Stabilization With Prescribed Instant via Lyapunov Method

Dear Editor,This letter presents a prescribed-instant stabilization approach to high-order integrator systems by the Lyapunov method. Under the presented controller, the settling time of controlled systems is independent of the initial conditions and equals the prescribed time instant.

Prescribed-Time Fully Distributed Nash Equilibrium Seeking Strategy in Networked Games

Dear Editor, This letter is concerned with prescribed-time fully distributed Nash equilibrium seeking for networked games under directed graphs. An adaptive algorithm is proposed to ensure the convergence of all players to the Nash equilibrium without requiring any knowledge of global parameters. Moreover, it is theoretically proved that the convergence time of the proposed seeking strategy can be predefined based on practical requirements. Finally, a numerical example is presented to validate the effectiveness of the proposed method.

Prescribed-Time Nash Equilibrium Seeking for Pursuit-Evasion Game

Dear Editor,This letter is concerned with prescribed-time Nash equilibrium(PTNE)seeking problem in a pursuit-evasion game(PEG)involving agents with second-order dynamics.In order to achieve the prior-given and user-defined convergence time for the PEG,a PTNE seeking algorithm has been developed to facilitate collaboration among multiple pursuers for capturing the evader without the need for any global information.Then,it is theoretically proved that the prescribedtime convergence of the designed algorithm for achieving Nash equilibrium of PEG.Eventually,the effectiveness of the PTNE method was validated by numerical simulation results.A PEG consists of two groups of agents:evaders and pursuers.The pursuers aim to capture the evaders through cooperative efforts,while the evaders strive to evade capture.PEG is a classic noncooperative game.It has attracted plenty of attention due to its wide application scenarios,such as smart grids[1],formation control[2],[3],and spacecraft rendezvous[4].It is noteworthy that most previous research on seeking the Nash equilibrium of the game,where no agent has an incentive to change its actions,has focused on asymptotic and exponential convergence[5]-[7].

Adaptive Consensus of Uncertain Multi-Agent Systems With Unified Prescribed Performance

Dear Editor,An adaptive consensus control algorithm for uncertain multi-agent systems(MAS),capable of guaranteeing unified prescribed performance,is presented in this letter.Unlike many existing prescribed performance related works,the developed control exhibits some features.Firstly,a distributed prescribed time observer is introduced so that not only each follower is able to estimate the leader’s signal within a predetermined time,but also the control design for each agent is independent with its neighbors.

Finite-time Prescribed Performance Time-Varying Formation Control for Second-Order Multi-Agent Systems With Non-Strict Feedback Based on a Neural Network Observer

This paper studies the problem of time-varying formation control with finite-time prescribed performance for nonstrict feedback second-order multi-agent systems with unmeasured states and unknown nonlinearities.To eliminate nonlinearities,neural networks are applied to approximate the inherent dynamics of the system.In addition,due to the limitations of the actual working conditions,each follower agent can only obtain the locally measurable partial state information of the leader agent.To address this problem,a neural network state observer based on the leader state information is designed.Then,a finite-time prescribed performance adaptive output feedback control strategy is proposed by restricting the sliding mode surface to a prescribed region,which ensures that the closed-loop system has practical finite-time stability and that formation errors of the multi-agent systems converge to the prescribed performance bound in finite time.Finally,a numerical simulation is provided to demonstrate the practicality and effectiveness of the developed algorithm.

A Novel Prescribed-Performance Path-Following Problem for Non-Holonomic Vehicles

The issue of achieving prescribed-performance path following in robotics is addressed in this paper,where the aim is to ensure that a desired path within a specified region is accu-rately converged to by the controlled vehicle.In this context,a novel form of the prescribed performance guiding vector field is introduced,accompanied by a prescribed-time sliding mode con-trol approach.Furthermore,the interdependence among the pre-scribed parameters is discussed.To validate the effectiveness of the proposed method,numerical simulations are presented to demonstrate the efficacy of the approach.

