Periodic economic model predictive control with bounded-state stability

This paper presents an economic model predictive control (EMPC) scheme for nonlinear affine systems employing the quadratic dissipativity constraint (QDC) previously introduced. The vector fields are included in the supply rate such that a dissipative condition based on linear matrix inequality (LMI) is rendered for nonlinear systems. Both storage function and supply rate are periodic and parameterized in this formulation. The closed-loop system stability is obtained as a result of having the QDC as an enforced stability constraint to the EMPC optimization. This is a constraint with respect to the current-time control vector. In finding a stability condition suitable for systems that may not operate at the optimal steady state with EMPC, we have chosen the bounded-state stability (BSS) and derive a stabilizability condition with QDC in the discrete-time domain. The BSS is characterized by a non-monotonically decreasing storage function and the boundedness property.