From 0105f2746c6dd8c3617f93fd3281f7e2708cae76 Mon Sep 17 00:00:00 2001
From: Nao Pross <np@0hm.ch>
Date: Wed, 24 May 2023 16:29:40 +0200
Subject: 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)
---
 templates/MPC.m       | 44 +++++++++++++++++++++++++++++++++++---------
 templates/lqr_maxPI.m | 37 +++++++++++++++++++++++++++++++++++--
 templates/traj_cost.m |  6 ++++++
 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
-- 
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