Hybrid modeling and optimal control of an asphalt base process

This paper addresses the issue of an optimal selection of the production and delivery plan for an asphalt base process. The process is modeled as a DHA (Discrete Hybrid Automaton) using the high level modeling language HYSDEL (HYbrid System DEscription Language) that allows converting the DHA model into an MLD (Mixed Logical Dynamical) model. The proposed solution applies to a class of optimal control problems where the goal is to minimize the total completion time. The solution algorithm, which takes into account a model of a hybrid system described as an MLD system, is based on the reachability analysis. The algorithm abstracts the behavior of the hybrid system into a “tree of evolution”, where nodes of the tree represent reachable states of the system and branches connect two nodes if a transition exists between the corresponding states. To each node the cost function value is associated and, based on this value, the tree exploration is driven, searching for the optimal control profile.

[1]  Julio R. Banga,et al.  Optimization of hybrid discrete/continuous dynamic systems , 2000 .

[2]  V. Borkar,et al.  A unified framework for hybrid control: model and optimal control theory , 1998, IEEE Trans. Autom. Control..

[3]  Christos G. Cassandras,et al.  A hierarchical decomposition method for optimal control of hybrid systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[4]  Alberto Bemporad,et al.  Discrete-time Hybrid Modeling and Verification of the Batch Evaporator Process Benchmark , 2001, Eur. J. Control.

[5]  A. Rantzer,et al.  Optimizing linear system switching , 2001 .

[6]  Alberto Bemporad,et al.  HYSDEL-a tool for generating computational hybrid models for analysis and synthesis problems , 2004, IEEE Transactions on Control Systems Technology.

[7]  Alberto Bemporad,et al.  Control of systems integrating logic, dynamics, and constraints , 1999, Autom..

[8]  Panos J. Antsaklis,et al.  Special issue on hybrid systems: theory and applications a brief introduction to the theory and applications of hybrid systems , 2000, Proc. IEEE.

[9]  M. Morari,et al.  Model predictive control — Ideas for the next generation , 1999, 1999 European Control Conference (ECC).

[10]  Alberto Bemporad,et al.  Performance driven reachability analysis for optimal scheduling and control of hybrid systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[11]  A. Rantzer,et al.  Optimal control of hybrid systems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[12]  Anders Rantzer,et al.  Piecewise linear quadratic optimal control , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[13]  Bart De Schutter,et al.  Equivalence of hybrid dynamical models , 2001, Autom..