SGER: Path Invariance for Optimal and Adaptive Maneuvering

SGER：最优和自适应路径不变性首席研究员Petar V.Kokotovic，Europe，UCSBSanta Barbara，CA 93106petar@ece.ucsb.eduPROPOSAL SUMMARY这项探索性提案追求几个有希望的新想法，这些想法是在美国国家科学基金会拨款ECS-0228846下的最后一年的研究中出现的，标题为“具有未建模动态的非线性和自适应控制”。首先对本研究的主要成果进行了简要回顾。它们展示了当跟踪问题被重新表述为限制较少的路径跟踪问题时获得的主要优点，在该问题中，时间变量被用作附加控制的自由参数所代替。路径跟踪公式更适用于最常见的应用。同时，它们避免了在具有不稳定零动态的系统(“非最小相位系统”)中的一些经典限制。这一点已经在我们最近发表的会议论文和已经出现或即将出现的期刊出版物中得到了报道。智力价值我们将探索一些不太确定但非常有希望的新可能性，以利用路径跟踪公式提供的设计自由。拟议的研究将试图描述存在这些可能性的路径的类别。然后，它将集中于它们对自动和操作员辅助车辆的最优和自适应机动中的一类重要问题的适用性。路径跟踪控制器所保证的关键动力学特性是使选定或优化的路径成为车辆控制器反馈系统的不变集或不变流形。这种反馈控制器的设计方法有待开发。然后，附加的设计自由度被用来在不变量集中实现所需的(最优的、自适应的)动态特性，从而保证沿路径的运动的性能。这一建议的智力价值在于澄清了在非线性设计中分离几何和动态任务的进一步可能性，从而使这一领域和其他工程领域更容易实现这一点。广泛影响在其应用方面，该建议旨在对最常用的车辆路径-轨道、转弯、转向-进行分类，并使它们在实际重要的标准方面达到最佳：努力、能量、安全。这一类的一个说明性应用将是四轮转向相对于更常见的前轮转向的优势的比较研究。这项研究的预期更广泛的影响是它对更安全、更高效的地面车辆的贡献。这项建议还将通过提供资金雇用一名研究生，在教育上有所帮助。

SGER: PATH INVARIANCE FOR OPTIMAL AND ADAPTIVEMANEUVERINGPrincipal InvestigatorPetar V. Kokotovic, ECE, UCSBSanta Barbara, CA 93106petar@ece.ucsb.eduPROPOSAL SUMMARYThis exploratory proposal pursues several promising new ideas which emerged from the final year of the research under the NSF Grant ECS-0228846 entitled "Nonlinear and adaptive control with unmodeled dynamics". The main results of this research are first briefly reviewed. They demonstrate major advantages achieved when a tracking problem is reformulated as a less restrictive path following problem in which the time variable is replaced by a free parameter to be used as an additional control. Path following formulations are more suitable for most common applications. At the same time they avoid some classical limitations in systems with unstable zero dynamics ("nonminimum phase systems".) This has been reported in our recent conference papers and journal publications which have appeared or are about to appear. Intellectual MeritWe will explore some less certain but highly promising new possibilities to exploit the design freedom provided by path following formulations. The proposed research will attempt to characterize the class of paths for which these possibilities exist. It will then focus on their applicability to an important class of problems in optimal and adaptive maneuvering for autonomous and operator assisted vehicles. The key dynamical property guaranteed by a path following controller is that a selected or optimized path becomes an invariant set, or an invariant manifold, of the vehiclecontroller feedback system. Methods are to be developed for design of such feedback controllers. The additional design freedom is then used to achieve desirable (optimal, adaptive) dynamical properties in the invariant set and thus guarantee the performance ofthe motion along the path. This proposals intellectual merit lies on clarifying further possibilities of separating geometric and dynamic tasks in nonlinear designs and thus making this more accessible to this and other areas of engineering.Broader impactsOn its applied side, this proposal aims at classifying most commonly used vehicular paths - orbits, turns, swerves, - and making them optimal with respect to practically important criteria: effort, energy, safety. An illustrative application of this kind will be a comparative study of advantages of four-wheel steering over the more common frontwheel steering. The expected broader impact of this research is its contribution to saferand more efficient ground vehicles. This proposal will also help educationally by providing funds to employ one graduate student.