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.

Advanced decision making in the process industries requires ecient use of information available at dierent decision levels. Traditionally, planning, scheduling and optimal control problems are solved in a decoupled way, neglecting their strong interdependence. Integrated Planning, Scheduling and optimal Control (iPSC) aims to address this issue. Formulating the iPSC, results in a large scale non-convex Mixed Integer Nonlinear Programming problem. In the present work, we propose a new approach for the iPSC of continuous processes aiming to reduce model and computational complexity. For the planning and scheduling, a Travelling Salesman Problem (TSP) based formulation is employed, where the planning periods are modelled in discrete time while the scheduling within each week is in continuous time. Another feature of the proposed iPSC framework is that backlog, idle production time and multiple customers are introduced. The resulting problem is a Mixed Integer Programming problem and dierent solution strategies are employed and analysed.

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