Self-triggered Condition Research Articles

Self-triggered fuzzy trajectory tracking control for the stratospheric airship

A self-triggered trajectory tracking control algorithm, which considers unknown disturbance and actuator saturation, has been studied to address the energy and onboard equipment life limitation problems of stratospheric airships. The controller is based on a backstepping-sliding mode method, utilizing the fuzzy logic systems and auxiliary systems to handle unknown disturbance and actuator saturation, respectively. Based on the continuity of the control law, the self-triggered condition is designed whose paradigm is used to build the fuzzy logic systems. Compared with the existing stratospheric airships event-triggered controller, continuous state detection and calculation are avoided. It is proved that the tracking errors and the weight matrix errors of the fuzzy logic system are uniformly ultimately bounded both at the trigger moment and within the trigger interval. Additionally, Zeno behavior is avoided without imposing additional parameter restrictions. Simulation results demonstrate the effectiveness of the proposed algorithm. Based on execution frequency, the proposed algorithm can conserve 98.3% of resources compared to the traditional algorithm and 97.5% of resources compared to the event-triggered algorithm.

Multi-muscle Synergies of Postural Control in Self- and External-Triggered Force Release During Simulated Archery Shooting

We investigated postural stability during simulated archery shooting. The experiment consisted of two force release conditions: self-triggered (time-set in a feedforward fashion) and external cue-triggered (time-set by reacting to external cue) conditions while standing on the force platform. The electromyography of leg muscles and the center of pressure (COP) were recorded. The notions of muscle-modes (M-modes) and multi-muscle synergies were employed to quantify the postural stability, which described covariation patterns of the M-modes to stabilize the COP. The result showed relatively strong postural stability in a self-triggered condition associated with consistent shooting performance. The current findings suggested that initiating force release in a feedforward fashion would be a beneficial strategy to ensure the consistency in shooting performance.

Self-Triggered Control of Multi-Agent Systems With External Disturbances

This paper investigates the consensus of multi-agent systems (MASs) by virtue of event-triggered mechanism. Considering the existence of external disturbances, we use a disturbance observer to estimate the disturbance signals and eliminate the corresponding effects by using estimators to compensate the input control terms. The self-triggered condition is designed and proved that there is no Zeno behavior. We show that the proposed disturbance observer can estimate the external disturbance signals well under the self-triggered condition. Finally, simulation examples are presented to verify the theoretical results.

Aperiodic sampled-data control of distributed networked control systems under stochastic cyber-attacks

This paper examines the stabilization problem of a distributed networked control system under the effect of cyber-attacks by employing a hybrid aperiodic triggering mechanism. The cyber-attack considered in the paper is a stochastic deception attack at the sensor-controller end. The probability of the occurrence of attack on a subsystem is represented using a random variable. A decentralized hybrid sampled-data strategy is introduced to save energy consumption and reduce the transmission load of the network. In the proposed decentralized strategy, each subsystem can decide independently whether its state should be transmitted to the controller or not. The scheme of the hybrid triggering mechanism for each subsystem composed of two stages: In the first stage, the next sampling instant is computed using a self-triggering strategy. Subsequently, in the second stage, an event-triggering condition is checked at these sampling instants and the control signal is computed only if the event-triggering condition is violated. The self-triggering condition used in the first stage is dependent on the selection of event-triggering condition of the second stage. Finally, a comparison of the proposed approach with other triggering mechanisms existing in the literature is presented in terms of the sampling instants, transmission frequency and performance measures through simulation examples.

Self‐triggered robust model predictive control for nonlinear systems with bounded disturbances

A self-triggered model predictive control (MPC) scheme for continuous-time perturbed nonlinear systems subject to bounded disturbances is investigated in this study. A self-triggered strategy is designed to obtain the inter-execution time before the next trigger using the current sampled state. An optimisation problem is addressed to obtain the optimal control trajectory at each triggered instant. The so-called dual-mode approach is used to stabilise the perturbed closed-loop system. Furthermore, sufficient conditions are derived to ensure the feasibility and stability, respectively. It is shown that with a properly designed prediction horizon, the feasibility of the proposed self-triggered MPC algorithm can be guaranteed if the disturbance is bounded in a small enough area. Meanwhile, the stability is proved under the self-triggered condition. Finally, a numerical example is given to illustrate the efficacy of the authors proposed scheme.

