Output Feedback Control of Parabolic PDE Systems with Nonlinear Spatial Differential Operators

Data-Driven H∞ Control for Nonlinear Distributed Parameter Systems

The data-driven H∞ control problem of nonlinear distributed parameter systems is considered in this paper. An off-policy learning method is developed to learn the H∞ control policy from real system data rather than the mathematical model. First, Karhunen-Loève 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∞ 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.

Model-order reduction of nonlinear models of electromagnetic phased-array hyperthermia

A method based on the Karhunen-Loéve (KL) transform is proposed for the reduction of large-scale, nonlinear ordinary differential equations such as those arising from the finite difference modeling of biological heat transfer. The method of snapshots is used to expedite computation of the required quantities in the KL procedure. Guidelines are presented and validated for snapshot selection and resultant basis series truncation, emphasizing the special physical features of the electromagnetic phased-array heat transfer physics. Applications to fast temperature prediction are presented.