Study of controllers that adjust themselves online to plants with unknown or changing parameters, developed around an unstable first-order plant, a discrete-time ARX plant, and a second-order system with nonlinear uncertainty. The course covers linear parametric models, gradient and least-squares estimation, persistence of excitation, the MIT rule and Lyapunov-based model reference adaptive control with state and output feedback, indirect adaptive control and self-tuning regulators, parameter drift and robust adaptive laws, L1 adaptive control, adaptive backstepping, neural network adaptive control with concurrent learning, extremum seeking, and dual control.
Study of continuous change and accumulation. The course covers limits and continuity, derivatives and their use for approximation and optimization, integrals and the fundamental theorem of calculus, techniques and applications of integration, sequences, series, and Taylor series, partial derivatives, gradients, and Jacobians, linearization and optimization in several variables, multiple integrals, and vector calculus, which are the foundation of differential equations, signals and systems, control, estimation, and learning.
Study of electrical circuits and the methods used to analyze them. The course covers current, voltage, and power, sources and resistors, Kirchhoff’s laws, series and parallel circuits, nodal and mesh analysis, superposition and Thévenin and Norton equivalents, operational amplifiers, capacitors and inductors, the transient response of first- and second-order circuits, phasors and impedance in sinusoidal steady state, ac power, the Laplace transform for circuits, and frequency response and filters, which are the foundation of electronics, signals and systems, and control.
Study of how analysis and design problems in control are posed and solved as convex optimization problems, mainly semidefinite programs with linear matrix inequalities. The course covers LMIs and semidefinite programming, Lyapunov-based stability analysis and LMI regions, system norms, dissipativity and integral quadratic constraints, closed-loop performance specifications, state-feedback and output-feedback synthesis, the Youla parameterization, model predictive control as a quadratic program, sum-of-squares methods for nonlinear systems, convergence certificates for optimization algorithms, and data-driven control.
Study of ordinary differential equations and their use as models of physical systems. The course covers first-order separable and linear equations, existence and uniqueness of solutions, autonomous equations and their equilibria, linear equations with constant coefficients and the oscillations of mechanical and electrical systems, forcing and resonance, the Laplace transform method, systems of linear equations and the matrix exponential, phase plane analysis, linearization of nonlinear systems, and numerical solution methods, which are the foundation of signals and systems, control, and robotics.
Study of reinforcement learning, in which an agent learns to make good decisions by interacting with its environment. The course covers multi-armed bandits, Markov decision processes and dynamic programming, Monte Carlo and temporal-difference learning, function approximation, eligibility traces, and policy gradient methods, and connects them to optimal control.
Study of vectors, matrices, and the linear equations and linear maps they describe. The course covers matrix algebra, solving systems of linear equations, vector spaces and the four fundamental subspaces, orthogonality and least squares, eigenvalues and diagonalization, the Jordan form and the matrix exponential, and symmetric matrices and the singular value decomposition, which are the foundation of signals and systems, control, estimation, and learning.
Study of the analysis and design of feedback controllers for linear state-space models, developed around a few running examples (a DC motor, an inverted pendulum, and a chain of masses) and computed with linear matrix inequalities as well as classical methods. The course covers modeling and linearization, solutions and modes, Lyapunov stability, linear matrix inequalities, controllability, observability, and minimal realizations, model reduction, pole placement, tracking with integral action, observers, the linear quadratic regulator, the Kalman filter, and LQG control as duals, robustness and fundamental limitations, robust LMI synthesis, and digital and model predictive control, which are the foundation of modern control engineering.
Study of the analysis and design of feedback systems whose dynamics are nonlinear, developed around a few running examples (a pendulum, the Van der Pol oscillator, and a linear system in feedback with a static nonlinearity). The course covers nonlinear phenomena, phase portraits and linearization, limit cycles and bifurcations, Lyapunov stability, the invariance principle and converse theorems, computing Lyapunov functions and regions of attraction with sums of squares, input-to-state stability, passivity and dissipativity, absolute stability and describing functions, feedback linearization and zero dynamics, backstepping, control Lyapunov and barrier functions, sliding mode control, adaptive control, and nonlinear observers.
