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Abstract

In order to illustrate the use of dynamic programming and the Bellman equation we now consider a classical engineering problem: The linear quadratic regulator or LQR. The LQR is a well-known design technique in which a process or machine 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.). Applications range from underactuated robotics to nanorobotics, general operation of technical systems such as power or climate control systems, physics, statistics, and econometrics.

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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 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_3

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