Self-Triggered Model Predictive Control for Linear Systems With Switched Cost Functions

This paper investigates the self-triggered model predictive control for networked linear systems. The self-triggered mechanism is designed based on switched cost functions, which can be used to enhance systems performance and are more appropriate for complex industrial requirements in contrast with a single cost function approach. The model predictive controller is designed by solving an optimization problem and the self-triggered condition is designed. With the proposed self-triggered mechanism, much network computation and communication burden are reduced and Zeno behavior can be excluded. Moreover, asymptotic stability of the networked systems with model predictive control strategy is shown via average dwell-time technique. Finally, the numerical simulation example is given to illustrate the effectiveness of the proposed methods.

A Min–Max Approach to Event- and Self-Triggered Sampling and Regulation of Linear Systems

This paper presents both an event- and a self-triggered sampling and regulation scheme for continuous time linear dynamic systems by using zero-sum game formulation. A novel performance index is defined wherein the control policy is treated as the first player and the threshold for control input error due to aperiodic dynamic feedback is treated as the second player. The optimal control policy and sampling intervals are generated using the saddle point or Nash equilibrium solution, which is obtained from the corresponding game algebraic Riccati equation. To determine the optimal event-based sampling scheme, an event-triggering condition is derived by utilizing the worst case control input error as the threshold. To avoid the additional hardware for the event-triggering mechanism, a near optimal self-triggering condition is derived to determine the future sampling instants given the current state vector. To guarantee Zeno-free behavior in both the event- and self-triggered closed-loop systems, the minimum intersample times are shown to be lower bounded by a nonzero positive number. Asymptotic stability of the closed-loop system is ensured using Lyapunov stability analysis. Finally, simulation examples are provided to substantiate the analytical claims.

Output consensus of heterogeneous linear MASs by self-triggered MPC scheme

Abstract In this paper, a self-triggered Model Predictive Control (MPC) scheme is proposed to solve the output consensus problem of heterogeneous linear Multi-agent Systems (MASs). First, a self-triggered condition is designed to determine the time for solving optimization problem of each agent. Then, a self-triggered MPC scheme is built. The scheme not only formulates the aperiodic control form, but also avoids the design of observers for each agent compared with conventional method. On the whole, the communication load and actuator burden can be reduced. Zeno behavior is excluded by detailed analysis. Moreover, parameters selection of the cost function is introduced and analysis of the scheme feasibility is conducted. Sufficient conditions are developed to guarantee the scheme feasibility. Finally, some simulation examples are given to demonstrate the effectiveness of the scheme.

Are gait initiation parameters early markers of Huntington's disease in pre-manifest mutation carriers?

Huntington's disease (HD) pre-manifest mutation carriers (PMCs) present early-onset gait disturbances. Gait initiation encompasses the preparation and execution of the first step. By using paradigms with and without external cues, a gait initiation analysis can highlight the interaction between motor and cognitive aspects of movement preparation and execution. Hence, gait initiation disorders may constitute particularly interesting early markers of HD. The objective of the present study was to quantify gait initiation in PMCs. In a case–control study, 17 PMCs (median age: 36.5) were compared with a group of 25 healthy controls (HCs, median age: 36) for gait initiation and a group of 57 HCs (median age: 38) for gait. Presymptomatic mutation carriers displayed a shorter first step duration and lower-amplitude postural adjustments. For the first step duration and speed, these impairments were more pronounced under self-triggered (ST) conditions. The PMCs displayed a lower gait speed, cadence and stride length and higher stride-to-stride variability. The latter parameter seemed capable of differentiating between PMCs and HCs with adequate sensitivity (0.81) and specificity (0.87). We confirmed the early-onset impairment of gait in general and first step execution in particular in PMCs (particularly under ST conditions). The temporal parameters of step execution (e.g. duration) and spatial parameters of postural adjustment (e.g. a backward shift in the centre of pressure) may be worth investigating as early markers of HD. However, two such parameters (stride-to-stride variability and first step duration under ST conditions) already appear to be sufficiently reliable diagnostic tools for differentiating between PMCs and HCs.

