Encyclopedia of Systems and Control

Living Edition
| Editors: John Baillieul, Tariq Samad

Linear Quadratic Optimal Control

  • Harry TrentelmanEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-1-4471-5102-9_201-3


Linear quadratic optimal control is a collective term for a class of optimal control problems involving a linear input-state-output system and a cost functional that is a quadratic form of the state and the input. The aim is to minimize this cost functional over a given class of input functions. The optimal input depends on the initial condition, but can be implemented by means of a state feedback control law independent of the initial condition. Both the feedback gain and the optimal cost can be computed in terms of solutions of Riccati equations.


Linear systems Quadratic cost functional Optimal control Finite horizon Infinite horizon Riccati differential equation Algebraic Riccati equation 
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Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  1. 1.Johann Bernoulli Institute for Mathematics and Computer Science, University of GroningenGroningenThe Netherlands