Quantitative Control of Nonlinear Systems Based on an Event Trigger Mechanism
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Quantitative Control of Nonlinear Systems Based on an Event Trigger Mechanism Yan Gao1
· Xin Guo1 · Rao Yao1 · Wuneng Zhou2
Received: 3 January 2020 / Revised: 29 August 2020 / Accepted: 4 September 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this study, we use an event-based mechanism for the quantitative control of nonlinear systems to obtain an optimized stable controller. We define a nonlinear system model based on an event trigger mechanism and a quantization mechanism. The layout of the model includes a sampler, which is continuously monitored, and the sampled signal. The latter is detected by the event trigger mechanism when a given threshold is fulfilled. The quantizer is used to discretize the incoming control signal, the controller output, the feedback, and the nonlinear system. As the second step, we define a neural network controller that is optimized using a suitable genetic algorithm. To reduce the conservativeness of the system, we use a piecewise Lyapunov–Krasovskii functional method. By analyzing the inherent transmission time delay, the synchronous controller is converted into the equivalent stability problem for the corresponding time-delayed system. The effectiveness and advantages of the proposed method are shown by numerical simulations based on an inverted pendulum. Keywords Quantitative control · Neural networks · Event trigger mechanism · Nonlinear system · Time delay
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Yan Gao [email protected] Xin Guo [email protected] Rao Yao [email protected] Wuneng Zhou [email protected]
1
School of Electric and Electronic Engineering, Shanghai University of Engineering Science, Songjiang District, Shanghai 201600, China
2
School of Information Science and Engineering, Donghua University, Songjiang District, Shanghai 201600, China
Circuits, Systems, and Signal Processing
1 Introduction During the analysis of any nonlinear sampled-data system, a continuous-time signal is sampled by a digital controller. The sampled data represent a discrete time series, where each sampled value is assumed to remain constant during the sampling period. Due to the simplicity of such algorithms, periodic sampling control is widely used in engineering applications. However, this simplicity comes at the cost of network data redundancy and a waste of network resources. To resolve this problem, aperiodic data sampling has been suggested. In particular, by using an event triggering mechanism, both the information redundancy and the load on the broadband communications network can be reduced. Many recent studies have investigated event trigger mechanisms. For example, adaptive control design for uncertain nonlinear systems with full state constraints was introduced in Ref. [24]. An event-driven communication scheme was proposed in [19] to ensure the effective use of network resources. This scheme is also suitable for network switching systems. Data sampling has been a very popular research topic in recent years, and several methods have been proposed [9, 21, 34]. The input
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