Numerical Discretization Methods for Linear Quadratic Control Problems with Time Delays

This paper presents the numerical discretization methods of the continuous-time linear-quadratic optimal control problems (LQ-OCPs) with time delays. We describe the weight matrices of the LQ-OCPs as differential equations systems, allowing us to derive the discrete equivalent of the continuous-time...

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Published inIFAC-PapersOnLine Vol. 58; no. 14; pp. 874 - 880
Main Authors Zhang, Zhanhao, Hørsholt, Steen, Jørgensen, John Bagterp
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 2024
Subjects
Linear Quadratic Optimal Control
Numerical Discretization
Time Delay Systems
Numerical Discretization
Linear Quadratic Optimal Control
Time Delay Systems
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Abstract This paper presents the numerical discretization methods of the continuous-time linear-quadratic optimal control problems (LQ-OCPs) with time delays. We describe the weight matrices of the LQ-OCPs as differential equations systems, allowing us to derive the discrete equivalent of the continuous-time LQ-OCPs. Three numerical methods are introduced for solving proposed differential equations systems: 1) the ordinary differential equation (ODE) method, 2) the matrix exponential method, and 3) the step-doubling method. We implement a continuous-time model predictive control (CT-MPC) on a simulated cement mill system, and the objective function of the CT-MPC is discretized using the proposed LQ discretization scheme. The closed-loop results indicate that the CT-MPC successfully stabilizes and controls the simulated cement mill system, ensuring the viability and effectiveness of LQ discretization.
AbstractList This paper presents the numerical discretization methods of the continuous-time linear-quadratic optimal control problems (LQ-OCPs) with time delays. We describe the weight matrices of the LQ-OCPs as differential equations systems, allowing us to derive the discrete equivalent of the continuous-time LQ-OCPs. Three numerical methods are introduced for solving proposed differential equations systems: 1) the ordinary differential equation (ODE) method, 2) the matrix exponential method, and 3) the step-doubling method. We implement a continuous-time model predictive control (CT-MPC) on a simulated cement mill system, and the objective function of the CT-MPC is discretized using the proposed LQ discretization scheme. The closed-loop results indicate that the CT-MPC successfully stabilizes and controls the simulated cement mill system, ensuring the viability and effectiveness of LQ discretization.
Author Hørsholt, Steen
Jørgensen, John Bagterp
Zhang, Zhanhao
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Cites_doi 10.23919/ECC.2007.7068799
10.1109/TAC.2010.2053478
10.1137/100788860
10.1016/j.ifacol.2015.08.034
10.1109/ACC.2013.6580084
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10.1109/ACC.2007.4283020
10.3182/20100705-3-BE-2011.00050
10.1137/04061101X
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Snippet This paper presents the numerical discretization methods of the continuous-time linear-quadratic optimal control problems (LQ-OCPs) with time delays. We...
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SubjectTerms Linear Quadratic Optimal Control
Numerical Discretization
Time Delay Systems
Title Numerical Discretization Methods for Linear Quadratic Control Problems with Time Delays
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