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首页> 外文期刊>IEEE Transactions on Automatic Control >H∞ control for discrete-time nonlinear stochastic systems
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H∞ control for discrete-time nonlinear stochastic systems

机译：离散时间非线性随机系统的H∞控制

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摘要

In this note, we develop an H∞-type theory for a large class of discrete-time nonlinear stochastic systems. In particular, we establish a bounded real lemma (BRL) for this case. We introduce the notion of stochastic dissipative systems, analogously to the familiar notion of dissipation associated with deterministic systems, and utilize it in the derivation of the BRL. In particular, this BRL establishes a necessary and sufficient condition, in terms of a certain Hamilton Jacobi inequality (HJI), for a discrete-time nonlinear stochastic system to have l2-gain≤γ. The time-invariant case is also considered as a special case. In this case, the BRL guarantees necessary and sufficient conditions for the system to have l2-gain≤γ, by means of a solution to a certain algebraic HJI. An application of this theory to a special class of systems which is a characteristic of numerous physical systems, yields a more tractable HJI which serves as a sufficient condition for the underlying system to possess l2-gain≤γ. Stability in both the mean square sense and in probability, is also discussed. Systems that possess a special structure (norm-bounded) of uncertainties in their model are considered. Application of the BRL to this class of systems yields a linear state-feedback stabilizing controller which achieves l2-gain≤γ, by means of certain linear matrix inequalities (LMIs).
机译：在本说明中，我们为大量离散时间非线性随机系统开发了一种H∞型理论。特别是，我们为这种情况建立了有界实数引理（BRL）。我们引入随机耗散系统的概念，类似于与确定性系统相关的常见耗散概念，并将其用于BRL的推导中。特别地，该BRL根据一定的Hamilton Jacobi不等式（HJI）建立了一个具有l2增益≤γ的离散时间非线性随机系统的充要条件。时不变的情况也被认为是特例。在这种情况下，BRL通过对某个代数HJI的求解，保证了系统具有l2增益≤γ的必要和充分条件。将该理论应用于具有许多物理系统特征的一类特殊系统中，会产生更易于处理的HJI，这是基础系统拥有12增益≤γ的充分条件。还讨论了均方和概率的稳定性。考虑在模型中具有特殊不确定性结构（范数界）的系统。将BRL应用于此类系统会产生线性状态反馈稳定控制器，该控制器通过某些线性矩阵不等式（LMI）达到l2-增益≤γ。

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