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The Continuous-Time Linear Quadratic Regulator

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Time-Inconsistent Control Theory with Finance Applications

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Abstract

In this chapter, we apply the dynamic programming theory to the continuous-time linear quadratic regulator problem (LQR). The LQR is a classical engineering problem and design technique in which a process has its settings optimized by minimizing a quadratic cost function. The cost function is often defined as the sum of deviations for key properties (altitude, temperature, etc.).

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References

  • Anderson, B. D. O., & Moore, J. B. (1990). Optimal control: Linear quadratic methods. Prentice-Hall

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  • Bertsekas, D. P. (2005). Dynamic programming and optimal control (3rd ed., vol. I). Athena Scientific.

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Björk, T., Khapko, M., Murgoci, A. (2021). The Continuous-Time Linear Quadratic Regulator. In: Time-Inconsistent Control Theory with Finance Applications. Springer Finance. Springer, Cham. https://doi.org/10.1007/978-3-030-81843-2_12

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