Synchronous MDADT-Based Fuzzy Adaptive Tracking Control for Switched Multiagent Systems via Modified Self-Triggered Mechanism

In this paper, a self-triggered fuzzy adaptive switched control strategy is proposed to address the synchronous tracking issue in switched stochastic multiagent systems (MASs) based on mode-dependent average dwell-time (MDADT) method. Firstly, a synchronous slow switching mechanism is considered in switched stochastic MASs and realized through a class of designed switching signals under MDADT property. By utilizing the information of both specific agents under switching dynamics and observers with switching features, the synchronous switching signals are designed, which reduces the design complexity. Then, a switched state observer via a switching-related output mask is proposed. The information of agents and their preserved neighbors is utilized to construct the observer and the observation performance of states is improved. Moreover, a modified self- triggered mechanism is designed to improve control performance via proposing auxiliary function. Finally, by analysing the re- lationship between the synchronous switching problem and the different switching features of the followers, the synchronous slow switching mechanism based on MDADT is obtained. Meanwhile, the designed self-triggered controller can guarantee that all signals of the closed-loop system are ultimately bounded under the switching signals. The effectiveness of the designed control method can be verified by some simulation results

Mathematical control of complex systems

Copyright © 2013 ZidongWang et al.This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

Output Reachable Set Estimation and Verification for Multi-Layer Neural Networks

In this paper, the output reachable estimation and safety verification problems for multi-layer perceptron neural networks are addressed. First, a conception called maximum sensitivity in introduced and, for a class of multi-layer perceptrons whose activation functions are monotonic functions, the maximum sensitivity can be computed via solving convex optimization problems. Then, using a simulation-based method, the output reachable set estimation problem for neural networks is formulated into a chain of optimization problems. Finally, an automated safety verification is developed based on the output reachable set estimation result. An application to the safety verification for a robotic arm model with two joints is presented to show the effectiveness of proposed approaches.Comment: 8 pages, 9 figures, to appear in TNNL

Filtering for nonlinear genetic regulatory networks with stochastic disturbances

In this paper, the filtering problem is investigated for nonlinear genetic regulatory networks with stochastic disturbances and time delays, where the nonlinear function describing the feedback regulation is assumed to satisfy the sector condition, the stochastic perturbation is in the form of a scalar Brownian motion, and the time delays exist in both the translation process and the feedback regulation process. The purpose of the addressed filtering problem is to estimate the true concentrations of the mRNA and protein. Specifically, we are interested in designing a linear filter such that, in the presence of time delays, stochastic disturbances as well as sector nonlinearities, the filtering dynamics of state estimation for the stochastic genetic regulatory network is exponentially mean square stable with a prescribed decay rate lower bound beta. By using the linear matrix inequality (LMI) technique, sufficient conditions are first derived for ensuring the desired filtering performance for the gene regulatory model, and the filter gain is then characterized in terms of the solution to an LMI, which can be easily solved by using standard software packages. A simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures

Switching Adaptive Concurrent Learning Control for Powered Rehabilitation Machines with FES

