Additive Disturbances Research Articles

Output feedback control with performance recovery analysis for a class of time-delay nonlinear systems

A class of nonlinear systems is considered in this paper which contains multiple time-varying delays and additional disturbances. Motivated by a robust model-free state-feedback controller, an observer-based output-feedback controller is designed to achieve uniformly ultimately bounded tracking. A high-gain-like observer is designed to estimate the unmeasurable current states utilizing the delayed output, and the estimated states are further used to facilitate the development of the output-feedback controller. The control input is saturated to avoid the side effects resulting from the high-gain-like observer’s peaking phenomenon. Under some sufficient conditions, it is proved that the saturation of the controller will no longer take place after a specific time, and both the estimation error and the tracking error will be uniformly ultimately bounded. In the stability analysis, Lyapunov–Krasovskii functionals are implemented to alleviate the difficulties resulting from the delays. Relationships among the delays, the desired trajectories, and the maximal tolerable error are identified. Behaviors of the closed-loop system under different observation and control gains are also analyzed. A two-link revolute robotic arm is taken as an example to conduct a series of simulations, and the results show that the output-feedback controller can recover the performance of the corresponding state-feedback controller.

Treatment of atrial tachycardia arising after superior transseptal approach mitral valve surgery: Insights from ultra‐high‐density mapping to prevent atrioventricular block

Mitral valve surgery employing a superior transseptal approach (STA) is associated with arrhythmogenicity and intra-atrial conduction delay, despite being optimal for visualization of the surgical field. It is sometimes difficult to treat atrial tachycardias (AT) that arise after STA. To investigate AT circuits that arise after STA in detail in order to identify the optimal ablation line, using ultra high-resolution mapping (UHRM). We retrospectively analyzed 12 AT from 10 patients (median age 70 years, 9 males) who had undergone STA surgery. The tachycardias were mapped using the Rhythmia mapping system (Boston Scientific, Natick, Massachusetts). The 12 STA-related AT (STA-AT) circuits were classifiable as follows according to location of the optimal ablation line: (1) peri-septal incision STA-AT (n = 3), (2) cavotricuspid isthmus dependent STA-AT (n = 7) and (3) biatrial tachycardia (n = 2). Radiofrequency (RF) application terminated 11 of the 12 STA-AT. We found that difference in STA-AT circuit type was due to characteristics of the septal incision line made for STA. UHRM was important in identifying optimal ablation sites that did not create additional conduction disturbances in the right atrium. ATs after STA involve complex arrhythmia circuits due to multiple and long incision lines in the right atrium. Accurate understanding of the arrhythmia circuit and sinus conduction in the right atrium after STA is recommended for treating post-surgical tachycardia in a minimally invasive manner. This article is protected by copyright. All rights reserved.

Linear time-varying matched filter for known and unknown SOI generalized cyclostationary signal with multiple cyclic frequencies

Chirp cyclic matched filter has been designed for chirp cyclostationary (CCS) signals, a kind of generalized cyclostationary signals, recently. However, it is designed based on statistical prior information and waveform of the signal-of-interest (SOI) CCS signal, which works only for CCS signal with a single chirp cyclic frequency. As known, the prior information of SOI signal may not be exactly known or the measured waveform of SOI signal is noised in practical applications, which decreases performance of the algorithm. In this study, by decomposing the imprecisely known SOI signal as the summation of SOI signal and an unknown additive disturbance, three kinds of chirp cyclic matched filters are designed according to the value of signal-to-noise ratio (SNR). Furthermore, noticing the CCS signal usually contains multiple chirp cyclic frequencies, three kinds of combined chirp cyclic matched filter are designed for known/unknown SOI CCS signals by linearly combining the chirp cyclic matched filter at every chirp cyclic frequency. Moreover, ramifications of the truncation process and complexity of the proposed algorithms are analyzed. Finally, simulation results validate the improvement of the chirp cyclic matched filter based on multiple chirp cyclic frequencies than on a single chirp cyclic frequency in different SNR situations.

