Optimal Thrust Programming Along the Brachistochronic Trajectory with Non-linear Drag
-
Oleg Cherkasov
,
Alena Zarodnyuk
Abstract
The problem of maximization of the horizontal coordinate of a mass-point moving in the vertical plane driven by gravity, non-linear viscous drag, and thrust is considered. The slope angle and the thrust are considered as a control variables. The problem is related to the modified brachistochrone problem. Principle maximum procedure allows to reduce the optimal control problem to the boundary value problem for a set of systems of two non-linear differential equations. The qualitative analysis of the trajectories of these systems is performed, and the characteristic features of the optimal solutions are determined. Thrust control depending on the velocity and slope angle is designed. Results obtained allow to construct quasi-optimal solutions for the more complex systems, where phase plane method is not applicable.
Acknowledgements
This work was supported by RFBR according to the research projects No. 18-01-00538, 17-08-01366.
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Articles in the same Issue
- Frontmatter
- Original Research Articles
- Existence Results of Mild Solutions for Impulsive Fractional Integrodifferential Evolution Equations With Nonlocal Conditions
- Conservation Laws of Space-Time Fractional mZK Equation for Rossby Solitary Waves with Complete Coriolis Force
- Abundant Lump Solution and Interaction Phenomenon of (3+1)-Dimensional Generalized Kadomtsev–Petviashvili Equation
- Multiple Solitary Wave Solutions for Nonhomogeneous Quasilinear Schrödinger Equations
- Fuzzy Logic Controller for Obstacle Avoidance of Mobile Robot
- Optimal Thrust Programming Along the Brachistochronic Trajectory with Non-linear Drag
- Numerical Treatment of the Fractional Modeling on Susceptible-Infected-Recovered Equations with a Constant Vaccination Rate by Using GEM
- The Fractional Chua Chaotic System: Dynamics, Synchronization, and Application to Secure Communications
- Dynamics of a Predator–Prey Model with Holling Type II Functional Response Incorporating a Prey Refuge Depending on Both the Species
