Optimal Control

Christiaan Heij (), André C.M. Ran () and Frederik van Schagen ()
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Christiaan Heij: Erasmus University Rotterdam, Department of Econometrics
André C.M. Ran: Vrije Universiteit, Department of Mathematics
Frederik van Schagen: Vrije Universiteit, Department of Mathematics

Chapter 5 in Introduction to Mathematical Systems Theory, 2021, pp 65-80 from Springer

Abstract: Abstract In this chapter we consider quantitative control objectives for rather general systems. The inputs are chosen to minimize a function that expresses the costs associated with the system evolution. This can be solved by dynamic programming. We pay special attention to the so-called LQ problem, where the system is linear and the cost function is quadratic. In this case the optimal control is given by state feedback, and the feedback matrix can be computed by solving certain matrix equations (so called Riccati equations).

Date: 2021
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DOI: 10.1007/978-3-030-59654-5_5

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