Abstract
This contribution addresses the task of computing optimal control trajectories for hybrid systems with switching dynamics. Starting from a continuous-time formulation of the control task we derive an optimization problem in which the system behavior is modelled by a hybrid automaton with linear discrete-time dynamics and discrete as well as continuous inputs. In order to transform the discrete dynamics into an equation-based form we present and compare two different approaches: one uses the ‘traditional’ M-formulation and one is based on disjunctive formulations. The control problem is then solved by mixed integer programming using a moving horizon setting. As illustrated for an example, the disjunctive formulation can lead to a considerable reduction of the computational effort.
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References
Branicky, M.S., Borkar, V.S., Mitter, S.K.: Auni fied framework for hybrid control: Model and optimal control theory. IEEE Trans. Automatic Contr. 43 (1998) 31–45
Sussmann, H.: Ama ximum principle for hybrid optimal conrol problems. In: Proc. 38th IEEE Conf. Decision and Control. (1999) 425–430
Broucke, M., Di Benedetto, M., Di Gennaro, S., Sangiovanni-Vincentelli, A.: Theory of optimal control using bisimulations. In: Proc. 3rd Int. Workshop of Hybrid Systems: Comp. and Control. Volume 1790 of LNCS., Springer (2000) 89–102
Bemporad, A., Morari, M.: Control of systems integrating logic, dynamics, and constraints. Automatica 35 (1999) 407–427
Hedlund, S., Rantzer, A.: Optimal control of hybrid systems. In: Proc. 38th Conf. Decision and Control (Phoenix). (1999)
Xu, X., Antsaklis, P.: An approach for solving general switched linear quadratic optimal control problems. In: Proc. 40th IEEE Conf. Decision and Control. (2001) 2478–2483
Zhang, P., Cassandras, C.: An improved forward algorithm for optimal control of a class of hybrid systems. In: Proc. 40th IEEE Conf. Decision and Control. (2001)1235–1236
Stursberg, O., Engell, S.: Optimized startup-procedures of processing systems. In: Proc. 6th IFAC Symp. Dynamics and Control of Process Sys. (2001) 231–236
Stursberg, O., Engell, S.: Optimal control of switched continuous systems using mixed-integer programming. In: Proc. 15th IFAC World Congress on Automatic Control (to appear). (July 2002)
Williams, H.P.: Model Building in Mathematical Programming. 1st edn. J. Wiley P. (1978)
Jaffar, J., Maher, M.: Constraint logic programming: Asu rvey. Journal of Logic Programming 19/20 (1994) 503–581
Balas, E.: Disjunctive programming and a hierarchy of relaxations for discrete optimization problems. SIAM Journal Alg. Disc. Meth. 6 (1985) 466–486
Lee, S., Grossmann, I.: New algorithms for nonlinear generalized disjunctive programming. Comp. and Chemical. Eng. 4 (2000) 2125–2141
Glover, F.: Improved linear integer programming formulations of nonlinear integer problems. Managem. Science 22 (1975) 455–460
Cavalier, T., Pardalos, P., Soyster, A.: Modeling and integer programming techniques applied to propositional calculus. Comp. and Oper. Res. 17 (1990) 561–570
Vecchietti, A., Grossmann, I.: Logmip: A disjunctive 0-1 nonlinear optimizer for process system models. Comp. and Chemical. Eng. 23 (1999) 555–565
Brooke, A., Kendrick, D., Meeraus, A., Raman, R.: GAMS/CPLEX-A User’s Guide. GAMS Development Corporation (1998)
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Stursberg, O., Panek, S. (2002). Control of Switched Hybrid Systems Based on Disjunctive Formulations. In: Tomlin, C.J., Greenstreet, M.R. (eds) Hybrid Systems: Computation and Control. HSCC 2002. Lecture Notes in Computer Science, vol 2289. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45873-5_33
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DOI: https://doi.org/10.1007/3-540-45873-5_33
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