承包商-扩展商与通用逆最优正非线性控制
Contractor-Expander and Universal Inverse Optimal Positive Nonlinear Control
AI总结：
本文提出两种逆最优方法论框架，用于正正交量系统的稳定控制，通过严格CLF和特定承包商-扩展商函数实现逆最优稳定。
摘要：
对于一般控制仿射非线性系统在正正交量中，并且具有正控制，我们展示了如何严格CLFs可以用于逆最优稳定。传统``LgV''逆最优反馈定律，对于具有无约束状态和控制的系统，假设符号无约束输入和输入惩罚，这些是类K在输入幅度中的，因此对称关于零。此类技术无法扩展到正状态和控制系统。需要主要定制，且在本文中引入，用于正系统，其中高度不对称（或非传统对称）成本不仅在状态上也必须在控制上必要。以捕食者-猎物正状态正输入基准系统为灵感，使用我们之前论文中构建的严格CLF，我们原型了两个通用逆最优方法论框架，这些框架利用特定的``承包商和扩展商函数''。一个框架（A）采用由CLF、稳定反馈和扩展商组成的三元组，而另一个框架（B）采用CLF和承包商函数的一对。两个框架都产生正正交量任意维度的逆最优稳定器构造。更强的构造结果来自更强的CLF条件。捕食者-猎物模型的生物解释表明，此类逆最优控制构造在生物生态上具有意义。除了通用框架外，我们还提出了两个完全显式的设计：两个Sontag-like通用公式，用于通过正反馈稳定正正交量系统，其中一个具有逆最优性。
英文摘要：
For general control-affine nonlinear systems in the positive orthant, and with positive controls, we show how strict CLFs can be utilized for inverse optimal stabilization. Conventional ``LgV'' inverse optimal feedback laws, for systems with unconstrained states and controls, assume sign-unconstrained inputs and input penalties that are class-K in the input magnitude, hence symmetric about zero. Such techniques do not extend to positive-state-and-control systems. Major customizations are needed, and introduced in this paper, for positive systems where highly asymmetric (or unconventionally symmetric) costs not only on the state but also on control are necessary. With the predator-prey positive-state positive-input benchmark system as inspiration, using a strict CLF built in our previous paper, we prototype two general inverse optimal methodological frameworks that employ particular ``contractor and expander functions.'' One framework (A) employs a triple consisting of a CLF, a stabilizing feedback, and an expander, whereas the other framework (B) employs a pair of a CLF and a contractor function. Both frameworks yield inverse optimal stabilizer constructions, on positive orthants of arbitrary dimensions. A stronger construction results from a stronger CLF condition. Biological interpretation for the predator-prey model illuminates that such inverse optimal control constructions are bio-ecologically meaningful. In addition to general frameworks, we present two fully explicit designs: two Sontag-like universal formulae for stabilization of positive-orthant systems by positive feedback, one of them with inverse optimality.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
