Event-Triggered Adaptive Control for Uncertain Constrained Nonlinear Systems With Its Application

This article is concerned with the adaptive event-triggered control (ETC) problem for uncertain nonlinear systems with full state constraints. By combining the asymmetric barrier Lyapunov functions with the backstepping technique, an adaptive ETC method is designed for the system under consideration. In addition, by introducing some well-defined smooth functions and the bounded estimation approach, the effects caused by the unknown virtual control coefficients and unknown nonlinear functions are counteracted. The asymptotic stability of the closed-loop system is ensured without violating the state constraints. Finally, the effectiveness of the control method is evaluated through simulations.

This paper addresses the problem of event-triggered control for a class of nonlinear systems with unknown control coefficients, time-varying delays, full state constraints and external disturbances, simultaneously. Firstly, based on integral Barrier-Lyapunov Functionals, an adaptive event-triggered controller is designed to account for the impacts of complete state constraints, unknown time-varying delays and external disturbances. Using fuzzy logic systems, the unknown functions of systems are then roughly estimated. The system redundancy can be significantly reduced by implementing the event-triggered control technique in the meanwhile. By introducing the separation technique and Lyapunov–Krasovskii functionals, it is shown that the strategy can ensure tracking performance greatly and all the closed-loop signals of the system are bounded. Compared with the existing results, the proposed design scheme is less conservative and has a wilder application range. Finally, the simulation results show the effectiveness of the proposed approach.

Special issue on PID control in the information age: Theoretical advances and applications

Event-triggered adaptive fixed-time NN control for constrained nonstrict-feedback nonlinear systems with prescribed performance

The majority of the results on constrained nonlinear multi-agent systems (MASs) control focused on output or state constraints without considering the saving of communication resources. In this paper, for a class of uncertain nonlinear MASs, we first present a new adaptive bounded consensus tracking control scheme in which the asymmetric and full-state constraints are jointly synthesized with a switching threshold event-triggered strategy, such that the communication resources are effectively utilized. The key to accomplishing the asymmetric and full-state constraints is that a kind of improved <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$tan$</tex-math> </inline-formula> -type barrier Lyapunov functions are constructed. The controller constructed for each agent by the switching threshold event-triggered strategy guarantees that the asymmetric and full-state constraints are not violated and the output of each agent can track the leader’s trajectory with an adjustable bounded tracking error. Furthermore, to achieve the asymptotic consensus tracking control, we give another kind of novel <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$tan$</tex-math> </inline-formula> -type barrier Lyapunov functions to design the desired controller for each agent. A simulation example of five single-link robots is proposed to illustrate the effectiveness of our control scheme. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —In this paper, the adaptive bounded consensus tracking control problem is considered for nonlinear MASs subject to full-state constraints, whose models are capable of describing a multitude of critical applications, including the formation of unmanned vehicles and robots. The research on the tracking control problem will be rather complicated yet challenging if the asymmetric and full-state constraints are taken into account in a complex environment. Additionally, the incorporation of an event-triggered mechanism aids in the reduction of communication resource usage, enhancing the ease of implementation and improving the user-friendliness of the proposed control scheme.

This article investigates the problem of dynamic memory event-triggered (DMET) fixed-time tracking control within time-varying asymmetric constraints for nonaffine nonstrict-feedback uncertain nonlinear systems with unmodeled dynamics and unknown disturbances. The existing dynamic event-triggered control methods cannot handle the nonlinear systems with unmodeled dynamics and nonaffine inputs, which greatly limits the applicability of the strategy. To this end, a novel DMET adaptive fuzzy fixed-time control protocol is constructed based on the idea of command filtered backstepping, in which a new dynamic signal function is established to deal with the unmodeled dynamics and an improved DMET mechanism (DMETM) is designed to solve the problem of nonaffine inputs. It is proved that the newly DMET control strategy ensures the tracking error converges to an arbitrarily small compact set in a fixed time and all the signals of the closed-loop systems are bounded. The effectiveness of the proposed approach is demonstrated by two simulation examples.

