Transformation of optimal control lagrange problems to Mayer problems with feedback linearized state equations

2001 ◽  
Author(s):  
Jaume Franch ◽  
Sunil K. Agrawal
Keyword(s):  
Optimal Control ◽  
State Equations ◽  
Lagrange Problems ◽  
Mayer Problems

scholarly journals Optimal Control of Diffusions with Hard Terminal State Restrictions

2012 ◽  
Vol 2012 ◽  
pp. 1-38
Author(s):  
Atle Seierstad
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Terminal State ◽  
The State ◽  
State Equations ◽  
Brownian Motions ◽  
Terminal Time ◽  
State Restrictions

A maximum principle is proved for certain problems of optimal control of diffusions where hard end constraints occur. The results apply to several dimensional problems, where some of the state equations involve Brownian motions, but not the equations corresponding to states being hard restricted at the terminal time.

scholarly journals An optimal control problem related to a 3D-chemotaxis-Navier-Stokes model

2021 ◽  
Author(s):  
Juan López-Ríos ◽  
Élder J. Villamizar-Roa
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimal Solution ◽  
Strong Solutions ◽  
External Source ◽  
Navier Stokes ◽  
State Equations ◽  
Velocity Equation ◽  
Concentration Equation

In this paper, we study an optimal control problem associated to a 3D-chemotaxis-Navier-Stokes model. First we prove the existence of global weak solutions of the state equations with a linear reaction term on the chemical concentration equation, and an external source on the velocity equation, both acting as controls on the system. Second, we establish aregularity criterion to get global-in-time strong solutions. Finally, we prove the existence of an optimal solution, and we establish a first-order optimality condition.

scholarly journals Kendali Optimal Model Prognosis Sindrom Metabolik Dengan Faktor Resiko Obesitas Dan Diabetes Melitus Tipe II Menggunakan Minimum Pontryagin

2020 ◽  
Vol 16 (2) ◽  
pp. 144-157
Author(s):  
Nurannisa ◽  
R Ratianingsih ◽  
J W Puspita
Keyword(s):  
Diabetes Mellitus ◽  
Risk Factors ◽  
Optimal Control ◽  
Type Ii Diabetes ◽  
Optimal Solution ◽  
Epidemiological Data ◽  
Type Ii Diabetes Mellitus ◽  
Type Ii ◽  
State Equations ◽  
Stability Type

ABSTRACTMetabolic syndrome (SM) is a compound of risk factors of cordiovascular disease occurancy. Obesity and type IIdiabetes mellitus are the main two of the risk factors. The epidemiological data shous that the prevalence ofmetabolic syndrome in the world is 20-25%. The objective of these research is control to minimize the prognosisof the disease among the SM population that have obesity and type II DM risk factors. The pontryagin minimumprinciple is used to determine the optimal solution of the prognosis model that the optimal control. The solution is derived from the state and co-state state equations that are evaluated of the drug that give to the sufferer in stationary conditions. The performance Index was designed to minimize the number of SM population that suffer obesity and type II diabetes mellitus and the use of sulfonilurea that given as the normoweighted populations and biguanid for obese populations. The simulation of the optional solution shows that the optimal control was derived to control the number SM that have population of the optional solution obesity and type II DM risk with optimal biguanide 500 mg and sulfonilurea 5 mg as much.Keywords : Metabolic Syndrome, Minimum Pontryagin, Obesity, Stability ,Type II Diabetes Mellitus.

Optimal Control Discipline Research of Hydraulic System of Sugarcane Harvester

2011 ◽  
Vol 199-200 ◽  
pp. 1281-1286
Author(s):  
Yi Zhi Hu ◽  
Ying Chun Hu ◽  
Jun Yan Hou ◽  
Hui Zhu
Keyword(s):  
Optimal Control ◽  
Minimum Principle ◽  
Control Valve ◽  
Flow Control Valve ◽  
State Equations ◽  
Controlling System ◽  
Spring Force ◽  
Time Optimal ◽  
Sugarcane Harvester ◽  
Theory Base

The actiyator of chassis mechanism of sugarcane harvester was a cubage flow regulation circuit consisted of a timing variable pump and a compensated flow control valve. The optimal controlling system described its movement from processing time using differential and state equations. The shortest-time optimal controlling trajectory of spring force of the variable pump was a group of concentric circles based on minimum principle, which controlling signal switched on origin trajectory. Under the condition of optimal control, the stator was pushed by spring to a new balance spot which left off origin 15.5 millimeter in the shortest time of 1.12 seconds, which provided theory base to further controlling system design. Its stability and validity has been proved well in physical product research.

scholarly journals Robust Inverse Optimal Control for a Boost Converter

Energies ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2507
Author(s):  
Mario Villegas-Ruvalcaba ◽  
Kelly Joel Gurubel-Tun ◽  
Alberto Coronado-Mendoza
Keyword(s):  
Optimal Control ◽  
Robust Control ◽  
Input Voltage ◽  
Boost Converter ◽  
Voltage Reference ◽  
Inverse Optimal Control ◽  
State Equations ◽  
Control Lyapunov Function ◽  
Operation Conditions ◽  
The Stability

The variability of renewable energies and their integration into the grid via power electronics demands the design of robust control algorithms. This work incorporates two techniques to ensure the stability of a boost converter through its state equations, implementing the inverse optimal control and the gain-scheduling technique for robust control settings. In such a way that, under a single adjustment, it is capable of damping different changes such as changes in the parameters, changes in the load, the input voltage, and the reference voltage. On the other hand, inverse optimal control is based on a discrete-time control Lyapunov function (CLF), and CLF candidate depends on fixed parameters that are selected to obtain the solution for inverse optimal control. Once these parameters have been found through heuristic or artificial intelligence methods, the new proposed methodology is capable of obtaining a robust optimal control scheme, without having to search for new parameters through other methods, since these are sometimes sensitive changes and many times the process of a new search is delayed. The results of the approach are simulated using Matlab, obtaining good performance of the proposed control under different operation conditions. Such simulations yielded errors of less than 1% based on the voltage reference, given the disturbances caused by changes in the input variables, system parameters, and changes in the reference. Thus, applying the new methodology, the stability of our system was preserved in all cases.

Sign in / Sign up

Export Citation Format

Share Document