Time-Certified Decision Making in Connected Autonomous Systems: Fixed-Time Equilibrium Seeking Control

互联交通系统（CTS）的进步将大大减少交通事故、二氧化碳排放和拥堵，仅在美国就产生了2000亿美元的影响。人类在CTS中造成了很大一部分挑战：他们闭合循环，增加不确定性和动态性，并排除使用基于模型的算法进行控制和优化。CTS和其他行业迫切需要具有稳定性、安全性和性能保证的无模型控制器和算法。该项目的主要目标是在决策用户规定的给定时间内，使用实时信息，在需要解决决策问题的环境中推进无模型优化算法的设计和分析。这样的控制器有一个巨大的潜力，以提高CTS中不同应用的性能，但需要超越传统的非线性控制理论及其平滑反馈工具的进步。该项目结合了与工业界的合作，为算法的开发提供信息，这些算法具有计算处理、有限的驱动和传感以及间歇性通信网络所带来的实际限制，并培养了进入国家技术需求重要领域的人才管道。开发的工具和算法将被纳入研究生和本科生课程，并通过在主要会议上提供的短期课程和讲习班传播。该项目将综合和分析新的无模型固定时间平衡寻求控制器的决策任务的特点是约束变分不等式。与传统的极值搜索算法相比，该算法只能实现指数收敛到稳态输入输出映射的最小值，该算法将通过新的反馈设计实现固定时间和规定时间的收敛，该反馈设计结合了联合收割机超线性反馈以加速从远处的收敛和次线性反馈以加速极值附近的收敛。该算法将能够解决标准的优化问题，以及多目标决策问题与一个定义良好的纳什或帕累托集。该方法改进了奇异摄动理论和平均理论，将它们从仅保证渐近稳定推广到保证固定时间稳定。这些算法将在不同的CTS应用中进行测试，包括交通拥堵控制、具有随时间变化的个性化舒适度相关回报函数的无模型领导者-跟随者跟踪，以及连接的移动的机器人网络的协调。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

Advances in connected transportation systems (CTS) will significantly reduce traffic accidents, CO2 emissions, and congestion, with impact estimated at $200B in the US alone. Humans cause a large share of challenges in CTS: they close loops, add uncertainty and dynamics, and preclude the use of model-based algorithms for control and optimization. Model-free controllers and algorithms with guarantees of stability, safety, and performance are critically needed in CTS and other industries. The main goal of this project is to advance the design and analysis of model-free optimization algorithms in settings where decision-making problems need to be solved, using real-time information, within a given time prescribed by the decision-making user. Such controllers have a tremendous potential to improve the performance of different applications in CTS but require advances beyond the traditional nonlinear control theory and its smooth feedback tools. The project incorporates collaborations with industry to inform the development of the algorithms with practical limitations imposed by computational processing, limited actuation and sensing, and intermittent communication networks, and cultivates a talent pipeline into important areas of national technology needs. The tools and algorithms developed will be integrated into graduate and undergraduate courses and disseminated through short courses and workshops offered at major conferences. The project will synthesize and analyze new classes of model-free fixed-time equilibrium-seeking controllers for decision-making tasks characterized by constrained variational inequalities. In contrast to traditional extremum seeking algorithms, which only achieve exponential convergence to the minimizer of the steady-state input-to-output map of a plant, the algorithms will achieve fixed-time and prescribed-time convergence via new feedback designs that combine super-linear feedback to accelerate convergence from a distance and sub-linear feedback to accelerate convergence near the extremum. The algorithms will be able to solve standard optimization problems, as well as multi-objective decision making problems with a well-defined Nash or Pareto set. The methodology will advance singular perturbation theory and averaging theory, so they are generalized from guaranteeing only asymptotic stability to guaranteeing fixed-time stability. The algorithms will be tested in different CTS applications, including traffic congestion control, model-free leader-follower tracking with time-varying personalized comfort-related payoff functions, and the coordination of connected mobile robotic networks.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.