Introduction to Modern Control

Course dates – MT – week beginning Monday 19th November 2018 – for Year 1 students
Paul Goulart , Alessandro Abate and Kostas Margellos


This module will introduce students to modern control theory based on state space methods and optimization. The focus will be primarily on modelling, analysis and controller design of continuous time, Linear Time Invariant (LTI) systems. The course will emphasise, through examples how to apply modern control techniques to system models using the MATLAB and Simulink environments.

  • Understanding the basis results in state-space analysis  of LTI systems
  • Learn fundamental control design architectures
  • Understand the role of optimisation in controller synthesis
  • Be exposed to research challenges and modern applications in control engineering
  • Introduction and outline of the course. Basic maths primer, some linear algebra and ODEs. Modelling, simulation and linearization. Link to  data, system ID. Illustrate with inverted pendulum or simple aircraft model. Examples and exercises.
  • Introduce LTI systems. Matrix exponential, SVD, analytic solutions for LTI systems. Observability, controllability. Observer design (possibly Kalman Filter). Examples and exercises.
  • Control synthesis. Define the control problem. Pole placement. State feedback, output feedback. Optimal control: LQR. Link to MPC. Examples and exercises.
  • Linear Matrix Inequalities and the KYP Lemma. Convex optimization primer, duality theory. Linear matrix inequalities, conic programming. KYP lemma. Link to Lyapunov, SOS, barrier functions. Examples and exercises.
  • Research frontiers: multi agent systems, decentralized control, synchronization. Applications in internet congestion control. Applications in biology. Examples and exercises.
  • Qualitative theory of ordinary differential equations
  • Linear algebra
  • Basics in optimisation