Health behavior outcomes in stroke survivors prescribed wearables for atrial fibrillation detection stratified by age

BACKGROUND Smartwatches have become readily accessible tools for detecting atrial fibrillation(AF).There remains limited data on how they affect psychosocial outcomes and engagement in older adults.We examine the health behavior outcomes of stroke survivors prescribed smartwatches for AF detection stratified by age.METHODS We analyzed data from the Pulsewatch study,a randomized controlled trial that enrolled patients(≥50 years)with a history of stroke or transient ischemic attack and CHA2DS2-VASc≥2.Intervention participants were equipped with a cardiac patch monitor and a smartwatch-app dyad,while control participants wore the cardiac patch monitor for up to 44 days.We evaluated health behavior parameters using standardized tools,including the Consumer Health Activation Index,the Generalized Anxiety Disorder questionnaire,the 12-Item Short Form Health Survey,and wear time of participants categorized into three age groups:Group 1(ages 50-60),Group 2(ages 61-69),and Group 3(ages 70-87).We performed statistical analysis using a mixedeffects repeated measures linear regression model to examine differences amongst age groups.RESULTS Comparative analysis between Groups 1,2 and 3 revealed no significant differences in anxiety,patient activation,perception of physical health and wear time.The use of smartwatch technology was associated with a decrease in perception of mental health for Group 2 compared to Group 1(β=-3.29,P=0.046).CONCLUSION Stroke survivors demonstrated a willingness to use smartwatches for AF monitoring.Importantly,among these study participants,the majority did not experience negative health behavior outcomes or decreased engagement as age increased.

Adaptive admittance tracking control for interactive robot with prescribed performance

An adaptive control approach is presented in this paper for tracking desired trajectories in interactive manipulators. The controller design incorporates prescribed performance functions (PPFs) to improve dynamic performance. Notably, the performance of the output error is confined in an envelope characterized by exponential convergence, leading to convergence to zero. This feature ensures a prompt response from admittance control and establishes a reliable safety framework for interactions. Simulation results provide practical insights,demonstrating the viability of the control scheme proposed in this paper.

Practical Prescribed Time Tracking Control With Bounded Time-Varying Gain Under Non-Vanishing Uncertainties

This paper investigates the prescribed-time control(PTC) problem for a class of strict-feedback systems subject to non-vanishing uncertainties. The coexistence of mismatched uncertainties and non-vanishing disturbances makes PTC synthesis nontrivial. In this work, a control method that does not involve infinite time-varying gain is proposed, leading to a practical and global prescribed time tracking control solution for the strict-feedback systems, in spite of both the mismatched and nonvanishing uncertainties. Different from methods based on control switching to avoid the issue of infinite control gain that involves control discontinuity at the switching point, in our method a softening unit is exclusively included to ensure the continuity of the control action. Furthermore, in contrast to most existing prescribed-time control works where the control scheme is only valid on a finite time interval, in this work, the proposed control scheme is valid on the entire time interval. In addition, the prior information on the upper or lower bound of gi is not in need,enlarging the applicability of the proposed method. Both the theoretical analysis and numerical simulation confirm the effectiveness of the proposed control algorithm.

Trajectory tracking guidance of interceptor via prescribed performance integral sliding mode with neural network disturbance observer

This paper investigates interception missiles’trajectory tracking guidance problem under wind field and external disturbances in the boost phase.Indeed,the velocity control in such trajectory tracking guidance systems of missiles is challenging.As our contribution,the velocity control channel is designed to deal with the intractable velocity problem and improve tracking accuracy.The global prescribed performance function,which guarantees the tracking error within the set range and the global convergence of the tracking guidance system,is first proposed based on the traditional PPF.Then,a tracking guidance strategy is derived using the integral sliding mode control techniques to make the sliding manifold and tracking errors converge to zero and avoid singularities.Meanwhile,an improved switching control law is introduced into the designed tracking guidance algorithm to deal with the chattering problem.A back propagation neural network(BPNN)extended state observer(BPNNESO)is employed in the inner loop to identify disturbances.The obtained results indicate that the proposed tracking guidance approach achieves the trajectory tracking guidance objective without and with disturbances and outperforms the existing tracking guidance schemes with the lowest tracking errors,convergence times,and overshoots.

Practical prescribed-time tracking control for uncertain strict-feedback systems with guaranteed performance under unknown control directions

In this paper,we consider the practical prescribed-time performance guaranteed tracking control problem for a class of uncertain strict-feedback systems subject to unknown control direction.Due to the existence of unknown nonlinearities and uncertainties,it is challenging to design a controller that can ensure the stability of closed-loop system within a predetermined finite time while maintaining the specified transient performance.The underlying problem becomes further complex as the control directions are unknown.To deal with the above problems,a special translation function as well as Nussbaum type function are introduced in the prescribed performance control(PPC)framework.Finally,a PPC as well as preset finite time tracking control scheme is designed,and its effectiveness is confirmed by both theoretical analysis and numerical simulation.

Prescribed-Time Stabilization of Singularly Perturbed Systems

Dear Editor, This letter investigates the prescribed-time stabilization of linear singularly perturbed systems. Due to the numerical issues caused by the small perturbation parameter, the off-the-shelf control design techniques for the prescribed-time stabilization of regular linear systems are typically not suitable here. To solve the problem, the decoupling transformation techniques for time-varying singularly perturbed systems are combined with linear time-varying high gain feedback design techniques.

