Stabilization and Performance Improvement of Control Systems under State Feedback

Event-triggering mechanisms reported in the existing prescribed-time (PT) control do not adequately capture the dynamic nature of network environments, and are not applied to distributed consensus tracking problems with unknown time delays. Therefore, designing a dynamic event-triggering mechanism is crucial to ensuring PT stability, even in the presence of unknown time delays. This article focuses on developing a dynamic event-triggering mechanism to achieve adaptive practical PT output-feedback consensus tracking for nonlinear uncertain multiagent systems with unknown time delays. Firstly, a delay-independent PT state observer using a time-varying gain function is designed to estimate the immeasurable states. Following this, a novel distributed delay-independent PT consensus tracking scheme is constructed, incorporating a dynamic event-triggered mechanism through the command-filtered backstepping approach. In this design, dynamic variables based on a time-varying gain function are developed to support the event-triggering mechanism, ensuring practical stability within the prescribed settling time. Consequently, the proposed output-feedback control protocol can achieve practical PT stability, meaning that consensus tracking errors are constrained to a neighborhood around zero within a pre-specified time, regardless of the initial states of the agents or design parameters, while also avoiding the Zeno phenomenon. Finally, the effectiveness of the proposed strategy is validated through an illustrative example, which includes a comparative analysis.

A novel dynamic event-triggered mechanism for dynamic average consensus

Design of output feedback semiglobally practically input-to-state (SPIS) stabilizing controllers for nonlinear strict-feedback networked systems is considered. We first design continuous-time state feedback globally asymptotically (GA) stabilizing controllers and discrete-time reduced-order observers and combine the emulation of state feedback controllers and the designed observers to construct discrete-time output feedback controllers. Then we show that the designed controllers SPIS stabilize nonlinear strict-feedback networked control systems when transmission intervals are sufficiently small and communication networks satisfy suitable assumptions. A numerical example is also given to illustrate the efficiency of proposed design of controllers.

In this article, impulsive control issue of the interval type-2 Takagi-Sugeno (IT2 T-S) fuzzy interconnected system is investigated via dynamic event-triggered mechanism (DETM), wherein deception attacks are considered. First of all, a more constrictive DETM is proposed, in which an exponential attenuation function is introduced to approximate the system states such that the error part is reconstructed. Then, under this exponential-type DETM, a new event-based impulsive control strategy is designed, which not only include the impulsive control on event instants, but also a state feedback control part with time-varying gains during the interval time of two consecutive events. The core idea is that the added feedback part can be regarded as a "bridge," which connects the two consecutive impulse injections. Besides, input-to-state stability of the concerned system is investigated by transforming the attack signals into a residual term, so that some stability criteria are derived in spite of the unpredictable deception attacks. The nonexistence of Zeno behaviors is also guaranteed indirectly by utilizing the comparison relationship between DETM and its static counterpart. Finally, the validity of the proposed control strategy is verified by two illustrative examples.

In this study, the adaptive finite-time leader-following consensus control for multi-agent systems (MASs) subjected to unknown time-varying actuator faults is reported based on dynamic event-triggering mechanism (DETM). Neural networks (NNs) are used to approximate unknown nonlinear functions. Command filter and compensating signal mechanism are introduced to alleviate the computational burden. Unlike the existing methods, by combining adaptive backstepping method with DETM, a novel finite time control strategy is presented, which can compensate the actuator efficiency successfully, reduce the update frequency of the controller and save resources. At the same time, under the proposed strategy, it is guaranteed that all followers can track the trajectory of the leader in the sense that consensus errors converge to a neighborhood of the origin in finite time, and all signals in the closed-loop system are bounded. Finally, the availability of the designed strategy is validated by two simulation results.

This article investigates the leader-following output consensus problem of heterogeneous linear multiagent systems, where the nonidentical followers are subject to norm bounded parameter uncertainties. Two novel distributed event-triggered consensus strategies based on state feedback and output feedback, respectively, are proposed to solve the leader-following output consensus problem. A dynamic event-triggering mechanism which involves internal state variables is proposed to determine the next triggering instant. It should be noted that the controllers can be designed without the knowledge of some global graph information, such as the eigenvalues of the Laplacian matrix associated with the corresponding communication graph and the number of agents. In addition, the interevent time can be prolonged and the Zeno behavior can be excluded with the proposed dynamic triggering mechanism. Finally, an example is presented to illustrate the effectiveness of the proposed controllers.

This paper overviews the research investigations pertaining to stability and stabilization of control systems with time‐delays. The prime focus is the fundamental results and recent progress in theory and applications. The overview sheds light on the contemporary development on the linear matrix inequality (LMI) techniques in deriving both delay‐independent and delay‐dependent stability results for time‐delay systems. Particular emphases will be placed on issues concerned with the conservatism and the computational complexity of the results. Key technical bounding lemmas and slack variable introduction approaches will be presented. The results will be compared and connections of certain delay‐dependent stability results are also discussed.

