Control Bootcamp: Linear Systems & Optimal Control

Overview lecture for bootcamp on optimal and modern control. In this lecture, we discuss the various types of control and the benefits of closed-loop feedback control.

Linear systems of ordinary differential equations are analyzed using eigenvalues and eigenvectors. This will be the mathematical foundation of this bootcamp on linear control theory.

Here we discuss the stability of a linear system (in continuous-time or discrete-time) in terms of eigenvalues. Later, we will actively modify these eigenvalues, and hence the dynamics, with feedback control.

This lecture describes how to obtain linear system of equations for a nonlinear system by linearizing about a fixed point. This is worked out for the simple pendulum "by-hand" and in Matlab.

This lecture explores when a linear system is controllable. We begin with the simple test in terms of the rank of the controllability matrix on a few intuitive examples.

This lecture discusses degrees of controllability using the controllability Gramian and the singular value decomposition of the controllability matrix.

This lecture introduces the inverted pendulum on a cart as a control system example. It covers state-space representation, fixed point analysis, and Matlab simulation, laying the groundwork for feedback control design.

This lecture demonstrates the application of the Kalman Filter using a Matlab implementation on the inverted pendulum on a cart system. It explores state estimation in a practical control scenario.