Slide: Starting from the penalty method, we extend to the augmented Lagrangian method for improved stability. By introducing \(s\), symmetric cone constraints are integrated, forming a unified framework for solving constrained optimization problems iteratively. Inspired by Dr. Zhepei Wang's Lecture "Numerical Optimization for Robotics".
Slide: Evolving from the classic Kalman Filter, the EKF, UKF, and Particle Filter address nonlinear estimation through local linearization, deterministic sampling, and stochastic sampling, respectively, forming the cornerstone of modern state estimation.
Slide: Overview of factor graphs in pose estimation, emphasizing their benefits over Kalman Filters for handling complex dependencies. Covers dynamic Bayesian networks, information forms, and smoothing for efficient state estimation.
Slide: Discover the Kalman Filter through the Geometric perspective of orthogonal projection, the Probabilistic perspective of Bayesian filtering, and the Optimization perspective of weighted least squares. Inspired by Ling Shi's 2024-25 Spring lecture "Networked Sensing, Estimation and Control".
Slide: This lecture begins with an introduction to the Karush-Kuhn-Tucker (KKT) conditions, which are fundamental in constrained optimization. We will explore their geometric interpretation, derive the necessary conditions for optimality, and discuss their applications in solving optimization problems.
Slide: Starting with the classical Newton's method, we will examine its limitations and the improvements introduced by quasi-Newton methods. Finally, we will delve into the L-BFGS algorithm, which is particularly suited for large-scale problems. Inspired by Dr. Zhepei Wang's Lecture "Numerical Optimization for Robotics".
Slide: Explore the duality between state observers and feedback controllers, focusing on KF and LQR. Understand why combining the "optimal observer" with the "optimal controller" might fail. Inspired by Dominikus Noll's page "A generalization of the Linear Quadratic Gaussian Loop Transfer Recovery procedure (LQG/LTR)".
Slide: Explore the Linear Quadratic Regulator (LQR) through the Indirect Shooting Method (Pontryagin's Principle), the Optimization Approach (Quadratic Programming), and the Recursive Solution (Riccati Equation). Inspired by Zachary Manchester's Spring 2024-25 lecture "Optimal Control and Reinforcement Learning".
Slide: Explore reinforcement learning (RL) by comparing the Markov Chain and the Markov Decision Process (MDP). Understand how RL functions as a direct adaptive optimal control method through the example of Q-Learning. Inspired by Sutton's paper "Reinforcement Learning is Direct Adaptive Optimal Control" and Pieter Abbeel's lecture "Foundations of Deep RL".
当我们谈论复杂系统时，德内拉·梅多斯的《系统之美》提供了一套理解动态问题的语法，而经典控制论则赋予我们分析和设计系统的数学语言。这两者结合，形成了一条从理解到驾驭动态系统的完整路径。