Optimal and Sub-optimal Control Design for Second Order Nonlinear Affine Systems using Krotov Sufficient Conditions

Avinash Kumar; Tushar Jain

doi:10.1109/SYSTOL.2019.8864735

Optimal and Sub-optimal Control Design for Second Order Nonlinear Affine Systems using Krotov Sufficient Conditions

Avinash Kumar
, Tushar Jain

Indian Institute of Technology Mandi

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

This article tackles the optimal control design problem for second order nonlinear affine systems using Krotov sufficient conditions. The computation of optimal control law(s) for nonlinear systems is usually done using the iterative methods based on the standard tools of optimal control theory which viz. Calculus of Variations (CoV), Hamilton-Jacobi-Bellman equation, Pontryagin's principle, etc. This work utilizes the Krotov sufficient conditions of global optimality to obtain non-iterative solutions. These conditions are derived by transforming the optimal control problem into another equivalent optimization problem. This translation is done via an ad-hoc selection of the so-called Krotov function. In this article, the Krotov function is chosen such that the equivalent optimization problem is solved non-iteratively to obtain optimal and sub-optimal control laws for the original optimal control problem. The proposed methodology is demonstrated by a numerical example.

Original language	English
Title of host publication	2019 4th Conference on Control and Fault Tolerant Systems, SysTol 2019
Publisher	IEEE Computer Society
Pages	401-405
Number of pages	5
ISBN (Electronic)	9781728103808
DOIs	https://doi.org/10.1109/SYSTOL.2019.8864735
Publication status	Published - 1 Sept 2019
Externally published	Yes
Event	4th Conference on Control and Fault Tolerant Systems, SysTol 2019 - Casablanca, Morocco Duration: 18 Sept 2019 → 20 Sept 2019

Publication series

Name	Conference on Control and Fault-Tolerant Systems, SysTol
ISSN (Print)	2162-1195
ISSN (Electronic)	2162-1209

Conference

Conference	4th Conference on Control and Fault Tolerant Systems, SysTol 2019
Country/Territory	Morocco
City	Casablanca
Period	18/09/19 → 20/09/19

Access to Document

10.1109/SYSTOL.2019.8864735

Cite this

Kumar, A., & Jain, T. (2019). Optimal and Sub-optimal Control Design for Second Order Nonlinear Affine Systems using Krotov Sufficient Conditions. In 2019 4th Conference on Control and Fault Tolerant Systems, SysTol 2019 (pp. 401-405). Article 8864735 (Conference on Control and Fault-Tolerant Systems, SysTol). IEEE Computer Society. https://doi.org/10.1109/SYSTOL.2019.8864735

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title = "Optimal and Sub-optimal Control Design for Second Order Nonlinear Affine Systems using Krotov Sufficient Conditions",

abstract = "This article tackles the optimal control design problem for second order nonlinear affine systems using Krotov sufficient conditions. The computation of optimal control law(s) for nonlinear systems is usually done using the iterative methods based on the standard tools of optimal control theory which viz. Calculus of Variations (CoV), Hamilton-Jacobi-Bellman equation, Pontryagin's principle, etc. This work utilizes the Krotov sufficient conditions of global optimality to obtain non-iterative solutions. These conditions are derived by transforming the optimal control problem into another equivalent optimization problem. This translation is done via an ad-hoc selection of the so-called Krotov function. In this article, the Krotov function is chosen such that the equivalent optimization problem is solved non-iteratively to obtain optimal and sub-optimal control laws for the original optimal control problem. The proposed methodology is demonstrated by a numerical example.",

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Kumar, A & Jain, T 2019, Optimal and Sub-optimal Control Design for Second Order Nonlinear Affine Systems using Krotov Sufficient Conditions. in 2019 4th Conference on Control and Fault Tolerant Systems, SysTol 2019., 8864735, Conference on Control and Fault-Tolerant Systems, SysTol, IEEE Computer Society, pp. 401-405, 4th Conference on Control and Fault Tolerant Systems, SysTol 2019, Casablanca, Morocco, 18/09/19. https://doi.org/10.1109/SYSTOL.2019.8864735

Optimal and Sub-optimal Control Design for Second Order Nonlinear Affine Systems using Krotov Sufficient Conditions. / Kumar, Avinash; Jain, Tushar.
2019 4th Conference on Control and Fault Tolerant Systems, SysTol 2019. IEEE Computer Society, 2019. p. 401-405 8864735 (Conference on Control and Fault-Tolerant Systems, SysTol).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - This article tackles the optimal control design problem for second order nonlinear affine systems using Krotov sufficient conditions. The computation of optimal control law(s) for nonlinear systems is usually done using the iterative methods based on the standard tools of optimal control theory which viz. Calculus of Variations (CoV), Hamilton-Jacobi-Bellman equation, Pontryagin's principle, etc. This work utilizes the Krotov sufficient conditions of global optimality to obtain non-iterative solutions. These conditions are derived by transforming the optimal control problem into another equivalent optimization problem. This translation is done via an ad-hoc selection of the so-called Krotov function. In this article, the Krotov function is chosen such that the equivalent optimization problem is solved non-iteratively to obtain optimal and sub-optimal control laws for the original optimal control problem. The proposed methodology is demonstrated by a numerical example.

AB - This article tackles the optimal control design problem for second order nonlinear affine systems using Krotov sufficient conditions. The computation of optimal control law(s) for nonlinear systems is usually done using the iterative methods based on the standard tools of optimal control theory which viz. Calculus of Variations (CoV), Hamilton-Jacobi-Bellman equation, Pontryagin's principle, etc. This work utilizes the Krotov sufficient conditions of global optimality to obtain non-iterative solutions. These conditions are derived by transforming the optimal control problem into another equivalent optimization problem. This translation is done via an ad-hoc selection of the so-called Krotov function. In this article, the Krotov function is chosen such that the equivalent optimization problem is solved non-iteratively to obtain optimal and sub-optimal control laws for the original optimal control problem. The proposed methodology is demonstrated by a numerical example.

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Optimal and Sub-optimal Control Design for Second Order Nonlinear Affine Systems using Krotov Sufficient Conditions

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