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首页> 外文期刊>IEEE Transactions on Automatic Control >A Modified Riccati Transformation for Decentralized Computation of the Viability Kernel Under LTI Dynamics
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A Modified Riccati Transformation for Decentralized Computation of the Viability Kernel Under LTI Dynamics

机译：LTI动力学下用于生存力核的分散计算的改进Riccati变换

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摘要

Computing the viability kernel is key in providing guarantees of safety and proving existence of safety-preserving controllers for constrained dynamical systems. Current numerical techniques that approximate this construct suffer from a complexity that is exponential in the dimension of the state. We study conditions under which a linear time-invariant (LTI) system can be suitably decomposed into lower dimensional subsystems so as to admit a conservative computation of the viability kernel in a decentralized fashion in subspaces. We then present an isomorphism that imposes these desired conditions, most suitably on two-time-scale systems. Decentralized computations are performed in the transformed coordinates, yielding a conservative approximation of the viability kernel in the original state space. Significant reduction of complexity can be achieved, allowing the previously inapplicable tools to be employed for treatment of higher dimensional systems. We show the results on two examples including a 6-D system.
机译：计算生存力内核对于确保安全性和约束动态系统的安全控制器的存在至关重要。当前近似于该构造的数值技术遭受着复杂度的复杂化，该复杂度在状态的维度上是指数的。我们研究的条件下，线性时不变（LTI）系统可以适当地分解为低维子系统，以便在子空间中以分散的方式对生存力核进行保守计算。然后，我们提出一个同构性，这些同构性强加了这些期望的条件，最适合在两尺度系统上。在变换后的坐标中执行分散计算，从而在原始状态空间中得出了生存力内核的保守近似值。可以实现复杂度的显着降低，从而允许将先前不适用的工具用于处理高维系统。我们在两个示例（包括6D系统）上显示了结果。

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