ELEC70065 Optimal ControlLecturer(s): Dr Simos Evangelou Aims
This module introduces the theory of optimal control, which involves control laws that maximise defined performance measures of linear and nonlinear dynamical systems. Optimal control problems are infinitedimensional, and special emphasis is given to the use of computer tools for their solution. The topics covered include calculus of variations, Pontryagin's maximum principle, and dynamic programming. Part of the module will involve calculating numerically solutions to optimal control problems with the use of modern optimal control software.
Learning Outcomes
By the end of this course you will be able to: 1 Formulate dynamic optimisation problems of practical significance, for linear and nonlinear systems, as optimal control problems. 2 Specify precise statements of the maximum principle for various general categories of optimal control problems, including freetime, fixedtime, freeendpoint, and fixedendpoint problems. 3 Derive solutions to continuoustime optimal control problems by application of the maximum principle. 4 Signify solution concepts for optimal control problems, including bangbang solutions and singular controls. 5 Calculate solutions to optimal control problems by dynamic programming techniques.
Syllabus
Calculus of variations: EulerLagrange equation, Hamiltonian formalism, variational problems with constraints. Pontryagin's maximum principle: proof of PMP, transversality condition, nonlinear twopoint boundaryvalue problem, path constraints, corner conditions, bangbang control, singular arcs. Dynamic programming: discrete problem, principle of optimality, HamiltonJacobiBellman equation, linear quadratic optimal control. Optimal control numerical solver software.
Exam Duration: 3:00hrs Coursework contribution: 25% Term: Spring Closed or Open Book (end of year exam): Open Coursework Requirement: N/A Oral Exam Required (as final assessment): N/A Prerequisite module(s): None required Course Homepage: unavailable Book List:
