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Boundary Control of 2-D Burgers’ PDE: An Adaptive Dynamic Programming Approach.
- Source :
-
IEEE Transactions on Neural Networks & Learning Systems . Aug2018, Vol. 29 Issue 8, p3669-3681. 13p. - Publication Year :
- 2018
-
Abstract
- In this paper, an adaptive dynamic programming-based near optimal boundary controller is developed for partial differential equations (PDEs) modeled by the uncertain Burgers’ equation under Neumann boundary condition in 2-D. Initially, Hamilton–Jacobi–Bellman equation is derived in infinite-dimensional space. Subsequently, a novel neural network (NN) identifier is introduced to approximate the nonlinear dynamics in the 2-D PDE. The optimal control input is derived by online estimation of the value function through an additional NN-based forward-in-time estimation and approximated dynamic model. Novel update laws are developed for estimation of the identifier and value function online. The designed control policy can be applied using a finite number of actuators at the boundaries. Local ultimate boundedness of the closed-loop system is studied in detail using Lyapunov theory. Simulation results confirm the optimizing performance of the proposed controller on an unstable 2-D Burgers’ equation. [ABSTRACT FROM AUTHOR]
- Subjects :
- *PARTIAL differential equations
*DYNAMIC programming
Subjects
Details
- Language :
- English
- ISSN :
- 2162237X
- Volume :
- 29
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Neural Networks & Learning Systems
- Publication Type :
- Periodical
- Accession number :
- 130886440
- Full Text :
- https://doi.org/10.1109/TNNLS.2017.2736786