Industrial applications of model based predictive control
Automatica (Journal of IFAC) - IFAC-IEEE special issue on meeting the challenge of computer science in the industrial applications of control
Finite-time optimal control of polynomial systems using successive suboptimal approximations
Journal of Optimization Theory and Applications
Representation and Control of Infinite Dimensional Systems (Systems & Control: Foundations & Applications)
Boundary Control of Pdes: A Course on Backstepping Designs
Boundary Control of Pdes: A Course on Backstepping Designs
Survey Constrained model predictive control: Stability and optimality
Automatica (Journal of IFAC)
Journal of Control Science and Engineering
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We propose a framework to solve a closed-loop, optimal tracking control problem for a parabolic partial differential equation (PDE) via diffusivity, interior, and boundary actuation. The approach is based on model reduction via proper orthogonal decomposition (POD) and Galerkin projection methods. A conventional integration-by-parts approach during the Galerkin projection fails to effectively incorporate the considered Dirichlet boundary control into the reducedorder model (ROM). To overcome this limitation we use a spatial discretization of the interior product during the Galerkin projection. The obtained low dimensional dynamical model is bilinear as the result of the presence of the diffusivity control term in the nonlinear parabolic PDE system. We design a closed-loop optimal controller based on a nonlinear model predictive control (MPC) scheme aimed at bating the effect of disturbances with the ultimate goal of tracking a nominal trajectory. A quasi-linear approximation approach is used to solve on-line the quadratic optimal control problem subject to the bilinear reduced-order model. Based on the convergence properties of the quasi-linear approximation algorithm, the asymptotical stability of the closed-loop nonlinear MPC scheme is discussed. Finally, the proposed approach is applied to the current profile control problem in tokamak plasmas and its effectiveness is demonstrated in simulations.