Modeling, simulation, sensitivity analysis, and optimization of hybrid systems

Abstract

Hybrid (discrete/continuous) systems exhibit both discrete state and continuous state dynamics which interact to such a significant extent that they cannot be decoupled and must be analyzed simultaneously. We present an overview of the work that has been done in the modeling, simulation, sensitivity analysis, and optimization of hybrid systems, paying particular attention to the interaction between discrete and continuous dynamics. A concise intuitive framework for hybrid system modeling is presented, together with discussions on robust state event location, transfer functions of the continuous state at discontinuities, parametric sensitivity analysis of hybrid systems, and challenges in optimization.

Review of Mixed‐Integer Nonlinear and Generalized Disjunctive Programming Methods

“…Lee [272]. Morari and Baric [273] present a review paper on developments in the control of hybrid systems.…”

“…Oldenburg and Marquardt [270] developed a GDP model of "fixed alternative sequences", formalizing modelling approaches proposed by several authors [272,274]. The authors solve the GDP model using a modified version of the logic based Outer Approximation, showing the efficiency of the algorithm in finding a global solutions fast.…”

Local optimization of dynamic programs with guaranteed satisfaction of path constraints

“…However, this simple approach requires sufficiently many points in approximating the path constraint and provides no direct error control. A more efficient way of controlling the error level involves formulating and solving a hybrid discretecontinuous dynamic system [2,9]. Specifically, an extra variable γ(t,ū) representing the maximal constraint violation up to t is appended to the dynamic system Algorithm 1.…”

Analysis of optimal operation of a fed-batch emulsion copolymerization reactor used for production of particles with core–shell morphology

“…The gPROMS environment for simulation and optimization offers an intuitive way to simulate mathematical models and it proved to be very efficient for optimization of hybrid and large-scale systems. Its features include solving systems of DAEs, automatic root finding of switching functions, when the process model is of discontinuous nature, as well as automatic sensitivity functions generation and evaluation which can be exploited for efficient run and implementation of CVP method [22]. As a consequence, gPROMS has gained a lot of interest from both academia and industry over the last decade.…”