Epistemic uncertainty in optimal control simulation - Eisentraudt, Markus; Leyendecker, Sigrid (Mechanical Systems and Signal Processing, 2019)
In the optimal control of temporally discretised mechanical systems, parameters like initial and final conditions, mass quantities or geometric quantities are usually assumed as precisely defined. Then, any optimal trajectory of control forces or coordinates defines a time dependent deterministic mapping. However, in practice, the parameters are usually uncertain. In this paper, epistemic parameter uncertainty in the optimal control of temporally discretised mechanical systems is considered. The uncertain parameters are modelled as fuzzy quantities. With the extension principle of fuzzy set theory, the deterministic mapping is transformed into a time dependent fuzzy mapping. The fuzzy output can be determined with the concept of α" role="presentation" style="display: inline-block; line-height: normal; font-size: 14.4px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border-width: 0px; border-style: initial; position: relative;">α-discretisation and α" role="presentation" style="display: inline-block; line-height: normal; font-size: 14.4px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border-width: 0px; border-style: initial; position: relative;">α-level optimisation. However, a straight forward application of α" role="presentation" style="display: inline-block; line-height: normal; font-size: 14.4px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border-width: 0px; border-style: initial; position: relative;">α-level optimisation leads to computationally inefficient hierarchical α" role="presentation" style="display: inline-block; line-height: normal; font-size: 14.4px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border-width: 0px; border-style: initial; position: relative;">α-level optimisation problems. An approximative formulation is developed, which can be used to replace the hierarchical α" role="presentation" style="display: inline-block; line-height: normal; font-size: 14.4px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border-width: 0px; border-style: initial; position: relative;">α-level optimisation problems by conventional finite dimensional α" role="presentation" style="display: inline-block; line-height: normal; font-size: 14.4px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border-width: 0px; border-style: initial; position: relative;">α-level optimisation problems.<br
Keywords: Epistemic uncertainty; Optimal control simulation; α-Level optimisation