« Previous « Start » Next »
92 Rigid Body Rotation
On smooth optimal control determination, Ilya Ioslovich and Per-Olof Gutman, Technion, Israel Institute of Technology.
Example 1: Rigid body rotation
92.1 Problem Description
Find u over t in [0; 1 ] to minimize:
subject to:
Reference: [18]
92.2 Problem setup
toms t
p = tomPhase('p', t, 0, 1, 20);
setPhase(p);
tomStates x y u1 u2
% Boundary constraints
cbnd = {initial({x == 0.9; y == 0.75})
final({x == 0; y == 0})};
% ODEs and path constraints
a = 2;
ceq = collocate({dot(x) == a*y+u1; dot(y) == -a*x+u2
dot(u1) == a*u2; dot(u2) == -a*u1});
% Objective
objective = 0.25*integrate((u1.^2+u2.^2).^2);
92.3 Solve the problem
options = struct;
options.name = 'Rigid Body Rotation';
solution = ezsolve(objective, {cbnd, ceq}, [], options);
t = subs(collocate(t),solution);
x = subs(collocate(x),solution);
y = subs(collocate(y),solution);
u1 = subs(collocate(u1),solution);
u2 = subs(collocate(u2),solution);
Problem type appears to be: con
Starting numeric solver
===== * * * =================================================================== * * *
TOMLAB - Tomlab Optimization Inc. Development license 999001. Valid to 2011-02-05
=====================================================================================
Problem: --- 1: Rigid Body Rotation f_k 0.470939062500256130
sum(|constr|) 0.000000000003070916
f(x_k) + sum(|constr|) 0.470939062503327070
f(x_0) 0.000000000000000000
Solver: snopt. EXIT=0. INFORM=1.
SNOPT 7.2-5 NLP code
Optimality conditions satisfied
FuncEv 3 GradEv 1 MinorIter 39
CPU time: 0.031250 sec. Elapsed time: 0.032000 sec.
92.4 Plot result
figure(1);
subplot(2,1,1);
plot(t,x,'*-',t,y,'*-');
legend('x','y');
subplot(2,1,2);
plot(t,u1,'*-',t,u2,'*-');
legend('u1','u2');
« Previous « Start » Next »
TOMLAB
