论文标题
具有输入约束的系统的安全验证和控制器合成
Safety Verification and Controller Synthesis for Systems with Input Constraints
论文作者
论文摘要
在本文中，我们考虑了非线性控制系统的安全验证和安全控制器的合成问题。提出了控制屏障证书（CBC）方法作为屏障证书方法的扩展。我们的方法可以用来表征给定集合的控制不变性，但要受到输入约束的一般非线性控制系统的安全性。从控制器设计的角度来看，提出的方法提供了一种合成安全控制定律的方法，该法律确保从给定初始集合开始的系统轨迹不会输入不安全的集合。与相关的控制屏障函数方法不同，我们的公式仅考虑证书定义的零级集合的切线锥内的向量场，并且通过数值证据被证明不太保守。对于具有半代数初始和安全集的多项式系统，可以使用平方分解和半明确编程合成CBC和安全控制定律。例子证明了我们的方法。
In this paper we consider the safety verification and safe controller synthesis problems for nonlinear control systems. The Control Barrier Certificates (CBC) approach is proposed as an extension to the Barrier certificates approach. Our approach can be used to characterize the control invariance of a given set in terms of safety of a general nonlinear control system subject to input constraints. From the point of view of controller design, the proposed method provides an approach to synthesize a safe control law that guarantees that the trajectories of the system starting from a given initial set do not enter an unsafe set. Unlike the related control Barrier functions approach, our formulation only considers the vector field within the tangent cone of the zero level set defined by the certificates, and is shown to be less conservative by means of numerical evidence. For polynomial systems with semi-algebraic initial and safe sets, CBCs and safe control laws can be synthesized using sum-of-squares decomposition and semi-definite programming. Examples demonstrate our method.