Semi-discrete optimal transport: hardness, regularization and numerical solution

Semi-discrete optimal transport problems, which evaluate the Wasserstein distance between a discrete and a generic (possibly non-discrete) probability measure, are believed to be computationally hard. Even though such problems are ubiquitous in statistics, machine learning and computer vision, however, this perception has not yet received a theoretical justification. To fill this gap, we prove that computing the Wasserstein distance between a discrete probability measure supported on two points and the Lebesgue measure on the standard hypercube is already #P-hard. This insight prompts us to seek approximate solutions for semi-discrete optimal transport problems. We thus perturb the underlying transportation cost with an additive disturbance governed by an ambiguous probability distribution, and we introduce a distributionally robust dual optimal transport problem whose objective function is smoothed with the most adverse disturbance distributions from within a given ambiguity set. We further show that smoothing the dual objective function is equivalent to regularizing the primal objective function, and we identify several ambiguity sets that give rise to several known and new regularization schemes. As a byproduct, we discover an intimate relation between semi-discrete optimal transport problems and discrete choice models traditionally studied in psychology and economics. To solve the regularized optimal transport problems efficiently, we use a stochastic gradient descent algorithm with imprecise stochastic gradient oracles. A new convergence analysis reveals that this algorithm improves the best known convergence guarantee for semi-discrete optimal transport problems with entropic regularizers.

Robust MPC for LPV systems via a novel optimization-based constraint tightening

We propose a novel approach to design a robust Model Predictive Controller (MPC) for constrained uncertain linear systems. The uncertain system is modeled as linear parameter varying with an additive disturbance. Set bounds for the system matrices and the additive uncertainty are assumed to be known. We formulate a novel optimization-based constraint tightening strategy around a predicted nominal trajectory which utilizes these bounds. With an appropriately designed terminal cost function and constraint set, we prove robust satisfaction of the imposed constraints by the resulting MPC in closed-loop with the uncertain system, and Input to State Stability of the origin. We highlight the efficacy of our proposed approach via a numerical example.

Guaranteed Cost Control for Interval Type-2 Fuzzy Semi-Markov Switching Systems Within a Finite-Time Interval

This article focuses on the finite-time guaranteed cost (FTGC) control problem for interval type-2 (IT2) fuzzy semi-Markov switching systems (S-MSSs) with additive disturbances. Based on the IT2 fuzzy S-MSSs and the state feedback control method, a novel IT2 mode-dependent fuzzy guaranteed cost (GC) controller is developed under the mismatched membership functions. Then, some new sufficient conditions are given to ensure that IT2 fuzzy S-MSSs are finite-time (FT) stochastically stable based on the designed IT2 mode-dependent fuzzy GC controller. Furthermore, the transition rate boundary condition is relaxed, and a new incomplete transition rate boundary model is constructed to reflect the transition rate information. For both the incomplete transition rate boundaries and the actuator fault phenomenon, the improved stability criteria are provided to stabilize the IT2 fuzzy S-MSSs within an FT interval and determine the gains of the IT2 mode-dependent fuzzy GC controller, resulting in a much greater design flexibility. Distinct from the existing results, the presented FTGC control scheme is more suitable for many practical systems because the IT2 fuzzy S-MSS model, which is more general compared with the traditional fuzzy system and S-MSSs, is considered. Finally, three illustrative examples are offered to explain the effectiveness and feasibility of the proposed FTGC control approach.

Breaking the Convergence Barrier: Optimization via Fixed-Time Convergent Flows

Accelerated gradient methods are the cornerstones of large-scale, data-driven optimization problems that arise naturally in machine learning and other fields concerning data analysis. We introduce a gradient-based optimization framework for achieving acceleration, based on the recently introduced notion of fixed-time stability of dynamical systems. The method presents itself as a generalization of simple gradient-based methods suitably scaled to achieve convergence to the optimizer in a fixed-time, independent of the initialization. We achieve this by first leveraging a continuous-time framework for designing fixed-time stable dynamical systems, and later providing a consistent discretization strategy, such that the equivalent discrete-time algorithm tracks the optimizer in a practically fixed number of iterations. We also provide a theoretical analysis of the convergence behavior of the proposed gradient flows, and their robustness to additive disturbances for a range of functions obeying strong convexity, strict convexity, and possibly nonconvexity but satisfying the Polyak-Łojasiewicz inequality. We also show that the regret bound on the convergence rate is constant by virtue of the fixed-time convergence. The hyperparameters have intuitive interpretations and can be tuned to fit the requirements on the desired convergence rates. We validate the accelerated convergence properties of the proposed schemes on a range of numerical examples against the state-of-the-art optimization algorithms. Our work provides insights on developing novel optimization algorithms via discretization of continuous-time flows.

