论文标题
非线性控制合成的凸数据驱动方法
A convex data-driven approach for nonlinear control synthesis
论文作者
论文摘要
我们考虑一类非线性控制合成问题，其中尚不清楚基础数学模型。我们提出了一种数据驱动的方法来稳定系统时，只有访问动力学的样本轨迹。我们的方法建立在密度函数上，几乎所有的稳定证书都对动态系统的Lyapunov函数是双重的。与基于Lyapunov的方法不同，密度函数可为控制策略和稳定证书的联合搜索提供凸的配方。可以通过调用平方之和（SOS）的机械来有效地解决此类凸问题。对于数据驱动的部分，我们利用了一个事实，即二元性可以使用线性Perron-Frobenius和Koopman运算符来理解动力系统的稳定性理论。这种连接使我们可以使用开发的数据驱动方法来近似这些操作员与SOS技术结合使用，以凸出控制合成。通过几个示例证明了所提出的方法的功效。
We consider a class of nonlinear control synthesis problems where the underlying mathematical models are not explicitly known. We propose a data-driven approach to stabilize the systems when only sample trajectories of the dynamics are accessible. Our method is founded on the density function based almost everywhere stability certificate that is dual to the Lyapunov function for dynamic systems. Unlike Lyapunov based methods, density functions lead to a convex formulation for a joint search of the control strategy and the stability certificate. This type of convex problem can be solved efficiently by invoking the machinery of the sum of squares (SOS). For the data-driven part, we exploit the fact that the duality results in the stability theory of the dynamical system can be understood using linear Perron-Frobenius and Koopman operators. This connection allows us to use data-driven methods developed to approximate these operators combined with the SOS techniques for the convex formulation of control synthesis. The efficacy of the proposed approach is demonstrated through several examples.
