Collaborative Research: Real-Time Iteration Governor for Constrained Nonlinear Model Predictive Control

模型预测控制被认为是工业过程高性能控制和自主系统安全高效运行的理想选择。尽管模型预测控制在化学过程控制行业取得了显著的成功，但将模型预测控制成功过渡到时间和安全关键应用受到其实时实施中面临的计算挑战的限制。该研究项目为一种新的实时实现策略奠定了理论基础，该策略将显著减少模型预测控制的运行时间，提高其整体可靠性，并将其应用于汽车和航空航天领域。传统的模型预测控制是通过在每个时间步上完全求解一个最优控制问题来实现的。本研究项目的重点是一个替代方案，其中最优控制问题的解决方案是跟踪在多个时间步长有界误差。通过将数值解算器视为与受控设备并行发展的动态系统，该项目将使用输入到状态稳定性参数确定渐近稳定性和约束满足的充分条件。然后通过引入实时迭代调控器来保证递归稳定性和约束满足，实时迭代调控器是一个附加的监督层，它适当地操纵模型预测控制器的参考，从而以可接受的小误差跟踪最优控制问题的解。这些理论贡献将由专门的数值算法和模拟电路补充，这些算法和模拟电路充分利用了相对于最优控制问题的变化率在更快的时间尺度上运行的优势。所提出的框架还将通过使用实时迭代调控器逐步引导数值求解器远离不希望的局部最小值来解决非凸约束。最后，为了证明实时迭代调控器及其支持理论的有效性，所提出的框架将应用于实际工程挑战，包括小型航天器靠近小行星的自主导航，自动驾驶汽车高效控制算法的开发以及无人机约束协调策略的实施。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Model predictive control is considered as a desirable candidate for high performance control of industrial processes and for safe and efficient operation of autonomous systems. Despite its remarkable success in the chemical process control industry, the successful transition of model predictive control into time-and-safety-critical applications is limited by the computational challenges faced in its real-time implementation. This research project lays the theoretical foundations for a new real-time implementation strategy that will significantly reduce the runtime of model predictive control, increase its overall reliability, and extend its applicability to the automotive and aerospace domains. Traditional model predictive control is implemented by fully solving an optimal control problem at every time step. This research project focuses on an alternative scheme where the solution to the optimal control problem is tracked with a bounded error over multiple time steps. By treating the numerical solver as a dynamic system that evolves in parallel to the controlled plant, the project will identify sufficient conditions for asymptotic stability and constraint satisfaction using Input-to-State Stability arguments. Recursive stability and constraint satisfaction will then be ensured by introducing the Real-Time Iteration Governor, which is an add-on supervision layer that suitably manipulates the reference of the model predictive controller so that the solution to the optimal control problem can be tracked with an acceptably small error. These theoretical contributions will be supplemented by dedicated numerical algorithms and analog circuits that take full advantage of running at a faster timescale with respect to the rate of change of the optimal control problem. The proposed framework will also address nonconvex constraints by using the Real-Time Iteration Governor to progressively steer the numerical solver away from undesirable local minima. Finally, to demonstrate the effectiveness of the Real-Time Iteration Governor and its supporting theory, the proposed framework will be applied to practical engineering challenges, which include the autonomous navigation of small spacecraft in close proximity to asteroids, the development of efficient control algorithms for self-driving cars, and the implementation of constrained coordination strategies for unmanned aerial vehicles.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.