Modeling and Adaptive Neural Network Control for a Soft Robotic Arm With Prescribed Motion Constraints

This paper presents a dynamic model and performance constraint control of a line-driven soft robotic arm.The dynamics model of the soft robotic arm is established by combining the screw theory and the Cosserat theory.The unmodeled dynamics of the system are considered,and an adaptive neural network controller is designed using the backstepping method and radial basis function neural network.The stability of the closed-loop system and the boundedness of the tracking error are verified using Lyapunov theory.The simulation results show that our approach is a good solution to the motion constraint problem of the line-driven soft robotic arm.

Eff ect of prescribed burning on the small-scale spatial heterogeneity of soil microbial biomass in Pinus koraiensis and Quercus mongolica forests of China

Prescribed burning can alter soil microbial activity and spatially redistribute soil nutrient elements.However,no systematic,in-depth studies have investigated the impact of prescribed burning on the spatial patterns of soil microbial biomass in temperate forest ecosystems in Northeast China.The present study investigated the impacts of prescribed burning on the small-scale spatial heterogeneity of microbial biomass carbon(MBC)and microbial biomass nitrogen(MBN)in the upper(0–10 cm)and lower(10–20 cm)soil layers in Pinus koraiensis and Quercus mongolica forests and explored the factors that infl uence spatial variations of these variables after prescribed burning.Our results showed that,MBC declined by approximately 30%in the 10–20 cm soil layer in the Q.mongolica forest,where there were no signifi cant eff ects on the soil MBC and MBN contents of the P.koraiensis forest(p>0.05)after prescribed burning.Compared to the MBC of the Q.mongolica forest before the prescribed burn,MBC spatial dependence in the upper and lower soil layers was approximately 7%and 2%higher,respectively.After the prescribed burn,MBN spatial dependence in the upper and lower soil layers in the P.koraiensis forest was approximately 1%and 13%lower,respectively,than that before the burn,and the MBC spatial variability in the 0–10 cm soil layer in the two forest types was explained by the soil moisture content(SMC),whereas the MBN spatial variability in the 0–10 cm soil layer in the two forests was explained by the soil pH and nitrate nitrogen(NO_(3)^(–)-N),respectively.In the lower soil layer(10–20 cm)of the Q.mongolica forest,elevation and ammonium nitrogen(NH 4+-N)were the main factors aff ecting the spatial variability of MBC and MBN,respectively.In the 10–20 cm soil layer of the P.koraiensis forest,NO_(3)^(–)-N and slope were the main factors aff ecting the spatial variability of MBC and MBN,respectively,after the burn.The spatial distributions of MBC and MBN in the two forests were largely structured with higher spatial autocorrelation(relative structural variance C/[C 0+C]>0.75).However,the factors infl uencing the spatial variability of MBC and MBN in the two forest types were not consistent between the upper and lower soil layers with prescribed burning.These fi ndings have important implications for developing sustainable management and conservation policies for forest ecosystems.

Robust output regulation problem with prescribed performance for nonlinear strict feedback systems

This paper investigates the problem of robust output regulation control with prospected transient property for strict feedback systems.By employing the internal model principle,the robust output regulation problem with a prospected property can be transformed to a robust stabilization problem with a new output constraint.Then,by constructing the speed function and adopting barrier Lyapunov function technique,the dynamic feedback controller can be designed not only to drive error output of the closed-loop system entering into a prescribed performance bound within a given finite time,but also to achieve that the error output converges to zero asymptotically.The effectiveness of the results is illustrated by a simulation example.

Refined disturbance observer based prescribed performance fixed-time control of high-speed EMS trains with track irregularities

High-speed Electromagnetic Suspension(EMS)train is continuously impacted by the irregularity of the track,which worsens the levitation performance of the train.In this paper,a composite control scheme for the EMS is proposed to suppress track irregularities by integrating a Refined Disturbance Observer(RDO)and a Prescribed Performance Fixed-Time Controller(PPFTC).The RDO is designed to estimate precisely the track irregularities and lumped disturbances with uncertainties and exogenous disturbances in the suspension system,and reduce input chattering by applying to the disturbance compensation channel.PPFTC is designed to converge the suspension air gap error to equilibrium point with prescribed performance by completing error conversion,and solve the fast dynamic issue of EMS.And the boundary of overshoot and steady-state is limited in the ranged prescribed.A theoretical analysis is conducted on the stability of the proposed control method.Finally,the effectiveness and reasonability of the proposed composite anti-disturbance control scheme is verified by simulation results.

