Topic 1: Linear Systems Analysis. Linear dynamical systems; controllability and observability; stability; realization theory; state-feedback and observers.

Topic 2: Multivariable Control Systems. Multivariable feedback systems; factorizations and controller parameterization; limitations and trade-offs of feedback; robust stability and performance; robust H2 and H-infinity control methods. Additional prerequisite: Aerospace Engineering 381P (Topic 1) or the equivalent.

Topic 3: Optimal Control Theory. Unconstrained and constrained finite-dimensional optimization, introduction to calculus of variations and optimal control, necessary and sufficient conditions for optimality, Pontryagin's Maximum Principle, minimum-time control, linear quadratic optimal control theory, introduction to dynamic programming, Hamilton-Jacobi-Bellman equation.

Topic 4: Numerical Methods in Optimization. Numerical methods for solving parameter optimization, suboptimal control, and optimal control problems.

Topic 5: Optimal Control Theory II. Dynamic programming; nonsingular, singular, and bang-bang control problems; state variable inequality constraints; introduction to differential game theory. Additional prerequisite: Aerospace Engineering 381P (Topic 1) and 381P (Topic 3) or their equivalents.

Topic 6: Statistical Estimation Theory. Modeling static and dynamic systems, linear and nonlinear estimation, Bayesian estimation, batch least squares, Kalman filtering, square-root and information filtering, introduction to advanced estimation methods.

Topic 7: Advanced Topics in Estimation Theory. Estimation in the presence of unmodeled accelerations; nonlinear estimators; continuous estimation methods. Additional prerequisite: Aerospace Engineering 381P (Topic 6).

Topic 8: Stochastic Detection, Estimation, and Control. An investigation of linear and nonlinear estimation theory; hypothesis testing; Kalman filtering, smoothing, and Linear Quadratic Gaussian (LQG) problems; emphasis on applications. Additional prerequisite: Electrical Engineering 351K or the equivalent.

Topic 9: Human Centered Robotics. Aerospace Engineering 381P (Topic 9) and 381P (Topic 13) may not both be counted.

Topic 10: Learning for Dynamics and Controls. Aerospace Engineering 389 (Topic: Learning for Dynamics/Controls) and Aerospace Engineering 381P (Topic 10) may not both be counted.

Topic 11: Nonlinear Dynamics and Control. Analysis and synthesis of nonlinear control systems. Stability theory, Center manifold analysis, feedback linearization, backstepping, time-scale separations, nonlinear observers, Aeromechanical system applications. Aerospace Engineering 381P (Topic 11) and 396 (Topic: Nonlinear Dynamics and Control) may not both be counted. Additional prerequisite: Aerospace Engineering 381P (Topic 1) or the equivalent, and consent of instructor.

Topic 12: Nonlinear Systems and Adaptive Control. Analysis and synthesis of nonlinear control systems. Stability theory, robustness, singular-perturbation analysis, backstepping design; nonlinear observers; aeromechanical and robotics applications. Additional prerequisite: Aerospace Engineering 381P (Topic 1) or the equivalent.

Topic 13: Decision and Control of Human-Centered Robots. Oriented towards graduate students in control and robotics who are interested in end-to-end performance of real-world human-centered robotic systems. Control theory for robotics; socio cognitive modeling of human activity; behavior intervention via optimal control; Kinodynamic motion planning; temporal logics and their application to human-centered robots; whole-Body Dynamic Locomotion Controllers; intelligent Collision Management for human-centered robots. Explores theory and application from state-of-the-art papers from venues such as IEEE CSS American Control Conference, Robotics Science and Systems, The International Workshop on the Algorithmic Foundation of Robotics, Dynamic Walking, and IEEE-RAS International Conference on Humanoid Robots. Aerospace Engineering 381P (Topic 13) and Mechanical Engineering 396D may not both be counted. Additional prerequisite: Consent of graduate adviser.

Topic 14: System ID and Adaptive Control. System identification, persistence of excitation, model reference adaptive control, projection operators, immersion and invariance techniques, applications to aeromechanical systems. Aerospace Engineering 381P (Topic 14) and 396 (Topic: System ID and Adaptive Control) may not both be counted. Additional prerequisite: Aerospace Engineering 381P (Topic 1) or the equivalent.

Topic 15: Formal Methods for Robotics. Aerospace Engineering 381P (Topic 15) and 389 (Topic: Ver/Synth Cybrphysicl Systm) may not both be counted.

Topic 16: Networked Control Systems. Aerospace Engineering 381P (Topic 16) and 389 (Topic: Networked Control Systems) may not both be counted.

Topic 17: Introduction to Optimization. Introduction to convex optimization (linear, quadratic, second order cone, and semi-definite programming). Review linear and matrix algebra, singular value decomposition, least squares optimization. Discuss engineering applications of optimization. Aerospace Engineering 381P (Topic 17) and 389 (Topic: Introduction to Optimization) may not both be counted.

Topic 18: Modeling Multi-Agent Systems. Introduction to the mathematics of dynamic game theory, and the use of self-driving vehicles as an ongoing case study. Discuss static games and complementarity programming, dynamic game theory, and game theory and multi-agent control. Aerospace Engineering 381P (Topic 18) and 389 (Topic: Modeling of Multi-Agent Sys) may not both be counted.

Topic 19: Architecting and Design of Autonomous Aerospace Systems. Introduction to the technical, operational, economic, market, environmental, regulatory, legal, manufacturing, and societal factors that must be considered; as well as the optimization problems and underlying mathematical solution approaches inherent to the architecting and design of systems with high levels of automation and autonomy. Discuss the framework and tools required to develop an appropriate architecture for a large, complex, multi-vehicle aerospace system. Aerospace Engineering 381P (Topic 19) and 389 (Topic: Arch/Dsgn Autonomous ASE Systems) may not both be counted.