Boundary Control of Two Dimensional Burgers PDE using Approximate Dynamic Programming
An approximate dynamic programming (ADP) based near optimal boundary control of distributed parameter systems (DPS) governed by uncertain two dimensional (2D) Burgers equation under Neumann boundary condition is introduced. First, Hamilton-Jacobi-Bellman (HJB) equation is formulated without any model reduction. Next, optimal boundary control policy is derived in terms of value functional which is obtained as the solution to the HJB equation. Subsequently, a novel identifier is developed to estimate the unknown nonlinearity in the partial differential equation (PDE) dynamics. The suboptimal control policy is obtained by forward-in-time approximation of the value functional using a neural network (NN) based online approximator and the identified dynamics. Adaptive weight tuning laws are proposed for online learning of the value functional and identifier. Local ultimate boundedness (UB) of the closed-loop system is verified by using Lyapunov theory.
B. Talaei et al., "Boundary Control of Two Dimensional Burgers PDE using Approximate Dynamic Programming," Proceedings of the 2016 American Control Conference (2016, Boston, MA), pp. 5243-5248, Institute of Electrical and Electronics Engineers (IEEE), Jul 2016.
The definitive version is available at https://doi.org/10.1109/ACC.2016.7526491
2016 American Control Conference, ACC (2016: Jul. 6-8, Boston, MA)
Electrical and Computer Engineering
Mathematics and Statistics
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