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连接通信进行交互的自主系统。这两项任务通常被区别对待，通过独立的设计来实现。因此，这两项任务相互干扰，并且至少需要在两项任务中做出性能妥协。例如，获得了最优性，但速度很慢，或者收敛速度很快，但运动不是最优的。控制和优化的深度集成前景广阔。当代控制系统复杂性的激增使得集成变得困难，这体现在动态顺序、模型不确定性和不可靠的网络上。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，或者如果确保稳定性的话，则是收敛速度。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，它们是并发控制和优化的特例。该项目将推进基于分布式优化的控制的数学基础，并为大规模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。该项目开发的工具具有变革性，适用于具有不确定性的大规模非线性系统的基于实时分布式优化的控制算法。设计的算法将适用于迄今为止棘手的大规模系统，包括不确定的网络非线性系统和由欧拉-拉格朗日方程描述的机器人网络。 为了消除优化和控制的纠缠，PI们追求三个研究任务：（1）综合对不确定性具有鲁棒性的分布式优化算法，（2）为每个局部系统设计跟踪控制器，实时跟踪期望的输出，从而全局最小化某些全局成本，以及（3）集成优化和控制算法，以实现优化算法的全局收敛和闭环网络的稳定性。该项目建立在 PI 在非线性小增益理论、用于模块化自适应控制设计的强化不确定性衰减控制器和估计器方面的基础贡献，以及他们在基于学习的控制和极值搜索实时优化方面的互补技能集的基础上。与依赖模块之间线性有界相互作用的当前方法相比，该成果是控制器-优化器协同设计，在非线性设备的通用性以及所实现的鲁棒性和适应性方面，其适用性大大扩大。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。

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.