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The explicit linear quadratic regulator for constrained systems
Automatica, 2002A technique to compute the explicit state-feedback solution of a discrete-time linear quadratic control problem subject to state and input constraints is presented. First the quadratic program (QP), which must be solved to determine the optimal control action, is derived. The original QP is viewed as a multi-parametric QP (mp-QP).
Alberto Bemporad +2 more
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An extended linear quadratic regulator for LTI systems with exogenous inputs [PDF]
Automatica, 2017 This paper proposes a cost effective control law for a linear time invariant (LTI) system having an extra set of exogenous inputs (or external disturbances) besides the traditional set of control inputs.
Abhinav Kumar Singh, Bikash Pal
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The Linear Quadratic Regulator
2021In 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
Tomas Björk +2 more
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The Linear Quadratic Regulator with chance constraints
2013 European Control Conference (ECC), 2013This paper is concerned with the design of linear state feedback control laws for linear systems with additive Gaussian disturbances. The objective is to find the feedback gain that minimizes a quadratic cost function in closed-loop operation, while observing chance constraints on the input and/or the state. It is shown that this problem can be cast as
Georg Schildbach +2 more
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Linear Quadratic Regulator for Autonomous Oscillation
2019 American Control Conference (ACC), 2019A recent result on eigenstructure assignment allows for a linear feedback control to achieve desired autonomous periodic behavior for linear plants, where the oscillation pattern is characterized by a frequency and mode shape (relative amplitudes and phase-offsets). We develop an optimal control theory based on the general result that parametrizes such
Taylor Ludeke, Tetsuya Iwasaki
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On the horizons in constrained linear quadratic regulation
2007 46th IEEE Conference on Decision and Control, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xiaodong Zhao, Zongli Lin
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Regression-Based Linear Quadratic Regulator
2018 IEEE International Conference on Robotics and Automation (ICRA), 2018We present the Regression-based Linear Quadratic Regulator (R-LQR), a new approach for determining locally-optimal control feedback policies for robots with non-linear dynamics and non-quadratic cost functions. Our proposal uses a free-derivative algorithm based on local quadratic regressions to obtain the robot motion policy.
Hugo Carlos 0001 +2 more
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Linear-quadratic regulator. I. a new solution
Automation and Remote Control, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mikhail V. Khlebnikov +2 more
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The Inconsistent Linear Quadratic Regulator
2021In this chapter we study a simple time-inconsistent version of the linear quadratic regulator in continuous time. Time inconsistency enters through an explicit dependence on the initial state for the final quadratic term. Loosely speaking, we want to control a system such that the final state is close to the initial point while at the same time keeping
Tomas Björk +2 more
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