In this paper, an event-triggered adaptive decentralised control strategy for a class of switched interconnected nonlinear systems is presented, which considers full-state constraints and unmodeled dynamics, simultaneously. In the controller design process, the approximation capability of radical basis function neural networks (RBF NNs) is used to estimate the unknown functions of the system. The interference caused by unmodeled dynamics is overcome by introducing a dynamic signal. In addition, the barrier Lyapunov function (BLF) is constructed for each subsystem to dispose the influence of state constraints. An adaptive control scheme with event-triggered mechanism is proposed to reduce communication burden. It is shown that the proposed event-triggered controller and an adaptive neural decentralised control strategy are designed such that all the signals in the closed-loop system are guaranteed to be bounded, the tracking errors of the system converge to a small neighbourhood of the origin and the full state constraints are not violated. Finally, a simulation result shows the effectiveness of the developed approach.

In this paper, a novel event-triggered (ET) adaptive neural tracking control scheme is proposed for uncertain strict-feedback systems subject to asymmetric time-varying full-state constraints, unknown virtual control coefficients and external disturbances. The lower-order time-varying asymmetric barrier Lyapunov function (TVABLF) is constructed to ensure that state constraints are not transgressed. Then, a simple backstepping-based control procedure is developed to remove the existing restrictions on a high power of piecewise TVABLF and high-order differentiability of virtual laws. In particular, a novel adaptive updating law is constructed to co-design the controller and the ET scheme by the combination of the Nussbaum gain technique, thereby solving the ET controller design difficulty resulting from unknown control coefficients. The proposed scheme can guarantee all states within the time-varying constrained areas, achieve the satisfactory tracking ability and save the communication resource. Finally, the effectiveness of the proposed scheme is testified by numerical and practical examples.

Periodic event-triggered adaptive tracking control design for nonlinear discrete-time systems via reinforcement learning

The adaptive fuzzy asymptotic tracking control (AFATC) method is presented for uncertain stochastic nonlinear systems by virtue of event-triggered mechanism. The fuzzy logic systems are borrowed to address system uncertainties. By applying the backstepping technique, the AFATC strategy is recursively constructed. Different from the existing approximation-based methods, the developed controller can achieve asymptotic convergence feature. Moreover, the event-triggered mechanism is integrated into the controller design process to reduce data transmission and unnecessary resource waste. By applying the Lyapunov analysis and several helpful lemmas, the stability and convergence of the considered systems are ensured. Finally, the availability of the theory analysis is verified by a chemical reactor system.

Adaptive event-triggered output-feedback controller for uncertain nonlinear systems

Event-triggered adaptive consensus for fuzzy output-constrained multi-agent systems with observers

In this chapter, we investigate the robust feedback stabilization for a class of continuous-time uncertain nonlinear systems via event-triggering mechanism and adaptive critic learning technique. The main idea is to combine the event-triggering mechanism with adaptive critic designs, so as to solve the nonlinear robust control problem under uncertain environment. This can not only make better use of computation and communication resources, but also conduct controller design from the view of intelligent optimization. Through theoretical analysis, the nonlinear robust stabilization can be achieved by deriving an event-triggered optimal controller of the nominal system with a newly defined cost function and a certain triggering condition. The adaptive critic technique is employed to facilitate the event-triggered control design, where a critic neural network is constructed to serve as the approximator of the learning phase. The performance of the event-triggered robust control strategy is verified via simulation studies and comparisons. The present method extends the application domain of both event-triggered control and adaptive critic learning control to nonlinear systems possessing dynamical uncertainties.

Event-triggered adaptive optimal tracking control for nonlinear stochastic systems with dynamic state constraints

In this paper, the problem of output tracking control is considered for a class of uncertain strict-feedback nonlinear systems with virtual control coefficients and full state constraints. It is assumed only that the nonlinear uncertainties of the systems are some smooth functions enough to guarantee the existence of solutions to the differential equations which describe uncertain systems, and that the virtual control coefficients are unknown. Based on backstepping algorithm, by combining the barrier Lyapunov function with an integral inequality reported in the current control literature, a design method is presented whereby a simple adaptive robust output tracking control scheme can be synthesised. The presented design method can evade the repeated differentiation problem appearing in using backstepping algorithm, and need not know all the nonlinear upper bounds of uncertainties, which are repeatedly employed at each step of backstepping procedure. It is also shown that the output tracking error of the uncertain nonlinear systems with both unknown virtual control coefficients and full state constraints can converge uniformly exponentially towards a ball which can be as small as desired. Finally, a numerical example is given, and the corresponding simulations are also implemented to demonstrate the simplicity of the proposed method and the validity of the theoretical results.