Model predictive control of nonlinear input-affine systems with feasibility and stability constraints

This paper presents a development for the model predictive control (MPC) of nonlinear systems employing the quadratic dissipativity constraint (QDC). In this QDC strategy for nonlinear input-affine systems, a compound output vector is engaged to the supply rate such that the stability condition based on linear matrix inequality (LMI) can be rendered for nonlinear systems. The compound vector shares similar properties of the so-called manifest variable defined in the behaviourial framework for dynamical systems. Unlike linear systems, the LMI-based condition for nonlinear systems has not been found widespread used in the control literature. The present method introduces an application of such condition to nonlinear systems in this paper. In conjunction with QDC, the MPC recursive feasibility is achievable by having a bounded condition on the local divergence of the Lyapunov function. Both the storage function and supply rate of the dissipation inequality are parameterized in this development. The multiplier matrices need to be re-computed at every time step in this approach. Numerical simulation with a network of two chemical reactors has demonstrated the success of QDC approach in MPC, employing the compound output vector.