Deterministic optimization: maximum principle, dynamic programming, calculus of variations, optimal control, dynamic games. Stochastic optimization: stochastic optimal control and dynamic programming, Markov processes, Ito calculus, Markov games. Applications. Dynamical systems: local and global analysis and chaos. The unifying theme of this course is best captured by the title of our main reference book: "Recursive Methods in Economic Dynamics". We start by covering deterministic and stochastic dynamic optimization using dynamic programming analysis. We then study the properties of the resulting dynamic systems. Finally, we will go over a recursive method for repeated games that has proven useful in contract theory and macroeconomics. We shall stress applications and examples of all these techniques throughout the course.

This course covers the mathematical modeling, analysis, and control of physical systems that are in rest, in motion, or acted upon by a force; it explores the dynamics of mechanical, thermal, fluid, electrical, and hybrid systems and sub-systems. Upon successful completion of this course, students will be able to: Define dynamic systems and types; Identify how mechanical, thermal, fluid, and electrical systems are modeled; Develop and review the required mathematical background for dynamic systems and control; Identify the characteristics of first- and second-order dynamic systems; Analyze dynamic systems in time-domain and frequency-domain; Identify stability of dynamic systems for controller design; Explain how dynamic systems are controlled; Define feedback control and identify various types of feedback controllers; Explain how controllers are designed for dynamic systems; Migrate from MATLAB to SCILAB; Analyze first- and second-order systems using SCILAB; Generate response and analyze response results using SCILAB; Identify and design controllers using SCILAB; Solve controller design through an example using SCILAB; Explain advanced control techniques such as digital controls, robust controls, and Z-transformations; Relate the application of control systems to real world problems using various case studies. (Mechanical Engineering 401)

The course addresses dynamic systems, i.e., systems that evolve with time. Typically these systems have inputs and outputs; it is of interest to understand how the input affects the output (or, vice-versa, what inputs should be given to generate a desired output). In particular, we will concentrate on systems that can be modeled by Ordinary Differential Equations (ODEs), and that satisfy certain linearity and time-invariance conditions. We will analyze the response of these systems to inputs and initial conditions. It is of particular interest to analyze systems obtained as interconnections (e.g., feedback) of two or more other systems. We will learn how to design (control) systems that ensure desirable properties (e.g., stability, performance) of the interconnection with a given dynamic system.

Principles of supervisory control and telerobotics. Different levels of automation are discussed, as well as the allocation of roles and authority between humans and machines. Human-vehicle interface design in highly automated systems. Decision aiding. Tradeoffs between human control and human monitoring. Automated alerting systems and human intervention in automatic operation. Enhanced human interface technologies such as virtual presence. Performance, optimization, and social implications of the human-automation system. Examples from aerospace, ground, and undersea vehicles, robotics, and industrial systems. Human Supervisory Control of Automated Systems discusses elements of the interactions between humans and machines. These elements include: assignment of roles and authority; tradeoffs between human control and human monitoring; and human intervention in automatic processes. Further topics comprise: performance, optimization and social implications of the system; enhanced human interfaces; decision aiding; and automated alterting systems. Topics refer to applications in aerospace, industrial and transportation systems.

This course provides students with ways of analyzing manufacturing systems in terms of material flow and storage, information flow, capacities, and times and durations of events. Fundamental topics covered include probability, inventory and queuing models, forecasting, optimization, process analysis, and linear and dynamic systems. This course also covers factory planning and scheduling topics including flow planning, bottleneck characterization, buffer and batch-size tactics, seasonal planning, and dynamic behavior of production systems.