Trajectory tracking control with convergence time assessment

This paper presents a general procedure for state feedback trajectory tracking control design for a class of nonlinear system that combines smoothness, robustness and convergence time assessment and reduction to a prescribed invariant residual set. In particular, it is well adapted to deal with the trajectory tracking control of a half-car kinematic model since only one simple design condition provides the control law that imposes to the closed-loop system, asymptotic tracking of a given trajectory with a prescribed yaw angle orientation. Norm bounded additive matched disturbances are considered in order to establish a trade-off between robustness and speed of convergence. Two examples and a case study are presented and discussed in order to clearly illustrate and compare the theoretical results.

Effects of land use and yak grazing on behavior and body mass of plateau pika in Tibetan plateau rangelands

AbstractThe body mass of small mammals is widely regarded as an indicator of habitat quality, with trade‐offs between anti‐predator and energy‐building behaviors noted across many species and habitat conditions as suggested by optimal foraging theory. In this study, however, grazing by domestic yak was noted to mediate this effect, affecting both the body mass and behaviors of plateau pika, Ochotona curzoniae, which deviated from expected ecological patterns. Specifically, we compared conditions of plateau pika at 16 trap sites across a range of habitats on the Tibetan plateau, each characterized by herders according to their seasonal use as winter, spring, or summer pastures, and to their vegetative conditions. Plateau pika body mass at herders' tent sites where female and young domestic yak sleep was about 6% higher than at yak foraging sites and 10% higher than fenced areas (where yak are excluded) despite the additional disturbance encountered at tent sites. Mean body mass of plateau pika also decreased with increasing slope, and adult body mass was lower in spring compared to winter and summer seasons. Furthermore, more pika burrows were found near herders' tent sites, with burrows exhibiting significantly lower vegetation cover. Pika foraging behavior was most frequent in yak bedding areas (near herders' tent sites), and pika vigilant behavior at yak foraging areas. Recalling that foraging and vigilant (predator avoidance) behaviors constitute energy trade‐offs, we speculate that these unexpected findings may result from the combined effects of soil erosion (due to surface disturbances) and fertilization (with yak dung) at yak resting sites, which could enable higher population densities and body masses of plateau pika despite lower vegetation cover at the tent sites – most likely due to critical behavioral adaptations, ecological dynamics such as predator‐prey relations and other multi‐dimensional and nonlinear reasons.

Deep Learning Piston Aberration Control of Fiber Laser Phased Array By Spiral Phase Modulation

The stochastic parallel gradient descent (SPGD) algorithm is usually employed as the control strategy for phase-locking in fiber laser phased array systems. However, the convergence speed of the SPGD algorithm will slow down as the number of array elements increases. To improve the control bandwidth, the convolutional neural network is introduced to quickly calculate the initial piston aberration in a single step. In addition, the irrationality of the commonly used Mean Square Error (MSE) evaluation function in existing convolutional neural networks is analyzed. A new evaluation function NPCD (Normalized Phase Cosine Distance) is proposed to improve the accuracy of the neural networks. The results show that the piston aberration residual is 0.005 and the power in the bucket (PIB) is 0.993 after accurate preliminary compensation, which means that the system directly enters the co-phase state. We also demonstrate the robustness and scalability by adding additional disturbance and expanding the scale of the array.

Self-triggered adaptive model predictive control of constrained nonlinear systems: A min–max approach

In this paper, a self-triggered adaptive model predictive control (MPC) method is proposed for constrained discrete-time nonlinear systems subject to parametric uncertainties and additive disturbances. Firstly, a real-time zonotope-based set-membership parameter estimator is developed to refine a set-valued description of the time-varying parametric uncertainty based on the available measurements. By approximating the reachable sets for the states between two successive triggering time instants, the proposed estimator can be used for dynamic systems sampled in an aperiodic manner, including the self-triggered scheduling. We leverage this estimation scheme to design a novel self-triggered adaptive MPC (ST-AMPC) approach for uncertain nonlinear systems. Compared with the existing self-triggered robust MPC methods, the proposed ST-AMPC method can further reduce the average sampling frequency while preserving comparable closed-loop performance. We theoretically show that, under some reasonable assumptions, the proposed ST-AMPC algorithm is recursively feasible, and the closed-loop system is input-to-state practical stable (ISpS) at triggering time instants. Numerical experiments and comparisons are conducted to demonstrate the efficacy of the proposed method.

