Finite-Time Adaptive Quantized Control of Stochastic Nonlinear Systems With Input Quantization: A Broad Learning System Based Identification Method

• Published in: IEEE transactions on industrial electronics (1982) Vol. 67; no. 10; pp. 8555 - 8565
• Main Authors: Sui, Shuai, Chen, C. L. Philip, Tong, Shaocheng, Feng, Shuang
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.10.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Actuators; Adaptive control; Broad learning system (BLS); Chemical reactors; Control design; Control methods; Design methodology; Feedback control; Learning; Measurement; Neural networks; Nonlinear control; Nonlinear systems; Quantization (signal); quantized input; State observers; stochastic nonlinear systems; Stochastic processes; Stochastic systems; stochastically finite time control
• ISSN: 0278-0046; 1557-9948
• DOI: 10.1109/TIE.2019.2947844

In this article, the problem of the stochastically finite time stabilization for an uncertain single-input and single-output stochastic system in presence of input quantization is studied. The broad learning system (BLS) is first applied to identify the uncertain system with unknown dynamics. The problem of unmeasured states can be solved by establishing a novel BLS-based state observer. Combining the stochastically finite time theorem with <inline-formula><tex-math notation="LaTeX">{\rm {It\hat{o}}}</tex-math></inline-formula> formula, a new finite time design method is proposed, which can reduce the difficulty in designing controllers by traditional methods. A stochastically finite time quantized control method is presented by utilizing a new finite time design Lemma <xref ref-type="lemma" rid="lemma3">3 and quantized input decomposition technique. The developed control approach can guarantee that the closed-loop system is semi-global finite-time stable in probability, and the convergence performances are well in presence of actuator quantization. The simulation on a chemical reactor is utilized to verify the proposed scheme, which demonstrates the advantage of BLS, as well as the validity of our control method.