Checking date: 16/05/2015

Course: 2020/2021

Control theory and applications
Study: Master in Mathematical Engineering (70)

Coordinating teacher: IBORT LATRE, LUIS ALBERTO

Department assigned to the subject: Department of Mathematics

Type: Electives
ECTS Credits: 6.0 ECTS


Students are expected to have completed
* Linear algebra * Ordinary differential equations * Partial differential equations
Competences and skills that will be acquired and learning results.
* Solve problems of affine-linear control in one and more variables. * Describe and solve of problems in motion. * Describe and solve of simple problems in control mechanical systems and robotics. * Solve of problems in optimal control LQ. * Apply specific software in the solution of linear control systems. * Solve Riccati equations. * Apply Pontryagin's maximum principle to solve optimal control problems in engineering and economics. * Analyze and apply bang-bang solutions to mechanical problems.
Description of contents: programme
* Basics in ordinary differential equations and control theory. * Control theory of linear affine systems. * Design of trajectories. * Control of systems in Lie groups * Optimal control theory: linear systems with regular and singular quadratic gains. * Riccati equation and quadratic systems. * Pontryagi's maximum principle.
Learning activities and methodology
* The academic activieties (1.4 ECTS) will be devided into the following formative aspects: Expository lectures: Its aim is to present to the students the main notions and tools of the corresponding subject. Notes will be distributed during the course to facilitate the students understanding. An extensive bibliography will be also given in order that the students can deepen their knowledge of particular topics of interst. Exercise or practical lectures: in these lectures (some of them to be held in the computer room) the students will develop their specific skills related to the topic. The students will also do oral and written presentations of subjects related to the course. * Moreover, 1.4 ECTS will be devoted to tutorials: this activity aims at an independent learning of the student with a periodic supervision by the lecturer. It includes, for example, the reading and understanding of research papers. Corrections of problems or suggestions for presentations. * The remaining credits (3.2) correspond to independent work by the student (without supervision by the lecturer). In this time the student will solve problems related to the course, read recommended bibliography and search for references and related material. During this time the students may have access to the lecture room.
Assessment System
  • % end-of-term-examination 60
  • % of continuous assessment (assigments, laboratory, practicals...) 40
Basic Bibliography
  • E. D. Sontag. Mathematical control theory : deterministic finite dimensional systems . Springer Verlag. 1998
  • F. Bullo and A. D. Lewis. Geometric Control of Mechanical Systems. Springer Verlag. 2004
  • K. Zhou (with J.C. Doyle and K. Glover). Robust and Optimal Control. Prentice Hall. 1996
Additional Bibliography
  • A.W. Naylor and G.R. Sell. Linear Operator Theory in Engineering and Science. Springer Verlag. 1982
  • E.R. Pinch. Optimal control and the calculus of variations . Oxford University Press. 1993
  • H.O. Fattorini. Infinite Dimensional Linear Control Systems. Elsevier. 2005
  • R.F.Curtain and H.J.Zwart. An Introduction to Infinite-Dimensional Linear System Theory. Springer Verlag. 1995

The course syllabus and the academic weekly planning may change due academic events or other reasons.