Optimality zone algorithms for hybrid systems: efficient algorithms for optimal location and control computation

Authors:
Peter E. Caines;M. Shahid Shaikh
Affiliations:
Department of Electrical & Computer Engineering, Centre for Intelligent Machines, McGill University, Montréal, Québec, Canada;Department of Electrical & Computer Engineering, Centre for Intelligent Machines, McGill University, Montréal, Québec, Canada
Venue:
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Year:
2006

Citing 5
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Abstract

A general Hybrid Minimum Principle (HMP) for hybrid optimal control problems (HOCPs) is presented in [1, 2, 3, 4] and in [4, 5], a class of efficient, provably convergent Hybrid Minimum Principle (HMP) algorithms were obtained based upon the HMP. The notion of optimality zones (OZs) ([3, 4]) provides a theoretical framework for the computation of optimal location (i.e. discrete state) schedules for HOCPs (i.e. discrete state sequences with the associated switching times and states). This paper presents the algorithm HMPOZ which fully integrates the prior computation of the OZs into the HMP algorithms class. Summing (a) the computational investment in the construction of the OZs for a given HOCP, and (b) the complexity of (i) the computation of the optimal schedule, (ii) the optimal switching time and optimal switching state sequence, and (iii) the optimal continuous control input, yields a complexity estimate for the algorithm HMPOZ which is linear (i.e. O(L)) in the number of switching times L.