ADD: init proj

27 files changed, 729 insertions, 0 deletions

diff --git a/templates/.MATLABDriveTag b/templates/.MATLABDriveTag
new file mode 100644
index 0000000..7aad4f3
--- /dev/null
+++ b/templates/.MATLABDriveTag
@@ -0,0 +1 @@
+f7c7757b-ada0-4bff-af70-1240edb65e6d
\ No newline at end of file
diff --git a/templates/LICENSE.txt b/templates/LICENSE.txt
new file mode 100644
index 0000000..685f12c
--- /dev/null
+++ b/templates/LICENSE.txt
@@ -0,0 +1,7 @@
+Copyright (c) 2023, Amon Lahr, Simon Muntwiler, Antoine Leeman & Fabian Flürenbrock Institute for Dynamic Systems and Control, ETH Zurich.
+
+All rights reserved.
+
+The files are provided for educational purposes only and should be distributed only to the attendees of the class "151-0660-00L Model Predictive Control FS2023".
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
diff --git a/templates/LQR.m b/templates/LQR.m
new file mode 100644
index 0000000..2a79da9
--- /dev/null
+++ b/templates/LQR.m
@@ -0,0 +1,27 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% 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.
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+classdef LQR
+    properties
+        K
+    end
+    
+    methods
+        %constructor
+        function obj = LQR(Q,R,params)
+            % YOUR CODE HERE
+            % obj.K = ... (save feedback matrix for use in eval function)
+        end
+        
+        function [u, ctrl_info] = eval(obj,x)
+            % YOUR CODE HERE
+            % u = ...
+            ctrl_info = struct('ctrl_feas',true);
+        end
+    end
+end
\ No newline at end of file
diff --git a/templates/MPC.m b/templates/MPC.m
new file mode 100644
index 0000000..3e9d2f1
--- /dev/null
+++ b/templates/MPC.m
@@ -0,0 +1,45 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% 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.
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+classdef MPC
+    properties
+        yalmip_optimizer
+    end
+
+    methods
+        function obj = MPC(Q,R,N,params)
+            nu = params.model.nu;
+            nx = params.model.nx;
+
+            % define optimization variables
+            U = sdpvar(repmat(nu,1,N),ones(1,N),'full');
+            X0 = sdpvar(nx,1,'full');
+
+            % YOUR CODE HERE
+            
+            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.
+            tic;
+            [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
diff --git a/templates/MPC_TE.m b/templates/MPC_TE.m
new file mode 100644
index 0000000..e0b55d2
--- /dev/null
+++ b/templates/MPC_TE.m
@@ -0,0 +1,36 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% 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.
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+classdef MPC_TE
+    properties
+        yalmip_optimizer
+    end
+
+    methods
+        function obj = MPC_TE(Q,R,N,params)
+            % YOUR CODE HERE
+            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.
+            tic;
+            [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
diff --git a/templates/MPC_TE_forces.m b/templates/MPC_TE_forces.m
new file mode 100644
index 0000000..5625f32
--- /dev/null
+++ b/templates/MPC_TE_forces.m
@@ -0,0 +1,38 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% 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.
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+classdef MPC_TE_forces
+    properties
+        forces_optimizer
+    end
+
+    methods
+        function obj = MPC_TE_forces(Q,R,N,params)
+            % YOUR CODE HERE
+            opts = getOptions('forcesSolver');
+            opts.printlevel = 0;
+            obj.forces_optimizer = % YOUR CODE HERE
+        end
+
+        function [u, ctrl_info] = eval(obj,x)
+            %% evaluate control action by solving MPC problem, e.g.
+            [optimizer_out,errorcode,info] = obj.forces_optimizer(x);
+            u = optimizer_out;
+            objective = info.pobj;
+            solvetime = info.solvetime;
+
+            feasible = true;
+            if any(errorcode ~= 1)
+                feasible = false;
+                warning('MPC infeasible');
+            end
+
+            ctrl_info = struct('ctrl_feas',feasible,'objective',objective,'solvetime',solvetime);
+        end
+    end
+end
\ No newline at end of file
diff --git a/templates/MPC_TS.m b/templates/MPC_TS.m
new file mode 100644
index 0000000..05f92ff
--- /dev/null
+++ b/templates/MPC_TS.m
@@ -0,0 +1,36 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% 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.
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+classdef MPC_TS
+    properties
+        yalmip_optimizer
+    end
+
+    methods
+        function obj = MPC_TS(Q,R,N,H,h,params)
+            % YOUR CODE HERE
+            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.
+            tic;
+            [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
diff --git a/templates/MPC_TS_SC.m b/templates/MPC_TS_SC.m
new file mode 100644
index 0000000..0e64767
--- /dev/null
+++ b/templates/MPC_TS_SC.m
@@ -0,0 +1,36 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% 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.