Spatial heterogeneity of soil respiration in a Larix gmelinii forest and the response to prescribed fire in the Greater Xing0an Mountains,China

This study was conducted in a fire-prone region in the Greater Xing＇an Mountains, the primary forested area of northeastern China. We measured soil respiration and the affecting soil factors, i.e., soil microbial biomass and soil moisture, within an experimental plot of Larix gmelinii Rupr. A low-intensity, prescribed fire was applied as the treatment. Traditional descriptive statistics and geostatistics were used to analyze the spatial heterogeneity of soil respiration and the response of respiration to fire disturbance. Coefficients of variation （CVs） for pre-fire and post-fire soil respiration were 23.4 and 32.0 %, respec- tively. CVs for post-fire soil respiration increased signifi- cantly, with a moderate variation of all CVs. Soil respiration pre-fire was significantly correlated with soil microbial biomass carbon, biomass nitrogen, and soil moisture （W）; post-fire soil respiration was not correlated with these factors. From the geostatistical analyses, the Co ＋ C （sill） for post-fire soil respiration increased sig- nificantly, indicating that the post-fire spatial heterogeneity of soil respiration increased significantly. The nugget effect （nc） of soil respiration and the affecting factors pre-fire and post-fire disturbance were in the range of 12.5-50 %, with strong spatial autocorrelation. Fire disturbance changed the components of spatial heterogeneity, and the proportion of functional heterogeneity increased significantly post-fire. The ranges （a） for pre-fire and post-fire soil respiration were 81.0 and 68.2 m, respectively. The homogeneity of the distribution of post-fire soil respiration decreased and the spatial heterogeneity increased, thus the range for post- fire soil respiration decreased significantly. The fractal dimension （D） for soil respiration increased post-fire, the spatial heterogeneity of soil respiration affected by random components increased, indicating that the change in spatial heterogeneity of post-fire soil respiration should be con- sidered within the scale of the forest stand. Following Kriging interpolation, the increase in the patchiness of post-fire soil respiration was illustrated using a contour map. Based on these preliminary results, the change in the spatial heterogeneity of post-fire soil respiration was likely caused by changes in the distribution of soil moisture and microbial activity within the experimental plot at the scale of the forest stand.

Dual solutions in boundary layer flow of a moving fluid over a moving permeable surface in presence of prescribed surface temperature and thermal radiation

An analysis of the heat transfer for a boundary layer forced convective flow past a moving permeable flat surface parallel to a moving fluid is presented. Prescribed surface temperature at the boundary is considered, A thermal radiation term in the energy equation is considered. The similarity solutions for the problem are obtained and the reduced ordinary differential equations are solved numerically. To support the validity of the numerical results, a comparison is made with the available results for some particular cases of this study. Dual solutions exist when the surface and the fluid move in the opposite directions.

Prescribed performance neural control to guarantee tracking quality for near space kinetic kill vehicle

A prescribed performance neural controller to guarantee tracking quality is addressed for the near space kinetic kill vehicle (NSKKV) to meet the state constraints caused by side window detection. Different from the traditional prescribed performance control in which the shape of the performance function is constant, this paper exploits new performance functions which can change the shape of their function according to different symbols of initial errors and can ensure the error convergence with a small overshoot. The neural backstepping control and the minimal learning parameters (MLP) technology are employed for exploring a prescribed performance controller (PPC) that provides robust tracking attitude reference trajectories. The highlight is that the transient performance of tracking errors is satisfactory and the computational load of neural approximation is low. The pseudo rate (PSR) modulator is used to shape the continuous control command to pulse or on-off signals to meet the requirements of the thruster. Numerical simulations show that the proposed method can achieve state constraints, pseudo-linear operation and high accuracy.

PID-type fault-tolerant prescribed performance control of fixed-wing UAV

This paper introduces a fault-tolerant control(FTC)design for a faulty fixed-wing unmanned aerial vehicle(UAV).To constrain tracking errors against actuator faults,error constraint inequalities are first transformed to a new set of variables based on prescribed performance functions.Then,the commonly used and powerful proportional-integral-derivative(PID)control concept is employed to filter the transformed error variables.To handle the fault-induced nonlinear terms,a composite learning algorithm consisting of neural network and disturbance observer is incorporated for increasing flight safety.It is shown by Lyapunov stability analysis that the tracking errors are strictly constrained within the specified error bounds.Experimental results are presented to verify the feasibility of the developed FTC scheme.