Influence of expectation on postural disturbance evoked by proprioceptive stimulation

Recent experiments have shown that the vestibular channel of balance control differs fundamentally from the visual channel. Whereas the response to a visual perturbation can be suppressed if the subject has awareness that an upcoming disturbance is likely to be caused by an external agent rather than by self-motion, a similar assumption cannot be made concerning the vestibular system. The present experiment investigated whether postural responses evoked by a proprioceptive perturbation (vibration of the Achilles' tendon at 90 Hz for 2.2 s) are either automatic and immune to expectation (similarly to vestibular responses) or cognitively penetrable (similarly to visual responses). Subjects (n = 12) stood on a force platform while stimuli were delivered either by the subject himself (self-triggered condition) or by the experimenter. For the latter condition, the stimulus was delivered either without warning (unpredictable condition) or at a fixed interval (500 ms) following an auditory cue (precue condition). Results showed that the backward CoP displacement induced by vibration was delayed by approximately 500 ms in the expected and self-triggered conditions compared to the unexpected condition. However, once initiated, the velocity of the backward displacement was higher in the self-triggered condition as compared to the unexpected condition. After a period of 2.2 s of vibration, the amplitude of this backward CoP displacement was similar in the three experimental conditions. Therefore, although expectation appears to delay the upcoming of the main backward body sway, it does not appear to be able to weight the impact of the proprioceptive stimulation. This suggested that afferents provided by the different sensory channels involved in postural control are not similarly susceptible to high level processes such as expectation.

A biomechanical study of gait initiation in Huntington's disease

Background Akinesia in basal ganglia disorders is essentially defined by delayed movement initiation; the reaction time increases and it becomes difficult (or even impossible) for the subject to initiate movement. A biomechanical study of gait initiation would help evaluate the role of akinesia in early stage Huntington's disease (HD) patients. Methods We recorded kinematic, spatiotemporal and angular parameters (using video motion analysis, a force platform and an optoelectronic system) for the first two steps taken by 15 HD patients and 15 gender- and age-matched controls. In order to evaluate the influence of an external cue on gait initiation parameters, we studied two movement paradigms: self-triggered initiation and initiation triggered (cued) by a “beep” sound. We analyzed kinematic, spatiotemporal (the speed, length and duration of the two first steps) and angular parameters (range of joint angles) as well as kinetic data (the trajectory of the centre of pressure (COP); the speed and trajectory of the centre of mass (COM)). Results HD patients presented akinesia in both externally triggered and self-triggered conditions. Patients had more difficulties with self-triggered gait than with triggered gait. In HD, anticipatory postural adjustments (APAs) were more impaired in self-triggered gait initiation than in cued initiation. Indeed, an alteration in the kinetic parameters revealed a reduction in first step speed in both conditions. Hypokinesia (as assessed by a reduction in the range of angle joints) played an important role in this reduction. Conclusion Akinesia is a major feature of impaired gait initiation in HD. The deficiencies in self-triggered initiation in HD seen here fit with a hypothesis whereby deficient internal cueing can be replaced by an external trigger.

Adjustments of prehension synergies in response to self-triggered and experimenter-triggered load and torque perturbations.