Interfacing robotic devices with humans presents significant control challenges, as the control algorithms governing these machines must accommodate for the inherent variability among individuals. This requirement necessitates the system’s ability to adapt to changes in the environment, particularly in the context of human-in-the-loop applications, wherein the system must identify specific features of the human interacting with the machine. In the field of rehabilitation, one promising approach for exercise-based rehabilitation involves the integration of hybrid rehabilitation machines, combining robotic devices such as motorized bikes and exoskeletons with functional electrical stimulation (FES) applied on lower-limb muscles. This integrated approach offers the potential for repetitive training, reduced therapist workload, improved range of motion, and therapeutic benefits. However, conducting prolonged rehabilitation sessions to maximize functional recovery using these hybrid machines imposes several difficulties. Firstly, the design and analysis of adaptive controllers are motivated, but challenges exist in coping with the inherent switching effects associated with hybrid machines. Notably, the transitions between gait phases and the dynamic switching of inputs between active lower-limb muscles and electric motors and their incorporation in the control design remain an open problem for the research community. Secondly, the system must effectively compensate for the influence of human input, which can be viewed as an external disturbance in the closed-loop system during rehabilitation. Robust methods for understanding and adapting to the variations in human input are critical for ensuring stability and accurate control of the human-robot closed-loop system. Lastly, FES-induced muscle fatigue diminishes the human torque contribution to the rehabilitation task, leading to input saturation and potential instabilities as the duration of the exercise extends. Overcoming this challenge requires the development of control algorithms that can adapt to variations in human performance by dynamically adjusting the control parameters accordingly. Consequently, the development of rehabilitative devices that effectively interface with humans requires the design and implementation of control algorithms capable of adapting to users with varying muscle and kinematic characteristics. In this regard, adaptive-based control methods provide tools for addressing the uncertainties in human-robot dynamics within exercise-based rehabilitation using FES, while ensuring stability and robustness in the human-robot closed-loop system. This dissertation develops adaptive controllers to enhance the effectiveness of exercise-based rehabilitation using FES. The objectives include the design and evaluation of adaptive control algorithms that effectively handle the switching effects inherent in hybrid machines, adapt to compensate for human input, and account for input saturation due to muscle fatigue. The control designs leverage kinematic and torque feedback and ensure the stability of the human-robot closed-loop system. These controllers have the potential to significantly enhance the practicality and effectiveness of assistive technologies in both clinical and community settings. In Chapter 1, the motivation to design switching adaptive closed-loop controllers for motorized FES-cycling and powered exoskeletons is described. A survey of closed-loop kinematic control methods related to the tracking objectives in the subsequent chapters of the dissertation is also introduced. In Chapter 2, the dynamic models for cycling and bipedal walking are described: (i) a stationary FES-cycling model with nonlinear dynamics and switched control inputs are introduced based on published literature. The muscle stimulation pattern is defined based on the kinematic effectiveness of the rider, which depends on the crank angle. (ii) A phase-dependent bipedal walking system model with switched dynamics is introduced to control a 4-degrees-of-freedom (DoF) lower-limb exoskeleton assuming single stance support. Moreover, the experimental setup of the cycle-rider and lower-limb exoskeleton system are described. Chapter 3 presents a switched concurrent learning adaptive controller for cadence tracking using the cycle-rider model. The control design is decoupled for the muscles and electric motor. An FES controller is developed with minimal parameters, capable of generating bounded muscle responses with an adjustable saturation limit. The electric motor controller employs an adaptive-based method that estimates uncertain parameters in the cycle-rider system and leverages the muscle input as a feedforward term to improve the tracking of crank trajectories. The adaptive motor controller and saturated muscle controller are implemented in able-bodied individuals and people with movement disorders. Three cycling trials were conducted to demonstrate the feasibility of tracking different crank trajectories with the same set of control parameters across all participants. The developed adaptive controller requires minimal tuning and handles rider uncertainty while ensuring predictable and satisfactory performance. This result has the potential to facilitate the widespread implementation of adaptive closed-loop controllers for FES-cycling systems in real clinical and home-based scenarios. Chapter 4 presents an integral torque tracking controller with anti-windup compensation, which achieves the dual objectives of kinematic and torque tracking (i.e., power tracking) for FES cycling. Designing an integral torque tracking controller to avoid feedback of high-order derivatives poses a significant challenge, as the integration action in the muscle loop can induce error buildup; demanding high FES input on the muscle. This can cause discomfort and accelerate muscle fatigue, thereby limiting the practical utility of the power tracking controller. To address this issue, this chapter builds upon the adaptive control for cadence tracking developed in Chapter 3 and integrates a novel torque tracking controller that allows for input saturation in the FES controller. By doing so, the controller achieves cadence and torque tracking while preventing error buildup. The analysis rigorously considers the saturation effect, and preliminary experimental results in able-bodied individuals demonstrate its feasibility. In Chapter 5, a switched concurrent learning adaptive controller is developed to achieve kinematic tracking throughout the step cycle for treadmill-based walking with a 4-DoF lower-limb hybrid exoskeleton. The developed controller leverages a phase-dependent human-exoskeleton model presented in Chapter 2. A multiple-Lyapunov stability analysis with a dwell time condition is developed to ensure exponential kinematic tracking and parameter estimation. The controller is tested in two able-bodied individuals for a six-minute walking trial and the performance of the controller is compared with a gradient descent classical adaptive controller. Chapter 6 highlights the contributions of the developed control methods and provides recommendations for future research directions