Security Control for Discrete-Time Stochastic Nonlinear Systems Subject to Deception Attacks

This paper is concerned with the security control problem with quadratic cost criterion for a class of discrete-time stochastic nonlinear systems subject to deception attacks. A definition of security in probability is adopted to account for the transient dynamics of controlled systems. The purpose of the problem under consideration is to design a dynamic output feedback controller such that the prescribed security in probability is guaranteed while obtaining an upper bound of the quadratic cost criterion. First of all, some sufficient conditions with the form of matrix inequalities are established in the framework of the input-to-state stability in probability. Then, an easy-solution version on above inequalities is proposed by carrying out the well-known matrix inverse lemma to obtain both the controller gain and the upper bound. Furthermore, the main results are shown to be extendable to the case of discrete-time stochastic linear systems. Finally, two simulation examples are utilized to illustrate the usefulness of the proposed controller design scheme.

本文关注一类遭受欺骗攻击的离散时间随机非线性系统的二次成本准则下的安全控制问题。采用概率安全的定义来考虑受控系统的瞬态动力学。所考虑问题的目的是设计一个动态输出反馈控制器，使得在获得二次成本准则的上界的同时保证规定的概率安全。首先，在概率输入到状态稳定性的框架下，建立了一些具有矩阵不等式形式的充分条件。然后，通过运用著名的矩阵求逆引理，提出了上述不等式的一种易解形式，以获得控制器增益和上界。此外，主要结果表明可扩展到离散时间随机线性系统的情形。最后，利用两个仿真例子来说明所提出的控制器设计方案的有效性。