Output feedback control of an uncertain input-delayed nonlinear system with bounded control commands

This study focused on controlling a class of nonlinear systems with actuation time delays. We proposed a novel output-feedback controller in which the magnitude of the input commands is saturated and can be adjusted by varying control parameters. In this design, a predictor term is used to compensate for delays in the input, and auxiliary systems are exploited to provide a priori bounded control commands and account for the lack of full-state information. The stability analysis results revealed that uniformly ultimately bounded tracking is guaranteed despite modeling uncertainties and additive time-varying disturbances in the system dynamics. The performance of the controller was evaluated through simulation.

Adaptive sliding mode-based active disturbance rejection control for a quadcopter

This paper presents an adaptive sliding mode-based active disturbance rejection control (ASM-ADRC) strategy for the altitude and attitude control of an unmanned quadcopter with disturbances. The quadcopter is an underactuated system subject to parametric perturbations, nonlinearity, unmodeled dynamics, strong coupling, and external disturbances. The proposed algorithm is based on the quadcopter’s dynamic model, where the effects of noise and wind are considered additive disturbances. The central concept is to combine the advantages of adaptive sliding mode control (SMC) to accurately track the reference trajectory with the ability of ADRC to reject the parameter uncertainties and external disturbances. The proposed control scheme is verified in simulation studies with sensor noise and external disturbances. The simulation results show that the proposed algorithm can significantly reduce the chattering phenomenon, owing to the estimation capability of the extended state observer (ESO). The proposed method also improves the robustness against modeling errors and disturbances and smoothly tracks the reference trajectory.

Robustness of Vibrational Control in the Presence of Additive Disturbances

Vibrational control seeks to stabilize an unstable system by judiciously injecting a state-free high-frequency dither. This article presents some robustness properties of vibrational control with respect to additive disturbances in a nonlinear system. We assume that, without disturbances, the appropriately averaged system is regionally asymptotically stable. Using perturbation techniques, our first result shows that the stabilization realized through vibrational control is robust with respect to additive disturbances of sufficiently small amplitude. Indeed, the perturbed system of vibrational control has a robustness feature similar to input-to-state stability in a local region. In the case of periodic disturbances, our second result indicates that vibrational control naturally dampens disturbances of sufficiently high frequency, which allows for relatively high amplitude disturbances. A tight bound for the effect of such periodic disturbances on the ultimate deviation of states from the desired equilibrium is presented. Simulation results from a planar manipulator support the theoretic analysis.

A Low Complexity Robust Output Synchronization Protocol With Prescribed Performance for High-Order Heterogeneous Uncertain MIMO Nonlinear Multiagent Systems

We consider the problem of synchronizing, with prescribed transient and steady-state performance guarantees, the output of high-order, nonlinear, multiagent systems in a leader–following scenario. The agent dynamics are MIMO in lower triangular form and uncertain, as all nonlinearities are unknown and moreover they are perturbed by external additive disturbances. Furthermore, no knowledge is provided regarding bounds or functions bounding the actual system nonlinearities. In addition, the dynamic orders of all agents may not be the same. Each agent utilizes only relative output information from its neighbors and its own state. The underlying communication graph is directed. The proposed control protocol is distributed and of low analytic and computational complexity; thus facilitating implementation. Simulation studies clarify the approach and highlight the theoretical findings.

Poor Sleep in Community-Dwelling Polysubstance Users: Association With Khat Dependence, Metacognition, and Socio-Demographic Factors.

PurposePoor sleep and cognitive deficits are often associated with increased drug use. However, no study has addressed the relationship between poor sleep, substance dependence, and metacognitive deficit in polysubstance users.MethodsThis was a cross-sectional study with a simple random sampling involving community-dwelling polysubstance users (n = 326, age = 18–43 years) in Mizan, Ethiopia. Participants completed a brief sleep questionnaire, severity of dependence on khat (SDS-Khat), a brief meta-cognition questionnaire, and a socio-demographic survey.ResultsMajority (56.4%) of the polysubstance users had sleep disturbance. Chronic health conditions [adjusted odds ratio (AOR) = 2.52, 95% confidence interval (CI) 1.31–4.85], chronic conditions in the family (AOR = 2.69, 95% CI 1.40–5.20), illiterate-primary level of educational status (AOR = 2.40, 95% CI 1.30–4.04), higher SDS-Khat score (AOR = 1.39, 95% CI 1.13–1.72), and lower meta-cognition score (AOR = 0.90, 95% CI 0.84–0.97) predicted poor sleep in the polysubstance users. Moreover, low metacognition score and high SDS score also predicted additional sleep disturbances like chronic sleep insufficiency, lethargy and restlessness after nighttime sleep, socio-occupational dysfunctions, and daytime disturbances in polysubstance users.ConclusionPoor sleep, severe khat dependence, and metacognitive deficits are common in community polysubstance users. Moreover, poor sleep is associated with higher khat dependence, lower metacognitive ability, lower educational status, and the presence of chronic conditions in polysubstance users or their families.

