The main contribution of this paper is to provide a unified treatment to the problems of constrained minimum-time trajectory generation, fault detection and identification, and (after a fault has been detected and identified) trajectory reconfiguration, in an integrated scheme using a differential flatness and B-splines parameterisation. Using the flatness/B-splines parameterisation the problem of minimum-time constrained trajectory planning is cast into a feasibility-search problem in the splines control-points space, in which the constraint region is characterised by a polytope. A close approximation of the minimum-time trajectory is obtained by systematically searching the end-time that makes the constraint polytope to be minimally feasible. Fault detection is carried out by using B-splines in an FIR filter implementation. Thus, the three - traditionally dealt with separately - problems (namely, trajectory generation, fault detection, and trajectory reconfiguration) are solved in a unified manner, using the same mathematical/computational tools. This, not only offers an elegant solution, but also has the potential to simplify the coding of the algorithms for the real-time application of the strategy. All through the paper, a case-study consisting in an input-constrained double-tank system is analysed in order to illustrate the techniques in an intuitive manner.
1st Australian Control Conference, 2011 (AUCC 2011). Proceedings of the 1st Australian Control Conference 2011 (Melbourne 10-11 November, 2011) p. 173-178