Approximation of PWA control laws using regular partitions : an ISS approach

Piecewise affine (PWA) feedback control laws defined on general polytopic partitions, as, for instance, obtained by explicit MPC, will often be prohibitively complex for application to fast systems. Therefore, we study the problem of approximating these high-complexity controllers by low-complexity PWA control laws defined on more regular partitions, facilitating faster on-line evaluation. The off-line approach is based on the existence of an input-to-state stable (ISS) Lyapunov function, which is exploited to obtain conditions that guarantee a priori asymptotic stability and constraint satisfaction of the resulting low-complexity control law. These conditions can be expressed as local semidefinite programs (SDPs) or linear programs (LPs), respectively, and apply to PWA plants.