论文标题
国家反馈抽象，用于最佳控制分段植物系统
State-feedback Abstractions for Optimal Control of Piecewise-affine Systems
论文作者
论文摘要
在本手稿中，我们研究了在输入约束和有限的外部噪声下捕获分段摩擦系统的行为的符号抽象。这是通过考虑与符号模型共同设计的局部仿射反馈控制器来实现的，该控制器确保了系统和抽象之间的交替模拟关系。由此产生的符号系统称为状态反馈抽象，我们证明即使原始的分段效果系统不稳定且非确定性，它也可以是确定性的。这种方法的一个好处是，输入空间不必离散化，符号输入空间将减少为有限的控制器。当考虑椭圆形细胞和仿射控制器时，我们提出了必要的和充分的条件，作为半准计划，用于过渡的存在和强大的上层界限。两个例子说明了理论的特定方面及其适用性。
In this manuscript, we investigate symbolic abstractions that capture the behavior of piecewise-affine systems under input constraints and bounded external noise. This is accomplished by considering local affine feedback controllers that are jointly designed with the symbolic model, which ensures that an alternating simulation relation between the system and the abstraction holds. The resulting symbolic system is called a state-feedback abstraction and we show that it can be deterministic even when the original piecewise-affine system is unstable and non-deterministic. One benefit of this approach is the fact that the input space need not be discretized and the symbolic-input space is reduced to a finite set of controllers. When ellipsoidal cells and affine controllers are considered, we present necessary and sufficient conditions written as a semi-definite program for the existence of a transition and a robust upper bound on the transition cost. Two examples illustrate particular aspects of the theory and its applicability.
