Hamiltonian Method for Steady State Optimal Control and Filtering

2018 ◽  
pp. 225-270
Author(s):  
Zoran Gajić ◽  
Myo-Taeg Lim ◽  
Dobrila Škatarić ◽  
Wu-Chung Su ◽  
Vojislav Kecman
Keyword(s):  
Optimal Control ◽  
Steady State ◽  
Hamiltonian Method

A quasi steady state approach to race car lap simulation in order to understand the effects of racing line and centre of gravity location

2005 ◽  
Vol 219 (6) ◽  
pp. 725-739 ◽  
Author(s):  
D L Brayshaw ◽  
M F Harrison
Keyword(s):  
Optimal Control ◽  
Steady State ◽  
Control Method ◽  
Interim Result ◽  
Quasi Steady State ◽  
Race Car ◽  
Centre Of Gravity ◽  
Optimal Control Method ◽  
Optimal Line ◽  
Set Up

Using an established seven-degree-of-freedom (7DOF) model of an open wheel race car, a new quasi steady state lap simulation method is described. The method is based on optimal control techniques. It produces a GG speed diagram as an interim result, and is shown to have a low computational expenditure when compared with the current transient optimal control method. This paper shows a validation step, reports a case study using the new method, and compares the result with a transient optimal control method. The sensitivity of the optimal line for simulation studies is discussed in terms of a centre of gravity location change. Both simulation methods show improvements in lap time owing to a 6 per cent centre of gravity set-up change. The difference in optimal lines caused by a 6 per cent CG change rearward is shown to be so small that a driver is unlikely to find the information useful. In light of this observation, the computational effort required to generate a new optimal line for each set-up change may be misspent

Optimal control of growth coefficient on a steady-state population model

2010 ◽  
Vol 11 (2) ◽  
pp. 688-704 ◽  
Author(s):  
W. Ding ◽  
H. Finotti ◽  
S. Lenhart ◽  
Y. Lou ◽  
Q. Ye
Keyword(s):  
Optimal Control ◽  
Steady State ◽  
Population Model ◽  
Growth Coefficient ◽  
State Population

Mathematical analysis and optimal control for Chikungunya virus with two routes of infection with nonlinear incidence rate

2021 ◽  
pp. 2150088 ◽  
Author(s):  
Miled El Hajji ◽  
Abdelhamid Zaghdani ◽  
Sayed Sayari
Keyword(s):  
Optimal Control ◽  
Steady State ◽  
Chikungunya Virus ◽  
Optimal Solution ◽  
Infection Model ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
State Formula ◽  
Number Formula ◽  
Global Threat

Chikungunya fever, caused by Chikungunya virus (CHIKV) and transmitted to humans by infected Aedes mosquitoes, has posed a global threat in several countries. In this paper, we investigated a modified within-host Chikungunya virus (CHIKV) infection model with antibodies where two routes of infection are considered. In a first step, the basic reproduction number [Formula: see text] was calculated and the local and global stability analysis of the steady states is carried out using the local linearization and the Lyapunov method. It is proven that the CHIKV-free steady-state [Formula: see text] is globally asymptotically stable when [Formula: see text], and the infected steady-state [Formula: see text] is globally asymptotically stable when [Formula: see text]. In a second step, we applied an optimal strategy in order to optimize the infected compartment and to maximize the uninfected one. For this, we formulated a nonlinear optimal control problem. Existence of the optimal solution was discussed and characterized using some adjoint variables. Thus, an algorithm based on competitive Gauss–Seidel-like implicit difference method was applied in order to resolve the optimality system. The theoretical results are confirmed by some numerical simulations.

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