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+classdef MPC_TS_SC
+    properties
+        yalmip_optimizer
+    end
+
+    methods
+        function obj = MPC_TS_SC(Q,R,N,H,h,S,v,params)            
+            % YOUR CODE HERE
+            opts = sdpsettings('verbose',1,'solver','quadprog','quadprog.TolFun',1e-8);
+            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.
+            tic;
+            [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
diff --git a/templates/MPC_TUBE.m b/templates/MPC_TUBE.m
new file mode 100644
index 0000000..bd62044
--- /dev/null
+++ b/templates/MPC_TUBE.m
@@ -0,0 +1,40 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% 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.
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+classdef MPC_TUBE
+    properties
+        yalmip_optimizer
+        K_tube
+    end
+
+    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
+
+            opts = sdpsettings('verbose',1,'solver','quadprog');
+            obj.yalmip_optimizer = optimizer(constraints,objective,opts,X0,{V{1} Z{1} objective});
+        end
+
+        function [u, ctrl_info] = eval(obj,x)
+            %% evaluate control action by solving MPC problem, e.g.
+            tic;
+            [optimizer_out,errorcode] = obj.yalmip_optimizer(x);
+            solvetime = toc;
+            % YOUR CODE HERE
+            
+            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
diff --git a/templates/compute_minRPI.m b/templates/compute_minRPI.m
new file mode 100644
index 0000000..0b4ffdb
--- /dev/null
+++ b/templates/compute_minRPI.m
@@ -0,0 +1,11 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% 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_tube,h_tube,n_iter] = compute_minRPI(K_tube,params)
+    % YOUR CODE HERE
+end
\ No newline at end of file
diff --git a/templates/compute_tightening.m b/templates/compute_tightening.m
new file mode 100644
index 0000000..8919d12
--- /dev/null
+++ b/templates/compute_tightening.m
@@ -0,0 +1,11 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% 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 params = compute_tightening(K_tube,H_tube,h_tube,params)  
+	% YOUR CODE HERE
+end
\ No newline at end of file
diff --git a/templates/compute_tube_controller.m b/templates/compute_tube_controller.m
new file mode 100644
index 0000000..adca95d
--- /dev/null
+++ b/templates/compute_tube_controller.m
@@ -0,0 +1,11 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% 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 K_tube = compute_tube_controller(p,params)
+	% YOUR CODE HERE
+end
\ No newline at end of file
diff --git a/templates/generate_constraints.m b/templates/generate_constraints.m
new file mode 100644
index 0000000..892b706
--- /dev/null
+++ b/templates/generate_constraints.m
@@ -0,0 +1,11 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% 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_u, h_u, H_x, h_x] = generate_constraints(params)
+    % YOUR CODE HERE
+end
\ No newline at end of file
diff --git a/templates/generate_disturbances.m b/templates/generate_disturbances.m
new file mode 100644
index 0000000..570a4c9
--- /dev/null
+++ b/templates/generate_disturbances.m
@@ -0,0 +1,11 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% 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 Wt = generate_disturbances(params)
+    % YOUR CODE HERE
+end
\ No newline at end of file
diff --git a/templates/generate_params.m b/templates/generate_params.m
new file mode 100644
index 0000000..ef51366
--- /dev/null
+++ b/templates/generate_params.m
@@ -0,0 +1,45 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% 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 [params] = generate_params()
+params = struct();
+
+Tf = 60*60*24 * 2; % = 2 days
+dt = 60 * 10; % = 10 minutes
+
+% model
+params.model = struct(...
+    'nx', 6, ...
+    'nu', 3, ...
+    'Mass', 300, ...
+    'GravitationalParameter', 3.986e14, ...
+    'ScalingMatrix', [1e-6*eye(3), zeros(3); zeros(3), 1e-3*eye(3)], ...
+    'TargetRadius', 7000e3, ...
+    'TimeStep', dt, ...
+    'HorizonLength', ceil(Tf / dt), ...
+    'InitialConditionA', [-15e-3; -400e-3; 24.4e-3; 0; 0.0081; 0], ...
+    'InitialConditionB', [-20e-3; 400e-3; 24.4e-3; 0; 0.0108; 0], ...
+    'InitialConditionC', [0.02; 0.01; -0.005; 0; 0; 0] ...
+);
+
+% constraints
+params.constraints = struct(...
+    'MaxAbsPositionXZ', 0.1, ...
+    'MaxAbsPositionY', 1, ...
+    'MaxAbsThrust', 1, ...
+    'MaxFinalPosDiff' , 3e-4, ...
+    'MaxFinalVelDiff',  1e-3 ...
