonlinear systems under nonvanishing disturbances, while ensuring the continuity and boundedness of all closed-loop signals. Note to Practitioners—The practical control of nonlinear systems, such as robotic manipulators and uncrewed vehicles, is significantly complicated by the presence of persistent nonvanishing disturbances. These disturbances, which do not decay to zero over time, can severely degrade tracking performance and even lead to instability. This work proposes a practical PT control framework for nonlinear systems subject to persistent nonvanishing disturbances, enabling error convergence to zero within a user-defined timeframe regardless of initial conditions. The core innovation integrates an improved PTO, a FTCF, and an adaptive event-triggered mechanism (ETM). The improved PTO ensures the global continuity of disturbance estimation error and its derivatives via a novel time-varying gain structure, eliminating the control signal jumps typical at switching instants in traditional PT designs. The FTCF completely circumvents the complexity explosion problem inherent in standard backstepping. The scheme allows engineers to directly and independently prescribe the convergence times for both disturbance observation and final tracking, independent of initial conditions. A prescribed performance function, based on a barrier Lyapunov function, guarantees that the system output adheres to predefined transient and steady-state performance bounds throughout operation. This work provides practitioners with a robust, high-performance, and implementable PT control solution for a wide class of disturbed nonlinear systems.
Haihang Hu, Bo Meng, Zhen Wang et al.· IEEE Transactions on Automat...· 0 citations
Most existing nonlinear adaptive filtering algorithms only account for output noise, neglecting the fact that input noise is also prevalent in practice. Although the recently proposed bias-compensated kernel least mean square (BCKLMS) algorithm addresses input noise in the nonlinear errors-in-variables (EIV) model, it still suffers from two major limitations. First, the use of a fixed-size dictionary restricts network growth but also prevents it from fully capturing the characteristics of the input signal. Second, as an least mean square (LMS) based algorithm, it exhibits poor robustness in the presence of non-Gaussian noise in the output signal. To overcome these issues, this paper proposes the random Fourier bias-compensated filter under general adaptive function (RFFBCGA) algorithm. Within the random Fourier feature based bias-compensated (RFFBC) framework, the proposed algorithm not only maintains a fixed network structure and effectively mitigates input noise interference through the BC term, but also achieves improved characterization of the input signal. Moreover, by leveraging the flexible form of the general adaptive (GA) function, the algorithm's robustness across various noise scenarios is further enhanced. Extensive simulations, including real-world time series prediction tasks, demonstrate the superiority of the proposed method.