Take deliverables for from LQR to MPC from yuanxu

According to table 7 that is

  - lqr_maxPI
  - traj_cost
  - MPC
  - MPC/eval (contained in MPC.m)

1 files changed, 35 insertions, 2 deletions

diff --git a/templates/lqr_maxPI.m b/templates/lqr_maxPI.m
index efa335a..251d766 100644
--- a/templates/lqr_maxPI.m
+++ b/templates/lqr_maxPI.m
@@ -6,7 +6,40 @@
 % Please see the LICENSE file that has been included as part of this package.
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-function [H, h] = lqr_maxPI(Q,R,params)
-	% YOUR CODE HERE
+
+function [H, h] = lqr_maxPI(Q, R, params)
+    % Define the linear system
+    A = params.model.A;
+    B = params.model.B;
+    nx=params.model.nx;
+    nu=params.model.nu;
+    
+    s_max= params.constraints.MaxAbsPositionXZ;
+    y_max= params.constraints.MaxAbsPositionY;
+    u_max = params.constraints.MaxAbsThrust;
+    
+    K = -dlqr(A, B, Q, R);
+    systemLQR = LTISystem('A', A+B*K);
+%     absxmax = ones(nx,1)*s_max;
+%     absumax = ones(nu,1)*u_max;
+%     Xp = Polyhedron('A',[eye(nx); -eye(nx); K; -K], 'b', [absxmax;absxmax; absumax;absumax]);
+    Hx=params.constraints.StateMatrix;
+    hx=params.constraints.StateRHS;
+    Hu=params.constraints.InputMatrix;
+    hu=params.constraints.InputRHS;
+    Xp = Polyhedron('A',[Hx;Hu*K], 'b', [hx;hu]);
+    
+    figure(1);
+    systemLQR.x.with('setConstraint');
+    systemLQR.x.setConstraint = Xp;
+    InvSetLQR = systemLQR.invariantSet();
+    InvSetLQR.plot(), alpha(0.25), title('Invariant Set for Triple Integrator under LQR Control'), xlabel('x_1'), ylabel('x_2'), zlabel('x_3');
+
+    H=InvSetLQR.A;
+    h=InvSetLQR.b;
+
+
 end
 
+
+