发表机构
Argonne National Laboratory（阿贡国家实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出ContEst框架，将控制与估计协同设计转化为两阶段一阶优化问题，利用包络定理从对偶变量直接获取设计梯度，避免对优化器求导，适用于LQG、H∞及非线性系统，显著提升设计效果。
AI 中文摘要
针对通常非最优的“被控对象—控制器—估计器”顺序设计流程，我们提出了控制与估计协同设计（ContEst）框架，将整个系统设计表述为一个由一阶方法求解的两阶段问题。其关键使能因素是：根据包络定理，每个内层控制/估计最优代价关于设计参数的梯度可从内层求解器已返回的对偶变量直接获得——在温和正则性（内层最小解唯一）下精确成立，在更宽松条件下作为次梯度成立。也就是说，无需对优化器或其最优性条件进行微分。我们首先在线性二次高斯（LQG）框架下展示该框架，其中控制与估计代价成为两个半定规划（SDP），其设计梯度从李雅普诺夫约束的对偶中读取。我们将结果扩展到鲁棒（$H_\infty$）形式以覆盖最坏情况下的控制与滤波问题。我们还提出了对约束和非线性系统的扩展，使用扩展卡尔曼滤波器（eKF）和信息状态动力学的局部线性化，以产生一个近似但凸的模型预测控制（MPC）问题，其设计梯度直接从协态读取。我们将我们的方法应用于来自不同领域的多种现实设计示例，并报告了显著的设计改进。
英文摘要
Instead of the sequential plant--control--estimator design pipeline, which is in general not optimal, we propose the Control and Estimation Co-Design (ContEst) framework, which poses the entire system design as a single two-stage problem solved by first-order methods. A key enabler is that the gradient of each inner control/estimation optimal cost with respect to the design parameters is available from the dual variables the inner solver already returns, by the envelope theorem: exactly under mild regularity (a unique inner minimizer), and as a subgradient under more relaxed conditions. That is, no differentiation through the optimizer or its optimality conditions is needed. We first present the framework in a linear quadratic Gaussian (LQG) regime, where the control and estimation costs become two semidefinite programs (SDPs) whose design gradients are read from the duals of the Lyapunov constraints. We extend the results to robust ($H_\infty$) formulation to cover worst-case control and filtering problems. We also present an extension to constrained and nonlinear systems, using an extended Kalman filter (eKF) and a local linearization of the information-state dynamics to yield an approximate but convex model predictive control (MPC) problem whose design gradients are read directly from the costates. We apply our methods to a variety of realistic design examples from different fields and report significant design improvements.