The problem of stabilization of networked control systems (NCSs) with data packet dropout is studied. Sufficient conditions are presented on the stability and stabilization of the NCSs with packet dropout. The novelty of this work lies in that NCSs with arbitrary but finite data packet dropout are modelled as switched linear systems, and this enables us to apply the result of switched systems to the analysis and synthesis of such NCSs. The admissible upper bound of the dropped packets can be determined by a set of linear matrix inequalities (LMIs) which guarantee the stability of the NCSs. Stabilizing controllers (via state feedback and static output feedback) can be constructed by solving a set of LMIs. Also, for an NCS with a convergence rate constraint, similar results are obtained. Examples are worked out to illustrate the effectiveness of the proposed method

As with a continuous-time linear system, the predictor state feedback law for a discrete-time linear system with input delay is the product of a feedback gain matrix with the predicted state at a future time instant ahead of the current time instant by the amount of the delay, which is the sum of the zero input solution and the zero state solution of the system. The zero state solution for a discrete-time system is a finite summation that involves past input. The zero input solution is the product of the transition matrix and the initial state. The truncated predictor feedback (TPF), which results from discarding the finite summation part of the predictor feedback law, reduces implementation complexity. The delay independent TPF law further discards the delay-dependent transition matrix in the TPF law and is thus robust to unknown delays. It was pointed out in Lin (Commun. Inf. Syst. 7(3), 227–264 (2007)) and Zhou and Lin (IEEE Trans. Circuits Syst. I Regular Papers 58(11), 2741–2754 (2011)) that such a delay independent TPF law stabilizes a discrete-time linear system with all its poles at z = 1 or inside the unit circle no matter how large the delay is.

In this paper, a robust fault-tolerant control with a dynamic event-triggered mechanism based on the observer is proposed for a nonlinear switched system with faults, external disturbances, and uncertainties. A first-order filter is utilized to equate sensor faults to actuator faults, and the augmented system is constructed. An adaptive observer with H∞ performance is designed based on the augmented system. The condition that the state error and fault error of the adaptive observer are uniformly bounded is given. To save communication resources and reduce the transmission of unnecessary information, an improved dynamic event-triggered mechanism is designed by introducing a fixed threshold and defining a sampling error function based on the observed state and the actual state. This mechanism can further expand the triggering time interval and effectively avoid the Zeno behavior. According to the observed state and real-time fault estimation information at the triggering moment, a fault-tolerant controller for the switched system based on the dynamic event-triggered mechanism is proposed, and the conditions for asymptotic stability of the closed-loop system are provided. Finally, the validity of the proposed method is verified by application simulation for the variant aircraft switched system.

This paper studies the decentralised adaptive tracking control problem for the interconnected nonlinear systems with asymmetric full state dynamic constraints and input quantisation using dynamic event triggering mechanism. The broad learning system (BLS) is firstly utilised to identify the unstructured uncertainties, and a BLS-based nonlinear observer is established to estimate the unmeasurable states. Then, a unified barrier function (UBF) is constructed to address the asymmetric full state dynamic constraints. Next, both of command-filtered backstepping control technique and dynamic event triggering mechanism are adopted to design the control scheme in the asymmetric full state dynamic constraints case. The proposed control scheme could guarantee that all signals of the closed-loop systems are semi-globally ultimately uniformly bounded (SGUUB), the tracking errors converge to the bounded compact set and the full states dynamic constraints are not violated. Finally, a simulation example is given to illustrate the effectiveness of the proposed control scheme.

In this study, a novel adaptive boundary control strategy with a dynamic event-triggered mechanism (dETM) is proposed for an aerial refueling hose system. The aerial refueling hose system is a typical distributed parameter system, which is modeled by partial differential equations, and a boundary controller is designed to suppress hose vibration based on this model. In the controller design process, the dynamic event triggering mechanism is introduced to reduce the frequent unnecessary signal transmission by the controller, thus minimizing actuator abrasion and improving the aerial refueling reliability. The stability of the closed-loop system is proved by the Lyapunov function method. Finally, numerical simulations are conducted to verify the effectiveness of the constructed control.

On stabilizability of multi-agent systems

The aim of this paper is to design regular feedback controls for the global asymptotic stabilization gas) of affine control systems with closed (convex) control value sets cvs) $U\subseteq\mathbb{R}^{m}$ with $0\in{int}U$, in the framework of Artstein and Sontag's control Lyapunov function clf) approach. We can consider this work as a continuation and complement of our paper [SIAM J. Control Optim., 51 (2013), pp. 2152--2175]. First, we resume some of the results achieved in that paper. Then, based on a method for approximation by compact convex sets, we propose an explicit formula for regular feedback controls for the gas of affine control systems with general compact cvs $U$ with $0\in{int}U$, provided an appropriate clf is known, but at the expense of small overflows in the control values. Moreover, if we assume smoothness on the system and the clf, a redesign yields practically smooth feedback controls. Consequently, we approximately solve the synthesis problem entailed by Artstein's theorem and also (in some degree) a Sontag's open problem with respect to general compact cvs $U$ with $0\in{int}U$. Finally, tools from convex analysis and the approximation method by compact convex sets allow us to address the problem of the global clf stabilization of affine control systems with respect to unbounded closed cvs $U$ with $0\in{int}U$, and also to the design of regular feedback controls. We illustrate the results with some examples.

Bipartite event-triggered impulsive output consensus for switching multi-agent systems with dynamic leader