+);
+
+params.exercise = struct( ...
+    'QdiagOptA', [94.0; 0.1579; 300; 0.01; 0.10; 0.10] ...
+);
+    
+% YOUR CODE HERE
+
+end
diff --git a/templates/generate_params_z.m b/templates/generate_params_z.m
new file mode 100644
index 0000000..a7cfaa9
--- /dev/null
+++ b/templates/generate_params_z.m
@@ -0,0 +1,55 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% 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 [params_z] = generate_params_z(params)
+% initialize params_z
+params_z = params;
+
+% add initial condition of z-subsystem
+params_z.model = rmfield(params_z.model,{'InitialConditionA', ...
+                             'InitialConditionB', ...
+                             'InitialConditionC'});
+params_z.model.InitialConditionA_z = [-0.07;0.04]; % TODO: tune
+
+% define projection matrices
+T_z_x = [0 0 1 0 0 0;
+         0 0 0 0 0 1];
+T_z_u = [0 0 1];
+
+% projected system dynamics
+params_z.model.A = T_z_x*params.model.A*T_z_x';
+params_z.model.B = T_z_x*params.model.B*T_z_u';
+params_z.model.nx = 2;
+params_z.model.nu = 1;
+
+% state constraints
+Hx = params.constraints.StateMatrix * T_z_x';
+hx = params.constraints.StateRHS;
+X = Polyhedron('A',Hx,'b',hx);
+X.minHRep();
+
+params_z.constraints.StateMatrix = X.A;
+params_z.constraints.StateRHS = X.b;
+
+% input constraints
+Hu = params.constraints.InputMatrix * T_z_u';
+hu = params.constraints.InputRHS;
+U = Polyhedron('A',Hu,'b',hu);
+
+params_z.constraints.InputMatrix = U.A; 
+params_z.constraints.InputRHS = U.b;
+
+% disturbance constraints
+max_disturbance = 1e-4; % TODO: chose
+params_z.constraints.MaxAbsDisturbance = max_disturbance;
+H_w = kron(eye(params_z.model.nx),[1;-1]);
+h_w = ones(2*params_z.model.nx, 1) * max_disturbance;
+
+params_z.constraints.DisturbanceMatrix = H_w;
+params_z.constraints.DisturbanceRHS = h_w;
+end
diff --git a/templates/generate_system.m b/templates/generate_system.m
new file mode 100644
index 0000000..9deb347
--- /dev/null
+++ b/templates/generate_system.m
@@ -0,0 +1,11 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% 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 [A, B] = generate_system(Ac, Bc, params)
+    % YOUR CODE HERE
+end
\ No newline at end of file
diff --git a/templates/generate_system_cont.m b/templates/generate_system_cont.m
new file mode 100644
index 0000000..2d3ee79
--- /dev/null
+++ b/templates/generate_system_cont.m
@@ -0,0 +1,11 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% 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 [Ac, Bc] = generate_system_cont(params)
+    % YOUR CODE HERE
+end
\ No newline at end of file
diff --git a/templates/generate_system_scaled.m b/templates/generate_system_scaled.m
new file mode 100644
index 0000000..eac8db8
--- /dev/null
+++ b/templates/generate_system_scaled.m
@@ -0,0 +1,11 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% 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 [A,B] = generate_system_scaled(At,Bt,params)
+    % YOUR CODE HERE
+end
\ No newline at end of file
diff --git a/templates/lqr_maxPI.m b/templates/lqr_maxPI.m
new file mode 100644
index 0000000..efa335a
--- /dev/null
+++ b/templates/lqr_maxPI.m
@@ -0,0 +1,12 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% 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)
+	% YOUR CODE HERE
+end
+
diff --git a/templates/lqr_tuning.m b/templates/lqr_tuning.m
new file mode 100644
index 0000000..4a26158
--- /dev/null
+++ b/templates/lqr_tuning.m
@@ -0,0 +1,11 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% 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 [tuning_struct, i_opt] = lqr_tuning(x0,Q,params)
+    % YOUR CODE HERE
+end
\ No newline at end of file
diff --git a/templates/plot_trajectory.m b/templates/plot_trajectory.m
new file mode 100644
index 0000000..9bcb696
--- /dev/null
+++ b/templates/plot_trajectory.m
