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

在许多应用中，控制和优化需要同时进行：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主系统。这两个任务通常被区别对待，通过独立的设计来处理。因此，这两个任务会相互干扰，并且至少在这两个任务中需要性能折衷。例如，获得最优性，但缓慢，或收敛是快速的，但次优运动。控制和优化的深度集成具有很大的前景。由于当代控制系统的复杂性激增，集成变得困难，反映在动态顺序，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，或者如果确保稳定性，则是收敛速度。控制优化干扰是经典自适应控制（预测器-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殊情况。该项目将推进基于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基于分布式优化的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。在本项目中开发的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的工具具有变革性。所设计的算法将适用于迄今为止棘手的大系统，包括不确定网络非线性系统和机器人网络描述的欧拉拉格朗日方程。 为了消除优化和控制的纠缠，PI追求三个研究任务：（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，以在真实的时间内跟随期望的输出，其目的是全局地最小化某些全局成本，（3）优化算法与控制算法相结合，保证了优化算法的全局收敛性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中的基础贡献，加强了模块化自适应控制设计的不确定性衰减控制器和估计器，以及他们在基于学习的控制和极值搜索的实时优化方面的互补技能。该成果是一个优化器-优化器协同设计，与当前依赖于模块间线性约束相互作用的方法相比，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.