ABSTRACT

A relevant family of control analysis and design problems can be reduced to the minimisation of a multivariate polynomial objective over a semialgebraic set. Such control problem formulations, however, are nonconvex in general and hard to solve in practice. In this paper, we propose a novel approach to polynomial control design based on iterations that involve either a fast coordinate-wise minimisation or a univariate minimisation along a randomly chosen direction. We provide a detailed iteration complexity analysis of the method, and we prove its convergence in probability to the global optimum. The practical effectiveness of the proposed method is also illustrated via a comparison with state-of-the-art tools available in the literature. An example of application to an automated space rendezvous manoeuvre is finally presented, showing how the method can be particularly relevant in the context of nonlinear model predictive control.

摘要

相关的控制分析和设计问题系列可以简化为半代数集上的多元多项式目标的最小化。然而，这种控制问题的公式一般是非凸的，在实践中很难解决。在本文中，我们提出了一种基于迭代的多项式控制设计的新方法，涉及快速坐标最小化或沿随机选择方向的单变量最小化。我们提供了该方法的详细迭代复杂度分析，并证明了其收敛到全局最优的概率。通过与文献中可用的最先进工具的比较，还说明了所提出方法的实际有效性。最后给出了一个应用到自动化空间交会机动的例子，