课堂教学 Teaching
上海交通大学 Shanghai Jiao Tong University
VV556: 应用数学方法 Applied Math Methods
Introduction to the theory of functional analysis, including review on math basics, normed spaces, measure theory, and Hilbert spaces. Review on calculus and linear algebra, basics of real analysis and complex analysis. Vector spaces, norms, Banach spaces. Lebesgue integral, sigma algebra, measure, measurable functions. Inner product, Hilbert spaces, orthonormal bases, Fourier series. Bounded linear operators, spectrum, adjoints, spectral theorem. Applications in control, optimization, and machine learning.
秋季学期开设 Offered in fall
VE558：随机控制与强化学习 Stochastic Control and Reinforcement Learning
Control and optimization of discretetime and continuoustime Markov processes. Learningbased methods with exact or approximate solutions. Probability model, convergence of random variables. Countablestate Markov chains, continuousstate Markov chains, FosterLyapunov stability theory, Markov decision processes, dynamic programming. Continuoustime Markov processes, Poisson processes, queuing theory, infinitesimal generator, piecewisedeterministic Markov processes. MonteCarlo method, temporaldifference method, approximate dynamic programming, Q learning, learningbased adaptive control. Applications include connected and autonomous vehicles, intelligent transportation systems, computer and communication systems, social networks, epidemics, and finance.
秋季学期开设 Offered in fall
ECE4530J：智慧城市中的决策问题 Decision making in smart cities
Introduction to key applications in smart cities and relevant decisionmaking problems. Concepts of connected and autonomous vehicles, intelligent transportation systems, smart grid, smart living, smart environment, smart economy, smart governance. Formulation of decisionmaking problems embedded in smart city applications, including linear, nonlinear, stochastic, and gametheoretic controloptimizationlearning problems. Computer simulation of the above applications and problems. Basic concepts in controloptimizationlearning theories. Suitable for junior/senior students interested in preliminary knowledge of smart cities and decisionmaking theories. Prepares students for more advanced courses on control, optimization, and learning.
夏季学期开设 Offered in summer
纽约大学 New York University
工程系统随机模型与方法 Stochastic models and methods for engineering systems
Basic theory of stochastic processes and random graphs with a variety of transportation applications. Random variables, events, laws of large numbers; Finitestate Markov chains, steadystate distribution, exponential convergence; Poisson process, Little’s theorem, M/M/1 queues, queuing networks, hybercube model, fluid model; Branching process, Erdős–Rényi model, geometric random graph; Applications in connected vehicles, intersections, highway traffic, transit, patrol, emergency services, air transportation, infrastructure maintenance, urban development.
智慧城市数据分析学习方法 Analytics and learning methods for smart cities
Basics of analytics and learning methods, with applications in smart cities. Focuses on introduction of algorithms in their very basic forms and their smart city applications. Topics include probability review, inference, linear regression, classification, neural networks, and introduction to reinforcement learning. Applications include autonomous vehicles, traffic control, public transit, ridesharing, urban emergency response, smart grid, and smart buildings
