Direct Numerical Solution of the LQR with Input Derivative Regularization Problem

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External Organisational units

  • École de Technologie Supériore Montréal


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.


Original languageEnglish
Pages (from-to)4846-4851
Number of pages6
Issue number2
Early online date22 Nov 2023
Publication statusPublished - 22 Nov 2023
EventIFAC World Congress 2023 - Yokohama, Japan
Duration: 9 Jul 202314 Jul 2023