From 1f12e47e6d1fe8b365806aa0b42de237970d53bf Mon Sep 17 00:00:00 2001
From: Nao Pross <np@0hm.ch>
Date: Wed, 24 May 2023 16:50:06 +0200
Subject: Take deliverables for Robust MPC from yanzhen

According to table 12

  - generate_disturbances
  - simulate_uncertain
  - compute_tube_contorller
  - compute_minRPI
  - compute_tightening
  - MPC_TUBE
  - MPC_TUBE/eval (contained in MPC_TUBE.m)
  - MPC_TUBE_script (and its output MPC_TUBE_params.mat)
---
 templates/MPC_TUBE.m | 47 +++++++++++++++++++++++++++++++++++++++++++++--
 1 file changed, 45 insertions(+), 2 deletions(-)

(limited to 'templates/MPC_TUBE.m')

diff --git a/templates/MPC_TUBE.m b/templates/MPC_TUBE.m
index bd62044..9a630c1 100644
--- a/templates/MPC_TUBE.m
+++ b/templates/MPC_TUBE.m
@@ -15,8 +15,48 @@ classdef MPC_TUBE
     methods
         function obj = MPC_TUBE(Q,R,N,H_N,h_N,H_tube,h_tube,K_tube,params)
             obj.K_tube = K_tube;
-
+    
             % YOUR CODE HERE
+            nx = params.model.nx;
+            nu = params.model.nu;
+
+            A = params.model.A;
+            B = params.model.B;
+
+            [~,P,~] = dlqr(A,B,Q,R);
+
+            V = sdpvar(repmat(nu,1,N),ones(1,N),'full');
+            Z = sdpvar(repmat(nx,1,N+1),ones(1,N+1),'full');
+
+            H_x = params.constraints.StateMatrix;
+            h_x = params.constraints.StateRHS;
+            H_u = params.constraints.InputMatrix;
+            h_u = params.constraints.InputRHS;
+
+            P_x_tightened = Polyhedron('A',H_x,'b',h_x).minus(Polyhedron('A',H_tube,'b',h_tube));
+            H_z = P_x_tightened.A;
+            h_z = P_x_tightened.b;
+
+            P_u_tightened = Polyhedron('A',H_u,'b',h_u).minus(K_tube*Polyhedron('A',H_tube,'b',h_tube));
+            H_v = P_u_tightened.A;
+            h_v = P_u_tightened.b;
+
+            X0 = sdpvar(nx,1,'full');
+            constraints = [H_tube*(X0-Z{1}) <= h_tube];
+            objective = 0;
+            for k = 1:N
+                constraints = [ ...
+                    constraints, ...
+                    Z{k+1} == A*Z{k} + B*V{k} , ...
+%                     H_z * Z{k} <= h_z, ...
+%                     H_v * V{k} <= h_v ...
+                    H_x * Z{k} <= h_x, ...
+                    H_u * V{k} <= h_u ...
+                ];
+                objective = objective + Z{k}'*Q*Z{k} + V{k}'*R*V{k};
+            end
+            constraints = [constraints, H_N * Z{end} <= h_N];
+            objective = objective + Z{end}'*P*Z{end};
 
             opts = sdpsettings('verbose',1,'solver','quadprog');
             obj.yalmip_optimizer = optimizer(constraints,objective,opts,X0,{V{1} Z{1} objective});
@@ -28,7 +68,10 @@ classdef MPC_TUBE
             [optimizer_out,errorcode] = obj.yalmip_optimizer(x);
             solvetime = toc;
             % YOUR CODE HERE
-            
+            [v0, z0, objective] = optimizer_out{:};
+            u = obj.K_tube*(x-z0)+v0;
+
+
             feasible = true;
             if (errorcode ~= 0)
                 feasible = false;
-- 
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