Modeling and predictive control of nonlinear hybrid systems using disaggregation of variables - A convex formulation

The current work is motivated by the need of achieving global solution and better computational efficiency for control of any arbitrary nonlinear hybrid dynamical systems (NHDS). In this work, we present a novel modeling and corresponding model predictive control (MPC) formulation for NHDS. The proposed modeling approach relies on disaggregation of polynomials of binary variables that appear in the multiple partially linearized (MPL) model. In particular, we use auxiliary continuous variables and linear constraints to model these polynomials and represent the MPL model in a linear fashion. Subsequently, disaggregation of the variables based multiple models are used to formulate the MPC law for NHDS. The MPC formulation takes similar form as multiple mixed logical dynamical (MMLD) model based MPC and yields a convex MIQP optimization problem. Moreover, the proposed modeling approach results in a compact model than the corresponding MMLD model as it refrains from adding any extra binary variables. Therefore, offers certain computational advantage when used for the predictive control of NHDS. The efficacy of the proposed solution is demonstrated on a three-tank benchmark hybrid system.