Explicit/multi-parametric model predictive control of dissipative distributed parameter systems

This work focuses on the development of an explicit/multi-parametric model predictive control algorithm to stabilize the discrete infinite-dimensional system arising from the discrete state space modeling of certain class of dissipative distributed parameter systems, specifically, parabolic partial differential equation (PDE) systems. In particular, the class of parabolic PDEs that captures a large number of transport-reaction systems yields a discrete modal representation which captures the dominant dynamics of the parabolic PDE system. The proposed explicit/multi-parametric model predictive control algorithm is constructed in a way that the objective function is concerned with only the low-order modes, while the state constraints involve both the low-order and higher-order modes. The explicit model predictive control problem is solved off-line by dynamic programming and multi-parametric quadratic programming techniques, and the solution is expressed as a piecewise affine function with its corresponding critical regions.