Humans are known to show anticipatory adjustments in the grip force prior to a self-generated or predictable action or perturbation applied to a hand-held object. We investigated whether humans can also adjust covariation of individual finger forces (multi-finger synergies) prior to self-triggered perturbations. To address this issue, we studied adjustments in multi-digit synergies associated with applied load/torque perturbations while the subjects held a customized handle steadily. The main hypothesis was that the subjects would be able to demonstrate the phenomenon of anticipatory covariation, that is changes in covariation patterns among digit forces and moments of force in anticipation of a perturbation, but only when the perturbation was triggered by the subjects themselves. Based on the principle of superposition (decoupled grasping force and resultant torque control), we also expected to see different adjustments in indices of multi-digit synergies stabilizing the total gripping force and the total moment of force. The task for the subjects (n = 8) was to return the initial handle position as quickly as possible after a perturbation, which consisted of removing one of three loads hanging from the handle. There were six experimental conditions: two types of perturbations (self-triggered and experimenter-triggered) by three positions of the load (left, center, and right). Three-dimensional forces and moments of force recorded from each digit contact were used for the analysis. Indices of covariation among digit forces and among moments of force, previously employed for studying motor synergies, were computed across trials. Positive values of the indices reflected negative covariations of individual digit forces and moments of force (their inter-compensatory changes) to stabilize the total force and moment acting on the handle. In steady-state conditions, subjects showed strong positive indices for both digit forces and digit moments. Under the self-triggered conditions, changes in the indices of digit force and moment covariation were seen about 150 ms prior to the perturbation, while such changes were observed only after the perturbation under the experimenter-triggered conditions. Immediately following a perturbation, the indices of force and moment covariation rapidly changed to negative revealing the lack of inter-compensation among the individual digit forces and moments. Later, both indices showed a recovery to positive values; the recovery was faster in the self-triggered conditions than in the experimenter-triggered ones. During the steady-state phase after the perturbation, the indices of force and moment covariation decreased and increased, respectively, as compared to their values during the steady-state phase prior to the perturbation. We conclude that humans are able to adjust multi-digit synergies involved in prehensile tasks in anticipation of a self-triggered perturbation. These conclusions speak against hypotheses on the organization of multi-element actions based on optimal control principles. Different changes in the indices of force and moment covariation after a perturbation corroborate the principle of superposition. We discuss relations of anticipatory covariation to anticipatory postural adjustments.

Anticipatory adjustments of multi-finger synergies in preparation for self-triggered perturbations

We studied changes in multi-finger synergies associated with predictable and unpredictable force perturbations applied to a finger during a multi-finger constant total force production task. The main hypothesis was that indices of multi-finger synergies can show anticipatory changes in preparation for a predictable perturbation. Subjects sat in a chair and pressed on force sensors with the four fingers of the right hand. The task was to produce a constant level of total force. The fingers acted against loads that produced upward directed forces. The loads (applied either to the index or to the ring finger) could be disengaged either by the subject or by the experimenter. An index of finger co-variation, DeltaV was computed across sets of 12 trials at each time sample and for all tasks separately. During steady-state force production, all subjects showed positive DeltaV values corresponding to strong negative covariation among finger forces interpreted as a force-stabilizing synergy. Prior to self-triggered unloading, subjects showed an anticipatory drop in DeltaV that started 100-125 ms prior to the unloading time. Such early changes were absent in trials with experimenter-triggered unloading. After an unloading, subjects changed forces of both perturbed and unperturbed fingers and reached a new sharing pattern of the total force. In experimenter-triggered conditions, changes in the forces of unperturbed fingers could be seen as early as 120 ms following an unloading. The index DeltaV dropped following a perturbation and then recovered; the recovery occurred faster in self-triggered conditions. We conclude that humans can use feed-forward changes in multi-finger synergies (anticipatory synergy adjustments) in anticipation of a predictable perturbation. These changes may help avoid prolonged weakening of a multi-digit force-stabilizing synergy. We discuss a possibility that anticipatory postural adjustments may represent a particular case of the phenomenon of anticipatory synergy adjustments and suggest a hierarchical control scheme that incorporates a possibility of independent control over the output of a multi-element system and covariation patterns among outputs of its elements.

Modulation of anticipatory postural adjustments in a reactive and a self-triggered mode in humans

Five subjects raised their preferred arm until horizontal in one of two experimental conditions: (1) in response to a visual signal (reactive condition), and (2) in a self-triggered condition. In both conditions, subjects were instructed to execute the movement at approximately 80% of their maximal velocity, such that all movements were nearly similar. EMG activity was recorded in a focal muscle (Anterior Deltoidus) and in three postural muscles (ipsi-lateral Gastrocnemius, contra-lateral Tensor Fascia Latae and ipsi lateral Semitendinosus) known to be activated prior to the focal muscle. Results showed greater anticipatory postural adjustments in the self-triggered than in the reactive condition for the three postural muscles. It is suggested that similar intentional movements can be triggered by different timing strategies.