Study of how to choose the inputs of a dynamical system to minimize a cost over time, developed around the double integrator, scalar linear–quadratic problems, and pendulum swing-up. The course covers the calculus of variations, necessary conditions and Pontryagin’s minimum principle, bang-bang and singular controls, the Hamilton–Jacobi–Bellman equation, linear quadratic optimal control, discrete-time dynamic programming, shooting and direct collocation, differential dynamic programming and iLQR, model predictive control and its stability, stochastic optimal control and LQG, and differential games and robust optimal control.
Study of how to make the best decision subject to constraints. The course covers the formulation and classification of optimization problems, optimality conditions, convex sets, functions, and problems, Lagrange multipliers and the KKT conditions, Lagrangian duality and linear programming, gradient descent, Newton and quasi-Newton methods, accelerated and momentum methods, projected, proximal, and interior-point methods for constrained and nonsmooth problems, stochastic gradient methods for machine learning, and the analysis of optimization algorithms as feedback systems, which are the foundation of estimation, learning, and optimal and model predictive control.
Study of uncertainty and how to reason about it. The course covers probability spaces, conditional probability and Bayes’ rule, discrete and continuous random variables and their common distributions, expectation, variance, and covariance, joint and transformed random variables, Gaussian random vectors, the law of large numbers and the central limit theorem, maximum likelihood and Bayesian estimation, information and entropy, and Markov chains, which are the foundation of estimation, filtering, decision making, and learning.
Study of how an agent learns to make good decisions by interacting with its environment, developed alongside optimal control so that each method can be checked on problems whose solution is known exactly. The course covers bandits and exploration, Markov decision processes, dynamic programming, the linear quadratic regulator as dynamic programming, Monte Carlo and temporal-difference learning, function approximation and eligibility traces, deep Q-networks, policy gradients, actor–critic and trust-region methods, learning controllers for unknown linear systems, model-based reinforcement learning, imitation and offline learning, and safe reinforcement learning.
Study of how to combine measurements from imperfect sensors with models of motion to estimate the state of a system, built on one idea: with Gaussian noise, the most probable estimate is the solution of a weighted least squares problem. The course covers sensor and noise models, least squares fusion, Bayesian estimation, stochastic state-space models, Kalman, extended, unscented, and particle filters, consistency testing and tuning, smoothing and factor graph optimization, rotations and inertial navigation, localization with data association, and SLAM, which are the foundation of navigation, robotics, and tracking.
Study of the probabilistic algorithms that allow robots to perceive, estimate, and act in uncertain environments. The course covers models of robot motion and sensing, Bayesian sensor fusion and filtering, localization, mapping, and simultaneous localization and mapping (SLAM), as well as planning and decision making under uncertainty and multi-agent coordination.
Study of the principles of signals and systems. The course combines lectures and simulation laboratory exercises to expose students to the theories and concepts of both continuous-time and discrete-time forms of signals and systems, as well as their applications in communication systems, control systems, and signal processing.
Study of signals and the systems that transform them, with continuous and discrete time developed side by side around a single idea: complex exponentials are the eigenfunctions of linear time-invariant systems. The course covers signals and their properties, impulses and convolution, differential and difference equation models, frequency response, Fourier series and transforms, the DFT and FFT, sampling and aliasing, Laplace and $z$-transforms, transfer functions, poles, and stability, Bode plots and filter design, modulation, and feedback, which are the foundation of communication, signal processing, and control.
This is a graduate-level course on dynamical systems that emphasizes linear state-space models in both continuous and discrete time. The material in this course is fundamental knowledge for students pursuing research in systems and control theory, signal processing, and robotics.