Stochastic LQR optimal control with white and colored noise: Dynamic programming technique

Escobedo-Trujillo, Beatris Adriana; Garrido, Javier

doi:10.24275/rmiq/sim2353

RMIQ

2021

DOI: 10.24275/rmiq/sim2353

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Stochastic LQR optimal control with white and colored noise: Dynamic programming technique

Beatris Adriana Escobedo-Trujillo

Javier Garrido²

Abstract: Modelado de la biodegradación en biorreactores de lodos de hidrocarburos totales del petróleo intemperizados en suelos y sedimentos (Biodegradation modeling of sludge bioreactors of total petroleum hydrocarbons weathering in soil and sediments)

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Cited by 2 publications

References 26 publications

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Applications of the Linear Quadratic Regulator Optimal Control With Completely and Partially Observed Markovian Switching

Escobedo-Trujillo

Garrido

2023

Journal of Dynamic Systems, Measurement, and Control

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We study optimal control problems where the dynamic system evolves according to a linear stochastic differential equation with (a) multiplicative and additive white noise, (b) a mixture of white noise, and (c) white noise and colored noise. The drift rate and the diffusion matrix of the linear dynamic system depend on a continuous-time Markov chain with finite state space which is (I) partially observed and (II) completely observed. Using the results of Wonham filter theory, we reduce the partially observed problems to one with complete observation. We solve the control optimal problems explicitly with the help of dynamic programming technique, and three applications are presented to illustrate our theoretical results.

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Applications of the Linear Quadratic Regulator Optimal Control With Completely and Partially Observed Markovian Switching

Escobedo-Trujillo

Garrido

2023

Journal of Dynamic Systems, Measurement, and Control

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Optimal Control with Partially Observed Regime Switching: Discounted and Average Payoffs

et al. 2022

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We consider an optimal control problem with the discounted and average payoff. The reward rate (or cost rate) can be unbounded from above and below, and a Markovian switching stochastic differential equation gives the state variable dynamic. Markovian switching is represented by a hidden continuous-time Markov chain that can only be observed in Gaussian white noise. Our general aim is to give conditions for the existence of optimal Markov stationary controls. This fact generalizes the conditions that ensure the existence of optimal control policies for optimal control problems completely observed. We use standard dynamic programming techniques and the method of hidden Markov model filtering to achieve our goals. As applications of our results, we study the discounted linear quadratic regulator (LQR) problem, the ergodic LQR problem for the modeled quarter-car suspension, the average LQR problem for the modeled quarter-car suspension with damp, and an explicit application for an optimal pollution control.

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Stochastic LQR optimal control with white and colored noise: Dynamic programming technique

Abstract: Modelado de la biodegradación en biorreactores de lodos de hidrocarburos totales del petróleo intemperizados en suelos y sedimentos (Biodegradation modeling of sludge bioreactors of total petroleum hydrocarbons weathering in soil and sediments)

Cited by 2 publications

References 26 publications

Applications of the Linear Quadratic Regulator Optimal Control With Completely and Partially Observed Markovian Switching

Applications of the Linear Quadratic Regulator Optimal Control With Completely and Partially Observed Markovian Switching

Optimal Control with Partially Observed Regime Switching: Discounted and Average Payoffs

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