This paper studies the problem of fault detection and estimation (FDE) for linear time-invariant (LTI) systems with a particular focus on frequency content information of faults, possibly as multiple disjoint continuum ranges, and under both disturbances and stochastic noise. To ensure the worst-case fault sensitivity in the considered frequency ranges and mitigate the effects of disturbances and noise, an optimization framework incorporating a mixed H_{_}/H₂ performance index is developed to compute the optimal detection filter. Moreover, a thresholding rule is proposed to guarantee both the false alarm rate (FAR) and the fault detection rate (FDR). Next, shifting attention to fault estimation in specific frequency ranges, an exact reformulation of the optimal estimation filter design using the restricted H_∞ performance index is derived, which is inherently non-convex. However, focusing on finite frequency samples and fixed poles, a lower bound is established via a highly tractable quadratic programming (QP) problem. This lower bound together with an alternating optimization (AO) approach to the original estimation problem leads to a suboptimality gap for the overall estimation filter design. The effectiveness of the proposed approaches is validated through applications of a non-minimum phase hydraulic turbine system and a multi-area power system.

Objective. Bi-directional electronic neural interfaces, capable of both electrical recording and stimulation, communicate with the nervous system to permit precise calibration of electrical inputs by capturing the evoked neural responses. However, one significant challenge is that stimulation artifacts often mask the actual neural signals. To address this issue, we introduce a novel approach that employs dynamical control systems to detect and decipher electrically evoked neural activity despite the presence of electrical artifacts. Approach. Our proposed method leverages the unique spatiotemporal patterns of neural activity and electrical artifacts to distinguish and identify individual neural spikes. We designed distinctive dynamical models for both the stimulation artifact and each neuron observed during spontaneous neural activity. We can estimate which neurons were active by analyzing the recorded voltage responses across multiple electrodes post-stimulation. This technique also allows us to exclude signals from electrodes heavily affected by stimulation artifacts, such as the stimulating electrode itself, yet still accurately differentiate between evoked spikes and electrical artifacts. Main results. We applied our method to high-density multi-electrode recordings from the primate retina in an ex vivo setup, using a grid of 512 electrodes. Through repeated electrical stimulations at varying amplitudes, we were able to construct activation curves for each neuron. The curves obtained with our method closely resembled those derived from manual spike sorting. Additionally, the stimulation thresholds we estimated strongly agreed with those determined through manual analysis, demonstrating high reliability ( R 2 = 0.951 for human 1 and R 2 = 0.944 for human 2). Significance. Our method can effectively separate evoked neural spikes from stimulation artifacts by exploiting the distinct spatiotemporal propagation patterns captured by a dense, large-scale multi-electrode array. This technique holds promise for future applications in real-time closed-loop stimulation systems and for managing multi-channel stimulation strategies.

We propose a novel approach to track the state of charge (SoC) of batteries in mobile robots to improve their capabilities. The batteries' status is critical to accomplish their mission, but limited battery life can be a challenge. Our methodology focuses on modeling and estimating the SoC of batteries through system identification and fractional-order models. These models are flexible and can adjust to transient responses, allowing for accurate estimation of battery characteristics. Specifically, we use cubic spline interpolation to obtain the open-circuit voltage (OCV) and the different resistors of the battery model. To estimate the SoC, we deploy a novel approach based on the moving horizon estimation (MHE) algorithm, which is suitable for handling poor initial estimation and constraints on the battery model. We consider the constraint on the peak discharging current, which can limit the performance of mobile robots in low-battery mode. We validate our approach by applying system identification and MHE to data from a mobile robot. The results show that our method accurately estimates the SoC despite poor initial values, enabling improved performance for mobile robots.

Proper monitoring of large complex spatially critical infrastructures often requires a sensor network capable of inferring the state of the system. Such networks enable the design of distributed estimators considering only local (partial) measurements, local communication capabilities with nearby sensors, as well as the system model. Solutions often assume perfect knowledge of the system model, and white process and measurement noise, which are limiting in engineering settings. In this paper, we consider the minimum energy setting where the model uncertainty and process and measurement noises are bounded but unknown. We provide the first distributed minimum energy estimator for discrete-time linear time-invariant systems, and we show that the error dynamics is input-to-state stable. Lastly, we illustrate the performance in some pedagogical examples, and compare the performance with respect to the centralized implementation of the minimum energy estimator.