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Overcoming limitations in stability theorems based on multiple nussbaum functions

MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS 2025年第1期37卷 205-246页

作者： Liu, Caiyun Liu, Yungang Shandong Univ Sch Control Sci & Engn Jinan 250061 Peoples R China Nanjing Forestry Univ Coll Mech & Elect Engn Nanjing 210037 Peoples R China

Among system uncertainties, unknown control direction is a rather essential one, whose compensation should entail the so-called nussbaum function. Recently, strategies based on multiple nussbaum functions (MNFs) have been proposed to make possible continuous adaptive control for the systems with nonidentical unknown control directions, such as large-scale systems and multi-agent systems, which cannot be addressed by a single nussbaum function. But the existing stability theorems required: MNFs have explicit expressions;MNFs are all odd or all even. This paper aims to overcome the limitations of the theorems. We first delineate MNFs by two aspects of basic properties, replacing their explicit expressions as in the literature. Specifically, MNFs have the bivariate-product form, where one variate delineates frequent changes of signs and persistent intensity of MNFs, and the other delineates the rapid growth of MNFs. Such a delineation can capture the essence of MNFs and cover as many MNFs as possible. Based on the delineated MNFs, we present two stability theorems overcoming the aforementioned limitations. Notably, the two theorems do not require MNFs to have explicit expressions. Specifically, Theorem 1 allows nonmonotonic dynamic variables of MNFs while requiring MNFs to be odd, avoiding too large gains and excessive control cost. Theorem 4 does not require all MNFs to be odd while requiring dynamic variables of MNFs to be monotonic, giving users more freedom in selecting MNFs. The two stability theorems are applied to a large-scale system and a nonlinear system with parameterized uncertainties, both with nonidentical unknown control directions, to avoid monotonicity of dynamic gains and overparameterization, respectively, in control design.

关键词： Unknown control directions multiple nussbaum functions Large-scale systems Systems with parameterized uncertainties

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Adaptive Neural Control of Nonlinear Cyber-Physical Systems Against Randomly Occurring False Data Injection Attacks

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IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2023年第4期53卷 2444-2455页

作者： Zhang, Qiang He, Dakuo Northeastern Univ Coll Informat Sci & Engn Shenyang 110819 Peoples R China Northeastern Univ State Key Lab Synthet Automat Proc Ind Shenyang 110819 Peoples R China Northeastern Univ Coll Informat Sci & Engn Shenyang 110819 Peoples R China

In this article, the main contribution is to introduce the adaptive backstepping technique into nonlinear cyber-physical systems against randomly occurring false data injection (ROFDI) attacks. And a new defense strategy based on nonlinear disturbance observer (NDO) is developed, which can not only effectively estimate the external compound disturbance in the presence of the attack, but also improve the robustness of the controlled system. Different from FDI attacks, it is a special case of ROFDI attacks, and the proposed method can deal with ROFDI attacks injected by attackers. Meanwhile, multiple nussbaum functions are introduced, which overcomes the design difficulty of unknown control directions caused by ROFDI attacks. Furthermore, the approximation of the unknown nonlinear function and the exponential growth problem in the traditional backstepping calculation process are handled by radial basis function neural network and dynamic surface control, respectively. Finally, a new adaptive neural control method based on NDO is proposed to make all signals bounded. Meanwhile, tracking errors and disturbance estimation errors converge on the neighborhood of zero. Numerical and practical examples further illustrate the rationality of the method.

关键词： Adaptive neural control cyber-physical systems (CPSs) multiple nussbaum functions nonlinear disturbance observer (NDO) randomly occurring false data injection (ROFDI) attacks

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