High-gain interval observer for continuous–discrete-time systems using an LMI design approach

In this paper, a high-gain interval observer (HGIO) for a class of partially linear continuous-time systems with sampled measured outputs in the presence of bounded noise and additive disturbances is proposed. The design of the HGIO is formulated in the Linear Matrix Inequality (LMI) framework. The gain of the HGIO is designed to satisfy the cooperative property using a time-varying change of coordinates based on pole placement in separate LMI regions. Moreover, a procedure for designing the HGIO gain to minimise the effect of the noise and disturbance in the estimation is provided. The stability of the proposed HGIO is also guaranteed. The proposed approach is assessed in simulation using a numerical example.

Unsteady aerodynamic modelling for dual-rotor wind turbines with lifting surface method and free wake model

A time-marching aerodynamic model for dual-rotor wind turbines (DRWT) is presented with the lifting surface method and free wake model. The performance of a reference DRWT by two axial connected NREL 5MW wind turbines is calculated to verify the algorithm. The output converges with remarkable oscillation. Free wakes swell under the coupling effect. The accumulated power of DRWT outranges single-rotor wind turbine (SRWT) by a limited extent under certain operating conditions. The front rotor (FR) produces the major portion of the power, especially for low inflow velocity. The unsteadiness of performance and spanwise load is further investigated, and the result shows that the power output of the rear rotor (RR) undergoes greater fluctuation than FR. The rotor-rotor induction strengthens both the rotors’ performance before they align and weakens it when they rotate away. The additional disturbance caused by FR’s tip vortices acts negatively on RR’s torque by upwashing the blade tip.

Advanced Contouring Compensation Approach via Newton-ILC and Adaptive Jerk Control for Biaxial Motion System

To achieve the precision contouring performance, this article presents a contouring compensation approach for the biaxial motion system even under extreme contour tasks. Two permanent magnet linear synchronous motors are installed in the biaxial motion platform. First, the dynamics of the biaxial motion servo system with the uncertainties such as model parameter variations, additive disturbance, and nonlinear friction are introduced. Since Newton algorithm is provided to realize dynamic contouring error estimation, accurate estimation of the contouring error can be achieved, even for the high velocity and complex contour with sharp corners and large curves. Then, iterative learning control (ILC) is used to control the contouring error for contouring performance improvement. An adaptive PD-type learning law based on an asymmetric Gaussian-like function is applied to improve the performance of the system. Moreover, adaptive jerk control (AJC) integrated with adaptive feedback gain is designed to address the negative effect of the uncertainties and enhance the robustness. The adaptive feedback gain is dominated and tuned by a novel adaptation law without the need for prior bound knowledge of the uncertainties. Meanwhile, parameter estimation is employed to handle the model parameter variations. Finally, the experimental results are presented to validate the efficiency and the achievable contouring performance of the proposed Newton-ILC and AJC approach.

Three-dimensional direct numerical simulation of Rayleigh–Taylor instability triggered by acoustic excitation

Rayleigh–Taylor instability (RTI) occurs when the interface between two fluids of different densities is removed, with the heavier (cold) fluid resting on top of the lighter (hot) fluid in the equilibrium state. This arrangement is unstable due to buoyancy, in the absence of any other forces. RTI is noted across a range of length scales from very small in nuclear fusion to supernova explosion at astrophysical scales. RTI is viewed as a baroclinic instability if viscous actions are ignored. An accurate non-overlapping parallel algorithm is used to solve a three-dimensional RTI problem, employing more than 4 × 109 points and a refined time step (7.69×10−8s) for the direct numerical simulation. Air masses at two different temperatures are initially separated by a non-conducting partition inside a box (with a temperature difference of 200 K). The impermeable partition is removed impulsively at t = 0, and the ensuing instability is triggered by an acoustic mechanism involving infra to ultrasonic pulses that travel to either side of the interface. Present high precision petascale computations enable one to capture acoustic disturbances with unprecedented accuracy without any additional interfacial disturbances. The creation of the vorticity is studied by performing enstrophy budget for the compressible flow for RTI, which shows that the viscous terms are dominant compared to the baroclinic one.