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## MA30061: Optimal control

Owning Department/School: Department of Mathematical Sciences
Credits: 6      [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Honours (FHEQ level 6)
Period:
Semester 2
Assessment Summary: EX-TH 100%*
Assessment Detail:
• Open book Examination with duration of 24 hours* (EX-TH 100%)

*Assessment updated due to Covid-19 disruptions
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites: Before taking this module you must take MA20218 AND take MA20220
In taking this module you cannot take MA40061 OR take MA50061
Description: Aims:
To introduce methods of optimal control, to explain their theoretical basis and give an appreciation of the variety of areas in which they are applicable.

Learning Outcomes:

* Recognise practical problems where optimal control methods can be used effectively.
* Apply appropriate optimal control methods.
* Justify calculations by appealing to relevant theorems.
* Write the relevant mathematical arguments in a precise and lucid fashion.

Skills:
Numeracy T/F A Problem Solving T/F A Written and Spoken Communication F

Content:
Formulation of the general optimal control problem. Sufficient conditions for the existence of an optimal control. The Pontryagin maximum principle: necessary conditions satisfied by an optimal control and sufficiency under additional convexity assumptions. Dynamical programming and the Bellman-Hamilton-Jacobi equation. The quadratic-cost control problem for linear systems. Illustration of the theory by examples. Applications to biology, economics, engineering and physics.
Programme availability:

#### MA30061 is Optional on the following programmes:

Department of Mathematical Sciences
• USMA-AFB15 : BSc(Hons) Mathematical Sciences (Year 3)
• USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 4)
• USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 4)
• USMA-AFB13 : BSc(Hons) Mathematics (Year 3)
• USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 4)
• USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 4)
• USMA-AFB01 : BSc(Hons) Mathematics and Statistics (Year 3)
• USMA-AAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 4)
• USMA-AKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 4)
• USMA-AFB05 : BSc(Hons) Statistics (Year 3)
• USMA-AAB06 : BSc(Hons) Statistics with Study year abroad (Year 4)
• USMA-AKB06 : BSc(Hons) Statistics with Year long work placement (Year 4)
• USMA-AFM14 : MMath(Hons) Mathematics (Year 3)
• USMA-AFM14 : MMath(Hons) Mathematics (Year 4)
• USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 4)
• USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 4)
• USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 5)

 Notes: This unit catalogue is applicable for the 2019/20 academic year only. Students continuing their studies into 2020/21 and beyond should not assume that this unit will be available in future years in the format displayed here for 2019/20. Programmes and units are subject to change 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. Undergraduates: Find out more about these and other important University terms and conditions here. Postgraduates: Find out more about these and other important University terms and conditions here.