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Data-Driven H∞ Control for Nonlinear Distributed Parameter Systems
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DOI：10.1109/TNNLS.2015.2461023.png)
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Abstract
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The data-driven H infinity control problem of nonlinear distributed parameter systems is considered in this paper. An off-policy learning method is developed to learn the H infinity control policy from real system data rather than the mathematical model. First, Karhunen-Loeve decomposition is used to compute the empirical eigenfunctions, which are then employed to derive a reduced-order model (ROM) of slow subsystem based on the singular perturbation theory. The H infinity control problem is reformulated based on the ROM, which can be transformed to solve the Hamilton-Jacobi-Isaacs (HJI) equation, theoretically. To learn the solution of the HJI equation from real system data, a data-driven off-policy learning approach is proposed based on the simultaneous policy update algorithm and its convergence is proved. For implementation purpose, a neural network (NN)based action-critic structure is developed, where a critic NN and two action NNs are employed to approximate the value function, control, and disturbance policies, respectively. Subsequently, a least-square NN weight-tuning rule is derived with the method of weighted residuals. Finally, the developed data-driven off-policy learning approach is applied to a nonlinear diffusion-reaction process, and the obtained results demonstrate its effectiveness.
Keywords:
Data driven
distributed parameter systems (DSPs)
Hamilton-Jacobi-Isaacs (HJI) equation
H infinity control
neural network (NN)
off-policy learning
partial differential equation (PDE)
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