Collaborative Research: EPCN: Distributed Optimization-based Control of Large-Scale Nonlinear Systems with Uncertainties and Application to Robotic Networks

控制和优化需要在许多应用中同时进行：智能电网、交通网络、协作机器人、医疗保健和其他通过无线或物理链接通信进行交互的自治系统。这两项任务通常被区别对待，由独立的设计来处理。因此，这两个任务相互干扰，并且至少需要两者中的性能折衷。例如，获得了最优性，但速度很慢，或者收敛很快，但运动不是最优的。控制和优化的深度整合有着很大的希望。现代控制系统复杂性的激增使集成变得困难，反映在动态秩序、模型不确定性和不可靠的网络中。同时运行相互干扰的优化和控制的关键挑战是整个系统的稳定性，或者在确保稳定性的情况下，收敛速度。控制-优化干扰一直是经典自适应控制(控制器-估计器干扰)和极值搜索(优化器-控制器干扰)的标志，它们都是并行控制和优化的特例。该项目将推进分布式优化控制的数学基础，并为大规模和非线性不确定系统的实时分布式优化控制设计开发新的工具和方法。该方法将通过协作机器人网络进行验证。该项目中开发的工具，用于大规模不确定非线性系统的基于实时分布式优化的控制算法，具有变革性。所设计的算法将适用于迄今难以处理的大系统，包括由欧拉-拉格朗日方程描述的不确定网络非线性系统和机器人网络。为了消除优化和控制的纠缠，PI进行了三个研究任务：(1)对不确定性具有鲁棒性的分布式优化算法的综合；(2)为每个局部系统设计跟踪控制器以实时跟踪期望输出，以全局最小化某些全局代价；(3)优化算法和控制算法的集成，以确保优化算法的全局收敛和闭环系统的稳定性。该项目建立在PI在非线性小增益理论、增强的不确定性衰减控制器和用于模块化自适应控制设计的估值器方面的基础贡献，以及他们在基于学习的控制和通过极值搜索进行实时优化方面的互补技能。与当前依赖于模块之间线性有界相互作用的方法相比，可交付的是控制器-优化器联合设计，在非线性对象的共性和实现的稳健性和自适应性方面具有极大的适用性。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Control and optimization need to be conducted simultaneously in numerous applications: smart grids, transportation networks, cooperative robotics, healthcare, and other autonomous systems interacting via wireless or physically-linked communications. These two tasks are typically treated distinctly, approached by independent designs. As a result, the two tasks interfere with one another and require performance compromises in at least of the two. For instance, optimality is obtained, but slowly, or convergence is rapid, but to suboptimal motions. A deep integration of control and optimization holds great promise. The integration is made difficult by the surge in complexity of contemporary control systems, reflected in the dynamic order, model uncertainty, and unreliable networking. The key challenge for concurrently running the mutually interfering optimization and control is the stability of the overall system or, if stability is ensured, the convergence rate. The control-optimization interference has been the hallmark of both classical adaptive control (controller-estimator interference) and extremum seeking (optimizer-controller interference), which are special cases of concurrent control and optimization. This project will advance the mathematical foundations of distributed optimization-based control and develop new tools and methods for real-time distributed optimization-based control design of large-scale and nonlinear uncertain systems. The methodology will be validated by means of cooperative robotic networks.The tools developed in this project, for real-time distributed optimization-based control algorithms for large-scale nonlinear systems with uncertainties, are of transformative nature. The algorithms designed will be applicable to heretofore intractable large-scale systems, including uncertain networked nonlinear systems and robotic networks described by Euler-Lagrange equations. To de-conflict the entanglement of optimization and control, the PIs pursue three research tasks: (1) the synthesis of distributed optimization algorithms that are robust to uncertainties, (2) the design of tracking controllers for each local system to follow in real time the desired output that aims to globally minimize certain global cost, and (3) the integration of optimization and control algorithms for global convergence of optimization algorithms and stability of the closed-loop network. The project builds on the PIs’ foundational contributions in nonlinear small-gain theory, fortified uncertainty-attenuating controllers and estimators for modular adaptive control design, and on their complementary skillsets in learning-based control and in real-time optimization by extremum seeking. The deliverable is a controller-optimizer co-design with a greatly enlarged applicability, in terms of the generality of the nonlinear plants and the achieved robustness and adaptivity, as compared to current methods which rely on linearly-bounded interactions among the modules.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.