Neural network adaptive optimized resilient event-triggered control for nonlinear systems

Jun Hu; Wei Liu; Shuai Cheng; Jun Hu; Wei Liu; Shuai Cheng

doi:10.3934/math.20261015

AIMS Mathematics

2026, Volume 11, Issue 8: 25265-25294. doi: 10.3934/math.20261015

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Neural network adaptive optimized resilient event-triggered control for nonlinear systems

1.
College of Software, Shenyang University of Technology, Shenyang 110870, China
2.
College of Computer Science and Engineering, Northeastern University, Shenyang 110819, China
3.
Neusoft Reach Automotive Technology (Shenyang) Co., Ltd., Shenyang 110179, China

Received: 25 May 2026 Revised: 19 July 2026 Accepted: 27 July 2026 Published: 17 August 2026
MSC : 93C10, 93C40

Considering an uncertain nonlinear system with unmeasurement states under denial-of-service (DoS) attacks, this paper presents an observer-based neural network (NN) adaptive optimal resilient event-triggered control (ETC) framework. First, the unknown dynamics of the system are approximated by neural networks (NNs), and therefore an NN state observer is developed to estimate the unmeasurable states of the system. Then, by introducing the hyperbolic tangent function and constructing an auxiliary variable, the adverse effect of the symmetric actuator saturation can be eliminated. Furthermore, an event-triggered (ET) mechanism is introduced to reduce controller update frequency and communication burden. During the reinforcemet learning algorithm, critic-actor NNs are employed to approximate the value function and control policy, respectively. Combining adaptive dynamic programming (ADP) and an adaptive backstepping technique, an adaptive event-triggered (ET) optimized secure control method is developed. According to the Lyapunov stability theory, all signals of the closed-loop system are proven as semi-globally uniformly ultimately bounded (SGUUB). Finally, the optimal resilient ETC control framework is utilized on a single-phase photovoltaic (PV) grid-connected power generation system, and the effectiveness of the investigated control approach is verified by simulation results.
- optimal control,
- nonlinear systems,
- coupled neural networks,
- DoS attacks,
- event-triggered control
Citation: Jun Hu, Wei Liu, Shuai Cheng. Neural network adaptive optimized resilient event-triggered control for nonlinear systems[J]. AIMS Mathematics, 2026, 11(8): 25265-25294. doi: 10.3934/math.20261015

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Abstract

Considering an uncertain nonlinear system with unmeasurement states under denial-of-service (DoS) attacks, this paper presents an observer-based neural network (NN) adaptive optimal resilient event-triggered control (ETC) framework. First, the unknown dynamics of the system are approximated by neural networks (NNs), and therefore an NN state observer is developed to estimate the unmeasurable states of the system. Then, by introducing the hyperbolic tangent function and constructing an auxiliary variable, the adverse effect of the symmetric actuator saturation can be eliminated. Furthermore, an event-triggered (ET) mechanism is introduced to reduce controller update frequency and communication burden. During the reinforcemet learning algorithm, critic-actor NNs are employed to approximate the value function and control policy, respectively. Combining adaptive dynamic programming (ADP) and an adaptive backstepping technique, an adaptive event-triggered (ET) optimized secure control method is developed. According to the Lyapunov stability theory, all signals of the closed-loop system are proven as semi-globally uniformly ultimately bounded (SGUUB). Finally, the optimal resilient ETC control framework is utilized on a single-phase photovoltaic (PV) grid-connected power generation system, and the effectiveness of the investigated control approach is verified by simulation results.

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