Convergence of an Upwind Finite-Difference Scheme for Hamilton–Jacobi–Bellman Equation in Optimal Control

Sun, Bing; Guo, Bao‐Zhu

doi:10.1109/tac.2015.2406976

Cited by 22 publications

(21 citation statements)

References 17 publications

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“…There is no doubt that the feedback control of dynamic systems has many merits compared with open-loop control (Guo and Sun, 2009; Sun and Guo, 2015). However, an undeniable fact is that the latter, open-loop control, has its own advantages in the investigation of infinite-dimensional systems, such as the efficiency and accuracy of open-loop control algorithms, as well as the robustness aspect of investigational systems (Datko, 1988; Sloss et al, 1998).…”

Section: Introductionmentioning

confidence: 99%

“…However, an undeniable fact is that the latter, open-loop control, has its own advantages in the investigation of infinite-dimensional systems, such as the efficiency and accuracy of open-loop control algorithms, as well as the robustness aspect of investigational systems (Datko, 1988; Sloss et al, 1998). As for the dynamic programming-viscosity solution approach, it is based on numerically solving the corresponding Hamilton–Jacobi–Bellman equation for optimal control problems (Sun and Guo, 2015). Most of these algorithms suffer from the so-called ‘curse’ of dimensionality (McEneaney, 2006) and are thus confined to only ‘toy’ problems of low dimension.…”

Section: Introductionmentioning

confidence: 99%

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Optimal boundary control of a continuum model for a highly re-entrant manufacturing system

Sun

2018

Transactions of the Institute of Measurement and Control

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In this paper, we are concerned with the optimal boundary control of a continuum model for a highly re-entrant manufacturing system. Using the Dubovitskii–Milyutin functional analytical approach, we establish the Pontryagin maximum principles for the optimal boundary control problems in both fixed and free final time horizon cases. A remark is then made about the application of the obtained results.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal boundary control of a continuum model for a highly re-entrant manufacturing system

Sun

2018

Transactions of the Institute of Measurement and Control

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“…The methods for numerical solution of HJB are currently developing . These methods are conceptually related to model‐based reinforcement learning methods, ie, value iteration and policy iteration .…”

Section: Introductionmentioning

confidence: 99%

“…The methods for numerical solution of HJB are currently developing. 34 These methods are conceptually related to model-based reinforcement learning methods, ie, value iteration and policy iteration. 35 As one of the popular methods, policy iteration manipulates the policy directly rather than finding it indirectly via value iteration.…”

Section: Introductionmentioning

confidence: 99%

Optimal codesign of controller and linear plants with input saturation: The sensitivity Lyapunov approach

Moradi

Naraghi

Eigoli

2017

Optim Control Appl Methods

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Summary Integrating the plant and controller designs reduces the unnecessary interactions, which increases the overall control cost. This is the main concern of the plant‐controller codesign (PCCD) theory that is extensively covered in the literature for linear plants. However, in the presence of input saturation, linear methods are not valid anymore. Indeed, for attaining the optimal controller with input saturation, the Hamilton‐Jacobi‐Bellman equation should be satisfied. In this paper, an iterative technique is proposed for solving the linear PCCD problem with input saturation. In order to achieve the optimal design, the plant is updated using the necessary condition for optimality expressed by sensitivity equations appended to the Hamilton‐Jacobi‐Bellman equation. Results indicate that the PCCD improves the control effort and reduces the overall performance index significantly.

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“…The upwind finite-difference scheme is such a well-adapted algorithm and has been successfully applied to many examples ( [13,14,15]). And most of all, its convergence has been rigorously proven in [28].…”

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confidence: 99%

A feedback design for numerical solution to optimal control problems based on Hamilton-Jacobi-Bellman equation

Tao

Sun

2021

era

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In this paper, we present a feedback design for numerical solution to optimal control problems, which is based on solving the corresponding Hamilton-Jacobi-Bellman (HJB) equation. An upwind finite-difference scheme is adopted to solve the HJB equation under the framework of the dynamic programming viscosity solution (DPVS) approach. Different from the usual existing algorithms, the numerical control function is interpolated in turn to gain the approximation of optimal feedback control-trajectory pair. Five simulations are executed and both of them, without exception, output the accurate numerical results. The design can avoid solving the HJB equation repeatedly, thus efficaciously promote the computation efficiency and save memory.

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Convergence of an Upwind Finite-Difference Scheme for Hamilton–Jacobi–Bellman Equation in Optimal Control

Cited by 22 publications

References 17 publications

Optimal boundary control of a continuum model for a highly re-entrant manufacturing system

Optimal boundary control of a continuum model for a highly re-entrant manufacturing system

Optimal codesign of controller and linear plants with input saturation: The sensitivity Lyapunov approach

A feedback design for numerical solution to optimal control problems based on Hamilton-Jacobi-Bellman equation

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