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-rw-r--r--templates/MPC.m44
-rw-r--r--templates/lqr_maxPI.m37
-rw-r--r--templates/traj_cost.m6
3 files changed, 76 insertions, 11 deletions
diff --git a/templates/MPC.m b/templates/MPC.m
index 3e9d2f1..355eb81 100644
--- a/templates/MPC.m
+++ b/templates/MPC.m
@@ -15,31 +15,57 @@ classdef MPC
function obj = MPC(Q,R,N,params)
nu = params.model.nu;
nx = params.model.nx;
-
- % define optimization variables
+ % YOUR CODE HERE
+ A=params.model.A;
+ B=params.model.B;
U = sdpvar(repmat(nu,1,N),ones(1,N),'full');
+ X = sdpvar(repmat(nx,1,N+1),ones(1,N+1),'full');
+
+ [K,P,~] = dlqr(A,B,Q,R);
+
+% s_max=params.constraints.MaxAbsPositionXZ;
+% y_max=params.constraints.MaxAbsPositionY;
+% u_max = params.constraints.MaxAbsThrust;
+ H_x = params.constraints.StateMatrix;
+ h_x = params.constraints.StateRHS;
+ H_u = params.constraints.InputMatrix;
+ h_u = params.constraints.InputRHS;
X0 = sdpvar(nx,1,'full');
+ objective = 0;
+ constraints = X{1} == X0;
+ for k = 1:N
+ constraints = [ ...
+ constraints, ...
+ X{k+1} == A*X{k} + B*U{k} , ...
+ H_x * X{k} <= h_x, ...
+ H_u * U{k} <= h_u ...
+ ];
- % YOUR CODE HERE
-
+ objective = objective + X{k}'*Q*X{k} + U{k}'*R*U{k};
+ end
+ objective=objective+X{N+1}'*P*X{N+1};
+ % terminal constraint
+% constraints = [ ...
+% constraints, ...
+% X{N+1} == zeros(nx,1)
+% ];
opts = sdpsettings('verbose',1,'solver','quadprog');
obj.yalmip_optimizer = optimizer(constraints,objective,opts,X0,{U{1} objective});
end
function [u, ctrl_info] = eval(obj,x)
- %% evaluate control action by solving MPC problem, e.g.
+ % evaluate control action by solving MPC problem
tic;
- [optimizer_out,errorcode] = obj.yalmip_optimizer(x);
+ [optimizer_out,errorcode,~] = obj.yalmip_optimizer{x};
solvetime = toc;
-
+
[u, objective] = optimizer_out{:};
feasible = true;
if (errorcode ~= 0)
feasible = false;
end
-
ctrl_info = struct('ctrl_feas',feasible,'objective',objective,'solvetime',solvetime);
end
end
-end \ No newline at end of file
+end
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
+
+
diff --git a/templates/traj_cost.m b/templates/traj_cost.m
index 7e0b443..57566c9 100644
--- a/templates/traj_cost.m
+++ b/templates/traj_cost.m
@@ -8,4 +8,10 @@
function J_Nt = traj_cost(Xt,Ut,Q,R)
% YOUR CODE HERE
+ J_Nt=0;
+ for i=1:length(Xt(1,:))-1
+ a= Xt(:,i)'*Q*Xt(:,i);
+ b= Ut(:,i)'*R*Ut(:,i);
+ J_Nt=J_Nt+a+b;
+ end
end \ No newline at end of file