物理可行数据驱动模型安全控制器综合
Controller Synthesis for Safety of Physically-Viable Data-Driven Models
摘要：
我们考虑的问题设计有限时域安全控制器的动力系统，其中没有明确的分析模型存在和有限的数据，只有沿一个单一的轨迹的系统。给定样本的状态和输入的系统，和额外的边信息的规律性的发展的状态和守恒律，我们合成一个控制器，这样的发展的状态避免一些预先指定的不安全设置在一个给定的有限的地平线。最近的惠特尼的扩展定理的结果的启发，我们使用分段多项式近似的轨迹的基础上的数据与规律性的边信息，制定一个数据驱动的微分包含模型，可以预测的轨迹的演变。对于这几类数据驱动的微分包含，我们提出了一个基于屏障证书的安全性分析定理。作为这个定理的推论，我们证明了我们可以设计控制器来保证有限时域上数据驱动的微分包含问题解的安全性。从计算的角度来看，我们的结果被铸造成一组的平方和方案时，证书的参数化多项式的固定程度和集是半代数的。这种计算方法允许将边信息的守恒定律和积分约束使用Positivstellensatz型参数。
英文摘要：
We consider the problem of designing finite-horizon safe controllers for a dynamical system for which no explicit analytical model exists and limited data only along a single trajectory of the system are available. Given samples of the states and inputs of the system, and additional side information in terms of regularity of the evolution of the states and conservation laws, we synthesize a controller such that the evolution of the states avoid some pre-specified unsafe set over a given finite horizon. Motivated by recent results on Whitney's extension theorem, we use piecewise-polynomial approximations of the trajectories based on the data along with the regularity side information to formulate a data-driven differential inclusion model that can predict the evolution of the trajectories. For these classes of data- driven differential inclusions, we propose a safety analysis theorem based on barrier certificates. As a corollary of this theorem, we demonstrate that we can design controllers ensuring safety of the solutions to the data-driven differential inclusion over a finite horizon. From a computational standpoint, our results are cast into a set of sum-of-squares programs whenever the certificates are parametrized by polynomials of fixed degree and the sets are semi-algebraic. This computational method allows incorporating side information in terms of conservation laws and integral constraints using Positivstellensatz-type arguments.
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