Solve the continuous-time nonconvex optimal control problems as the attached file drawed with high efficiency. If you have a good idea, can you provide me with the example?
Hi, if a problem is nonconvex by nature, it is impossible to convert it in a convex problem. Nevertheless, convexity is not mandatory in case you want to solve the problem numerically by means of direct or indirect methods. The only drawback is that the optimum is not unique and diffirent local optima may exist
Yes, if a problem is nonconvex by nature, it is impossible to convert it in a convex problem. But I want to find a way to get an approximate expression which is convex.And, I have tried to discretize the time, but the efficiency is very poor, and it may be of poor convergence, it may be sensitive to initial boundary conditions,can you solve it by your method? If you can, can you show me a example with code?
Hi, as recommended by Hui-Liang, you can use GPOPS II or BOCOP:
http://bocop.org/
@Chun Liu
GPOPS is efficient in discretizing optimal control problems, no matter the problem is linear or nonlinear, convex or nonconvex. I tried to solve this problem with GPOPS but it failed to find a solution this time.
@Richard Epenoy
I have tried to use the ACADO to solve me problem, but the codes listed can't pass anyway, can you help me with it?
Codes:
clear;
BEGIN_ACADO; % Always start with "BEGIN_ACADO".
acadoSet('problemname', 'lujingguihua');% Set your problemname. If you
DifferentialState x;
DifferentialState y;
DifferentialState theata;
DifferentialState V;
Control a; % acceleration
Control u; % cruve rate
h = 0.0001;
Parameter T
%% Diferential Equation
f = acado.DifferentialEquation(0, T); % We would like to minize the time.
f.add(dot(x) == V*cos(theata)); % Write down your ODE.
f.add(dot(y) == V*sin(theata)); %
f.add(dot(theata) == V*u/7); %
f.add(dot(V) == a);
%% Optimal Control Problem
ocp = acado.OCP(0.0, T); % Set up the Optimal Control Problem (OCP) Start at 0 and go to T.
ocp.minimizeMayerTerm(T);
ocp.subjectTo( f );
ocp.subjectTo( 'AT_START', x == 0 );
ocp.subjectTo( 'AT_START', y == 0 );
ocp.subjectTo( 'AT_START', theata == pi/6 );
ocp.subjectTo( 'AT_START', V == 0 );
ocp.subjectTo( 'AT_END' , x == 100 );
ocp.subjectTo( 'AT_END' , y == 100 );
ocp.subjectTo( 'AT_END' , theata == 0 );
ocp.subjectTo( 'AT_END' , V == 0 );
ocp.subjectTo( 0
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