Event-triggered Control and Coordination of Uncertain Nonlinear Systems Based on Fuzzy Approximation

不確定非線性系統基於模糊估計的事件驅動控制與協調

Student thesis: Doctoral Thesis

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Author(s)

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Detail(s)

Awarding Institution
Supervisors/Advisors
  • Lu LIU (Supervisor)
  • Qiu Jianbin (External person) (Supervisor)
Award date29 Oct 2020

Abstract

Most physical systems are nonlinear, and inevitably, these systems have some sorts of uncertainties because of factors such as aging effect and/or external disturbances. Studies on uncertain nonlinear systems have great significance in both theory and practical applications. Among various control approaches, fuzzy-approximation-based approach is considered as an effective alternative for handling complex uncertain nonlinear systems, because fuzzy logic systems (FLSs) can incorporate linguistic information from human experts and have the property of universal function approximation. With rapid development of computer and network technologies, it is desirable to design novel control strategies to meet a number of practical network constraints, including limited communication and limited computational capacities. To this end, event-triggered control has been developed to improve communication efficiency while maintaining the desired control performance. Though much progress has been made on event-triggered control of linear systems and some special classes of nonlinear systems, few results are available for uncertain nonlinear systems with unknown nonlinearities, due to the complexity and challenges involved. This thesis focuses on the event-triggered control and coordination problems of uncertain nonlinear systems based on fuzzy approximation.

In the first part of this thesis, we will investigate the event-triggered adaptive fuzzy control problems for some classes of single uncertain nonlinear systems with unknown nonlinearities. We will start our study from single uncertain nonlinear systems with matched uncertainties, then move on to the more complicated single uncertain nonlinear systems with unmatched uncertainties. Studies on single uncertain nonlinear systems with various performance requirements, such as finite-time convergence and output constraints, are also considered. The main contributions of this part are summarized as follows:

1. The robust adaptive fuzzy control problem for a class of uncertain nonlinear systems with matched uncertainties is studied. Fuzzy logic systems are used to approximate the unknown nonlinear functions in the nonlinear system. A novel robust adaptive control scheme together with a novel event-triggering mechanism (ETM) is proposed to reduce communication burden. Both the control signal and the adaptive parameters are updated only at the triggering time instants in the proposed scheme, which further saves the system energy and resources. The stability of the closed-loop system is proved based on Lyapunov stability theory.

2. The finite-time adaptive fuzzy control problem for a class of nonstrict-feedback uncertain nonlinear systems is considered. Based on the backstepping technique and the adding power integration technique, a novel design scheme, consisting of the finite-time adaptive fuzzy controller and the event-triggering mechanism, is proposed to decrease the number of data transmission and the number of control actuation updates. The restrictions on nonlinearities are relaxed and more general uncertain nonlinear systems are considered. The stability of the closed-loop system is proved based on Lyapunov stability theory.

3. The event-triggered adaptive fuzzy output feedback control problem for a class of nonstrict-feedback nonlinear systems with asymmetric and time-varying output constraint is addressed. By designing a linear observer to estimate the unmeasurable states, a novel event-triggered adaptive fuzzy output feedback control scheme is proposed. Barrier Lyapunov function (BLF) and error transformation technique are used to handle output constraint under completely unknown initial tracking condition. The stability of the closed-loop system is proved based on Lyapunov stability theory, while output constraint is satisfied within a predetermined finite time, even when the constraint condition is violated initially.

The second part of this thesis addresses the consensus problem of some classes of unknown nonlinear multi-agent systems via event-triggered control. Consensus problem is one of the fundamental cooperative control problems of multi-agent systems. It lays the foundation for many other cooperative control problems such as flocking, rendezvous, and formation control. We intend to design appropriate distributed event-triggering mechanisms, and develop compensator based adaptive fuzzy control strategies, such that consensus is achieved with aperiodic intermittent communication under a more general scenario. The main contributions of this part are summarized as follows:

1. The leader-following consensus problem of multiple uncertain Euler-Lagrange (EL) systems with unknown nonlinear dynamics is considered. By introducing a dynamic compensator for each agent, a fully distributed control strategy is developed based on the fuzzy approximation approach, which is independent of any priori global information associated with the communication topology. Meanwhile, a distributed event-triggering mechanism is designed such that each agent broadcasts its states only when an event occurs. With the proposed control strategies, leader-following consensus is achieved with aperiodic intermittent communication.

2. The cooperative output tracking problem for strict-feedback uncertain nonlinear multi-agent systems subject to unknown and nonidentical agent dynamics is addressed. A novel distributed adaptive fuzzy control strategy is developed based on the event-triggered transmission scheme. With the proposed approach, cooperative output tracking is achieved with aperiodic intermittent communication. Moreover, only sampled output information needs to be exchanged among the communication network, which not only reduces the communication burden, but also makes the controller implementation more flexible.

In the above two parts, the feasibility of the proposed event-triggering mechanism is verified by ruling out Zeno behavior.