# Direct Numerical Solution of the LQR with Input Derivative Regularization Problem

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**Direct Numerical Solution of the LQR with Input Derivative Regularization Problem.**/ Handler, Johannes; Harker, Matthew; Rath, Gerhard.

In: IFAC-PapersOnLine, Vol. 56.2023, No. 2, 22.11.2023, p. 4846-4851.

Research output: Contribution to journal › Article › Research › peer-review

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*IFAC-PapersOnLine*, vol. 56.2023, no. 2, pp. 4846-4851. https://doi.org/10.1016/j.ifacol.2023.10.1253

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*IFAC-PapersOnLine*,

*56.2023*(2), 4846-4851. https://doi.org/10.1016/j.ifacol.2023.10.1253

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TY - JOUR

T1 - Direct Numerical Solution of the LQR with Input Derivative Regularization Problem

AU - Handler, Johannes

AU - Harker, Matthew

AU - Rath, Gerhard

PY - 2023/11/22

Y1 - 2023/11/22

N2 - This paper develops a new method for computing the state feedback gain of a Linear Quadratic Regulator (LQR) with input derivative weighting that circumvents solving the Riccati equation. The additional penalty on the derivatives of the input introduces intuitively tunable weights and enables smoother control characteristics without the need of model extension. This is motivated by position controlled mechanical systems. The physical limitations of these systems are usually their velocity and acceleration rather than the position itself. The presented algorithm is based on a discretization approach to the calculus of variations and translating the original problem into a least-squares with equality constraints problem. The control performance is analyzed using a laboratory setup of an underactuated crane-like system.

AB - This paper develops a new method for computing the state feedback gain of a Linear Quadratic Regulator (LQR) with input derivative weighting that circumvents solving the Riccati equation. The additional penalty on the derivatives of the input introduces intuitively tunable weights and enables smoother control characteristics without the need of model extension. This is motivated by position controlled mechanical systems. The physical limitations of these systems are usually their velocity and acceleration rather than the position itself. The presented algorithm is based on a discretization approach to the calculus of variations and translating the original problem into a least-squares with equality constraints problem. The control performance is analyzed using a laboratory setup of an underactuated crane-like system.

UR - https://pureadmin.unileoben.ac.at/portal/en/publications/direct-numerical-solution-of-the-lqr-with-input-derivative-regularization-problem(e2182aca-a979-4a60-bf90-9aeb4c00f273).html

U2 - 10.1016/j.ifacol.2023.10.1253

DO - 10.1016/j.ifacol.2023.10.1253

M3 - Article

VL - 56.2023

SP - 4846

EP - 4851

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

SN - 2405-8963

IS - 2

T2 - IFAC World Congress 2023

Y2 - 9 July 2023 through 14 July 2023

ER -