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MA40061: Nonlinear & optimal control theory

Follow this link for further information on academic years Academic Year: 2013/4
Further information on owning departmentsOwning Department/School: Department of Mathematical Sciences
Further information on credits Credits: 6
Further information on unit levels Level: Masters UG & PG (FHEQ level 7)
Further information on teaching periods Period: Semester 2
Further information on unit assessment Assessment: EX 100%
Further information on supplementary assessment Supplementary Assessment: MA40061 Mandatory Extra Work (where allowed by programme regulations)
Further information on requisites Requisites: Before taking this unit you must (take MA30046 or take MA40062) and take MA30041
Further information on descriptions Description: Aims & Learning Objectives:
Aims:
Four concepts underpin control theory: controllability, observability, stabilizability and optimality. Of these, the first two essentially form the focus of the Year 3/4 course on linear control theory. In this course, the latter notions of stabilizability and optimality are developed. Together, the courses on linear control theory and nonlinear & optimal control provide a firm foundation for participating in theoretical and practical developments in an active and expanding discipline.
Objectives: To present concepts and results pertaining to robustness, stabilization and optimization of (nonlinear) finite-dimensional control systems in a rigorous manner. Emphasis is placed on optimization, leading to conversance with both the Bellman-Hamilton-Jacobi approach and the maximum principle of Pontryagin, together with their application.

Content:
Topics will be chosen from the following: Controlled dynamical systems: nonlinear systems and linearization. Stability and robustness. Stabilization by feedback. Lyapunov-based design methods. Stability radii. Small-gain theorem. Optimal control. Value function. The Bellman-Hamilton-Jacobi equation. Verification theorem. Quadratic-cost control problem for linear systems. Riccati equations. The Pontryagin maximum principle and transversality conditions (a dynamic programming derivation of a restricted version and statement of the general result with applications). Proof of the maximum principle for the linear time-optimal control problem.
Further information on programme availabilityProgramme availability:

MA40061 is Optional on the following programmes:

Department of Mathematical Sciences
  • USMA-AFB15 : BSc (hons) Mathematical Sciences (Full-time) - Year 3
  • USMA-AKB16 : BSc (hons) Mathematical Sciences (Full-time with Thick Sandwich Placement) - Year 4
  • USMA-AAB16 : BSc (hons) Mathematical Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
  • USMA-AFB13 : BSc (hons) Mathematics (Full-time) - Year 3
  • USMA-AKB14 : BSc (hons) Mathematics (Full-time with Thick Sandwich Placement) - Year 4
  • USMA-AFB01 : BSc (hons) Mathematics and Statistics (Full-time) - Year 3
  • USMA-AKB02 : BSc (hons) Mathematics and Statistics (Full-time with Thick Sandwich Placement) - Year 4
  • USMA-AAB02 : BSc (hons) Mathematics and Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
  • USMA-AAB14 : BSc (hons) Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
  • USMA-AFB05 : BSc (hons) Statistics (Full-time) - Year 3
  • USMA-AKB06 : BSc (hons) Statistics (Full-time with Thick Sandwich Placement) - Year 4
  • USMA-AAB06 : BSc (hons) Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
  • USMA-AFM14 : MMath Mathematics (Full-time) - Year 3
  • USMA-AFM14 : MMath Mathematics (Full-time) - Year 4
  • USMA-AAM15 : MMath Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
  • TSMA-AFM09 : MSc Mathematical Sciences (Full-time)
  • TSMA-APM09 : MSc Mathematical Sciences (Part-time)
  • TSMA-AFM08 : MSc Modern Applications of Mathematics (Full-time)
  • TSMA-AWM14 : MSc Modern Applications of Mathematics (Full-time incorporating placement)
  • TSMA-AFL02 : PG Dip Modern Applications of Mathematics (Full-time)
Department of Physics
  • USXX-AFM01 : MSci (hons) Mathematics and Physics (Full-time) - Year 4

Notes:
* This unit catalogue is applicable for the 2013/4 academic year only. Students continuing their studies into 2014/15 and beyond should not assume that this unit will be available in future years in the format displayed here for 2013/14.
* Programmes and units are subject to change at any time, in accordance with normal University procedures.
* Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.