# Optimal Robust Linear Quadratic Regulator for Systems Subject to Uncertainties

@article{Terra2014OptimalRL, title={Optimal Robust Linear Quadratic Regulator for Systems Subject to Uncertainties}, author={Marco H. Terra and Jo{\~a}o P. Cerri and Jo{\~a}o Yoshiyuki Ishihara}, journal={IEEE Transactions on Automatic Control}, year={2014}, volume={59}, pages={2586-2591} }

In this technical note, a robust recursive regulator for linear discrete-time systems, which are subject to parametric uncertainties, is proposed. The main feature of the optimal regulator developed is the absence of tuning parameters in online applications. To achieve this purpose, a quadratic cost function based on the combination of penalty function and robust weighted least-squares methods is formulated. The convergence and stability proofs for the stationary system and a numerical…

## 52 Citations

Robust Linear Quadratic Regulator for uncertain systems

- Mathematics2016 IEEE 55th Conference on Decision and Control (CDC)
- 2016

The robust LQR problem is formulated as a minimax optimization problem, resulting in a robust optimal controller which in addition to minimizing the quadratic cost it also minimizes the level of disturbance variability.

Robust Linear Quadratic Regulator for Uncertain Linear Discrete-Time Systems with Delay in the States: an augmented system approach

- Mathematics, Computer Science2018 European Control Conference (ECC)
- 2018

The regulation problem for a class of uncertain discrete-time systems with known constant delays in the states is dealt with, in terms of augmented Riccati equations presented in a framework given by an array of matrices.

Optimal guaranteed cost control of discrete-time linear systems subject to structured uncertainties

- MathematicsInt. J. Control
- 2021

This method enables the convex synthesis for a more general class of systems, where uncertainties are uncorrelated block diagonal, and no feed-through uncertainty is multiplicative with control input ones.

Guaranteed cost approach for robust model predictive control of uncertain linear systems

- Mathematics2017 American Control Conference (ACC)
- 2017

The proposed technique is computationally more efficient then an enumeration-based approach and requires only a Quadratically Constrained Quadratic Problem (QCQP) optimization, whereas LMI-based GCMPC approaches require a Semi-Definite Programming (SDP) optimization.

Error minimizing linear regulation for discrete-time systems

- MathematicsTrans. Inst. Meas. Control
- 2018

Stability analysis of the closed loop system using EMLR is presented along with simulation results for regulation of discretized model of underactuated fourth-order ball and beam system.

Recursive Robust Regulator for Discrete-Time Markovian Jump Linear Systems

- MathematicsIEEE Transactions on Automatic Control
- 2017

A robust regulator for discrete-time Markovian jump linear systems (DMJLS) subject to structured parameter uncertainties is proposed through a regularization approach based on robust least-squares and penalty functions.

A convex approach to robust LQR

- Mathematics, Computer Science2020 59th IEEE Conference on Decision and Control (CDC)
- 2020

The problem of designing finite-horizon linear quadratic regulator for uncertain discrete-time systems focusing on minimax strategies is treated, and a time-invariant linear control law is obtained just solving sequentially two convex optimization problems.

Asymptotically stable critic designs for approximate optimal stabilization of nonlinear systems subject to mismatched external disturbances

- Mathematics, EngineeringNeurocomputing
- 2020

Guaranteed cost control for uncertain discrete-time systems with state and input delays

- Mathematics2015 IEEE Advanced Information Technology, Electronic and Automation Control Conference (IAEAC)
- 2015

The problem of guaranteed cost control for norm-bounded uncertain discrete-time systems with both state and input delays is studied. Delay-dependent conditions for the existence of the guaranteed…

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