1 files changed, 45 insertions, 0 deletions
diff --git a/Submission files/lqr_maxPI.m b/Submission files/lqr_maxPI.m
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+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Copyright (c) 2023, Amon Lahr, Simon Muntwiler, Antoine Leeman & Fabian Flürenbrock Institute for Dynamic Systems and Control, ETH Zurich.
+%
+% All rights reserved.
+%
+% Please see the LICENSE file that has been included as part of this package.
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+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
+
+
+