Optimization Problem for ecms fcmincon

Hello. I reviewed a work that I got from the matlab library. In this study, it calculates the minimum value. But I couldn't find how it is calculated in real mathematics. I need help on how to solve this account. Does anyone know the solution or suggest a resource I can look into?

The code;

Pbatt_char= 1500;

SOC_min=60; SOC_max=90; Pfc_min=850;Pfc_max=8800; Pbatt_max=3400;

Aeq=[0 1 0;1 0 1];

mu=0.6;

beq=[1-2*mu*((u(2)-0.5*(SOC_max+SOC_min))/(SOC_max+SOC_min)); u(1)];

lb=[Pfc_min, 0, -Pbatt_char];

ub=[Pfc_max, 100, Pbatt_max];

x0=[3000, 0.1, 3000];

options = optimoptions('fmincon','Algorithm','active-set','Display','off','MaxFunctionEvaluations',1000,'MaxIterations',100);

[y,fval] = fmincon(@ecmsfun,x0,[],[],Aeq,beq,lb,ub,[],options);

Pfc=y(1); Pbatt=y(3); alpha=y(2);

sys = [Pfc Pbatt alpha];

Source: https://www.mathworks.com/help/physmod/sps/ug/energy-management-systems-for-a-hybrid-electric-source-application-for-a-more-electric-aircraft.html?s_tid=srchtitle_energy%20management%20system_8

From: ECMS s-funtion

[Walter Roberson]

I am not clear about what you are looking for? Are you looking for a mathematical function corresponding to that particular call to fmincon?

[Yusuf DOGAN]

Actually not. I want to find out by which mathematical method the algorithm solves the problem. example When 1st value is 1200 2nd value is 70, Algorithm shows 1st output as 2700 2nd output as -1500. How does he get this result? What math formula or math problem does he use. I will be happy if you can help.

Answer 1

[patrick1704]

Hi there,

the active-set algorithm you specified in your script is discussed in this Matlab article: Constrained Nonlinear Optimization Algorithms - MATLAB & Simulink - MathWorks Deutschland

In the end, the algorithm tries to solve the the Karush-Kuhn-Tucker optimality conditions by means of sequentially solving quadratic optimization problems, using gradient information, considering whether or not constraints are active or inactive.

You will also find a lot on this topic in general optimization/optimal control books like: Practical Methods for Optimal Control and Estimation Using Nonlinear Programming, Second Edition | SIAM Digital Library

[Yusuf DOGAN]

Thanks for information. İ going to review these articles

Answer 2

[Achmad]

Hello @Yusuf DOGAN. I am now trying to do analysis on that problem with same source as yours Energy Management Systems for a Hybrid Electric Source (Application for a More Electric Aircraft). But I can not find the S-function for the ECMS method. It is not included in the example. Could you help me by sharing your S-function m file if you still have it? Thank you.