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Linear Quadratic Optimal Control Design: A Novel Approach Based on Krotov Conditions
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-17, 17 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-10-13
Country of Publication
Egypt
No. of Pages
17
Main Subjects
Abstract EN
This paper revisits the problem of synthesizing the optimal control law for linear systems with a quadratic cost.
For this problem, traditionally, the state feedback gain matrix of the optimal controller is computed by solving the Riccati equation, which is primarily obtained using calculus of variations- (CoV-) based and Hamilton–Jacobi–Bellman (HJB) equation-based approaches.
To obtain the Riccati equation, these approaches require some assumptions in the solution procedure; that is, the former approach requires the notion of costates and then their relationship with states is exploited to obtain the closed-form expression of the optimal control law, while the latter requires a priori knowledge regarding the optimal cost function.
In this paper, we propose a novel method for computing linear quadratic optimal control laws by using the global optimal control framework introduced by V.
F.
Krotov.
As shall be illustrated in this article, this framework does not require the notion of costates and any a priori information regarding the optimal cost function.
Nevertheless, using this framework, the optimal control problem gets translated to a nonconvex optimization problem.
The novelty of the proposed method lies in transforming this nonconvex optimization problem into a convex problem.
The convexity imposition results in a linear matrix inequality (LMI), whose analysis is reported in this work.
Furthermore, this LMI reduces to the Riccati equation upon imposing optimality requirements.
The insights along with the future directions of the work are presented and gathered at appropriate locations in this article.
Finally, numerical results are provided to demonstrate the proposed methodology.
American Psychological Association (APA)
Kumar, Avinash& Jain, Tushar. 2019. Linear Quadratic Optimal Control Design: A Novel Approach Based on Krotov Conditions. Mathematical Problems in Engineering،Vol. 2019, no. 2019, pp.1-17.
https://search.emarefa.net/detail/BIM-1200640
Modern Language Association (MLA)
Kumar, Avinash& Jain, Tushar. Linear Quadratic Optimal Control Design: A Novel Approach Based on Krotov Conditions. Mathematical Problems in Engineering No. 2019 (2019), pp.1-17.
https://search.emarefa.net/detail/BIM-1200640
American Medical Association (AMA)
Kumar, Avinash& Jain, Tushar. Linear Quadratic Optimal Control Design: A Novel Approach Based on Krotov Conditions. Mathematical Problems in Engineering. 2019. Vol. 2019, no. 2019, pp.1-17.
https://search.emarefa.net/detail/BIM-1200640
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1200640