Robust maneuvering envelope estimation based on reachability analysis in an optimal control formulation
This paper discusses an algorithm for estimating the safe maneuvering envelope of damaged aircraft. The algorithm performs a robust reachability analysis through an optimal control formulation while making use of time scale separation and taking into account uncertainties in the aerodynamic derivatives. Starting with an optimal control formulation, the optimization problem can be rewritten as a Hamilton-Jacobi-Bellman equation. This equation can be solved by level set methods. This approach has been applied on an aircraft example involving structural airframe damage. Monte Carlo validation tests have confirmed that this approach is successful in estimating the safe maneuvering envelope for damaged aircraft.
An Adaptive Nonlinear Aircraft Maneuvering Envelope Estimation Approach for Online Applications
A nonlinear aircraft model is presented and used to develop an overall unified approach to online trim and maneuverability envelope estimation with uncertainty quantification without any requirement for active input excitation. The concept of time scale separation makes this method suitable for the adaptive characterization of altered safe maneuvering limitations based on aircraft performance after impairment. The results can be used to provide pilot feedback and/or be combined with flight planning, trajectory generation, and guidance algorithms to help maintain safe aircraft operations in both nominal and off-nominal scenarios.
Mathematical Time and Physical Time in the Theory Of Relativity
In the Theory of Relativity time is an imaginary quantity that can not be observed; it is a multiplication of a number that indicates duration of material change and number i that is an imaginary number. i on the square is -1. Time i⁄t is a mathematical time that describes the speed and the duration of material change. In the Universe one can observe physical time only as a stream of material change. It is not that change run in physical time, change itself is physical time.. Distinction between imaginary mathematical time and visible physical time opens some new perspectives into interpretation of Theory of Relativity. c