Abstract
Bang-bang control problems subject to a state inequality constraint are considered. It is shown that the control problem induces an optimization problem, where the optimization vector assembles the switching and junction times for bang-bang and boundary arcs. Second order sufficient conditions (SSC) for the state-constrained control problem are given which require that SSC for the induced optimization problem are satisfied and a generalized strict bang-bang property holds at switching and junction times. This type of SSC ensures solution differentiability of optimal solutions under parameter perturbations and allows to compute parametric sensitivity derivatives. A numerical algorithm is presented that simultaneously determines a solution candidate, performs the second-order test and computes parametric sensitivity derivatives. We illustrate the algorithm with two state-constrained optimal control problems in biomedicine.
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Maurer, H., Vossen, G. (2009). Sufficient Conditions and Sensitivity Analysis for Optimal Bang-Bang Control Problems with State Constraints. In: Korytowski, A., Malanowski, K., Mitkowski, W., Szymkat, M. (eds) System Modeling and Optimization. CSMO 2007. IFIP Advances in Information and Communication Technology, vol 312. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04802-9_4
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DOI: https://doi.org/10.1007/978-3-642-04802-9_4
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