Explicit model predictive control of hybrid systems and multiparametric mixed integer polynomial programming

Abstract

Hybrid systems are dynamical systems characterized by the simultaneous presence of discrete and continuous variables. Model-based control of such systems is computationally demanding. To this effect, explicit controllers which provide control inputs as a set of functions of the state variables have been derived, using multiparametric programming mainly for the linear systems. Hybrid polynomial systems are considered resulting in a Mixed Integer Polynomial Programming problem. Treating the initial state of the system as a set of bounded parameters, the problem is reformulated as a multiparametric Mixed Integer Polynomial optimization (mp-MIPOPT) problem. A novel algorithm for mp-MIPOPT problems is proposed and the exact explicit control law for polynomial hybrid systems is computed. The key idea is the computation of the analytical solution of the optimality conditions while the binary variables are treated as relaxed parameters. Finally, using symbolic calculations exact nonconvex critical regions are computed.

Stability criterion for the intensification of batch processes with model predictive control

“…The mathematical formulation for MPC at the i th step used in this work is given by (Charitopoulos and Dua, 2016;Rawlings and Mayne, 2015):…”

Process design and control optimization: A simultaneous approach by multi‐parametric programming

“…An alternative formulation could be the treatment of integer parameters as continuous parameters (similar to handling binary variables in Ref. 133) since the integer value realization of the parameter is a subset of their continuous values and the realization is not an mpMPC decision.…”

Parameter estimation using multiparametric programming for implicit Euler’s method based discretization

“…Hence, a multiparametric programming approach was proposed to overcome these limitations by obtaining model parameters as an explicit function of measurements in our earlier work (Che Mid and Dua, 2017). Multiparametric programming provides the optimization variables as an explicit function of the parameter (Dua and Pistikopoulos, 1999, Pistikopoulos, 2009, Oberdieck et al, 2016, Pistikopoulos et al, 2007b, Pistikopoulos et al, 2007a, Charitopoulos and Dua, 2016. In that work, the model parameters were considered as optimization variables and the measurements as the parameters in the context of multiparametric programming.…”