@@ -0,0 +1,126 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% 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 [fig_time,axes_time,fig_pos,axes_pos] = plot_trajectory(x,u,ctrl_info,params)
+    fig_time = figure;
+    
+    % check if input is 3-dimensional
+    n_traj = size(x,3);
+    assert(size(u,3) == n_traj);
+    assert(size(ctrl_info,3) == n_traj);
+
+    nx = params.model.nx;
+    assert(nx == size(x,1));
+
+    t = 0:params.model.TimeStep:params.model.TimeStep*params.model.HorizonLength;
+
+    % plot
+    axes_time = cell(5,1);
+    axes_time{1} = subplot(5,1,1);
+    hold on;
+
+    for i = 1:n_traj
+        plot(axes_time{1},t,x(1,:,i),'DisplayName',sprintf('x_%d',i));
+        plot(axes_time{1},t,x(3,:,i),'DisplayName',sprintf('z_%d',i));
+    end
+    legend('Location','EastOutside')
+
+    % max position
+    x_max = params.constraints.MaxAbsPositionXZ;
+    plot(axes_time{1}, [t(1); t(end)],[x_max; x_max],'k--','HandleVisibility','off');
+    plot(axes_time{1}, [t(1); t(end)],[-x_max; -x_max],'k--','HandleVisibility','off');
+    ylabel('Position [Mm]')
+
+    axes_time{2} = subplot(5,1,2);
+    hold on;
+    for i = 1:n_traj
+        plot(axes_time{2},t,x(2,:,i),'DisplayName',sprintf('y_%d',i));
+    end
+
+    % max position
+    y_max = params.constraints.MaxAbsPositionY;
+    plot(axes_time{2},[t(1); t(end)],[y_max; y_max],'k--','HandleVisibility','off');
+    plot(axes_time{2},[t(1); t(end)],[-y_max; -y_max],'k--','HandleVisibility','off');
+
+    legend('Location','EastOutside')
+    ylabel('Position [Mm]')
+
+    axes_time{3} = subplot(5,1,3);
+    hold on;
+    for i = 1:n_traj
+        plot(axes_time{3},t,x(4,:,i),'DisplayName',sprintf('v_{x%d}',i));
+        plot(axes_time{3},t,x(5,:,i),'DisplayName',sprintf('v_{y%d}',i));
+        plot(axes_time{3},t,x(6,:,i),'DisplayName',sprintf('v_{z%d}',i));
+    end
+
+    legend('Location','EastOutside')
+    ylabel('Velocity [km/s]')
+
+    axes_time{4} = subplot(5,1,4);
+    hold on;
+    % append one input value for plotting
+    u(:,length(t),:) = u(:,length(t)-1,:);
+    for i = 1:n_traj
+        stairs(axes_time{4},t,u(1,:,i)','DisplayName',sprintf('u_{x%d}',i));
+        stairs(axes_time{4},t,u(2,:,i)','DisplayName',sprintf('u_{y%d}',i));
+        stairs(axes_time{4},t,u(3,:,i)','DisplayName',sprintf('u_{z%d}',i));
+    end
+
+    % max thrust
+    thrust_max = params.constraints.MaxAbsThrust;
+    plot([t(1); t(end)],[thrust_max; thrust_max],'k--','HandleVisibility','off');
+    plot([t(1); t(end)],[-thrust_max; -thrust_max],'k--','HandleVisibility','off');
+    legend('Location','EastOutside')
+    ylabel('Thrust [N]')
+
+    % feasibility
+    axes_time{5} = subplot(5,1,5);
+    hold on;
+    for i = 1:n_traj
+        % append one input value for plotting
+        ctrl_feas = [ctrl_info(:,:,i).ctrl_feas];
+        ctrl_feas(length(t)) = ctrl_feas(length(t) - 1);
+        stairs(axes_time{5},t,ctrl_feas','DisplayName',sprintf('feas_%d',i));
+    end
+    legend('Location','EastOutside')
+    ylabel('Controller feasible [0/1]')
+
+    % link axes
+    axes_time = [axes_time{:}];
+    linkaxes(axes_time,'x');
+    xlabel('Time [s]')
+
+    % plot without time
+    % YX-plane
+    fig_pos = figure;
+    axes_pos = cell(2,1);
+    axes_pos{1} = subplot(2,1,1);
+    hold on
+    colormap('hsv')
+
+    for i = 1:n_traj
+        plot(axes_pos{1},x(2,:,i),x(1,:,i));
+    end
+
+    axis equal
+    xlabel('Y-Position [m]')
+    ylabel('X-Position [Mm]')
+
+    % YZ plane
+    axes_pos{2} = subplot(2,1,2);
+    hold on
+    for i = 1:n_traj
+        plot(axes_pos{2},x(2,:,i),x(3,:,i))
+    end
+    axis equal
+    xlabel('Y-Position [Mm]')
+    ylabel('Z-Position [Mm]')
+
+    axes_pos = [axes_pos{:}];
+    linkaxes(axes_pos,'x');
+end
\ No newline at end of file
diff --git a/templates/plot_trajectory_z.m b/templates/plot_trajectory_z.m
new file mode 100644
index 0000000..1b5a842
--- /dev/null
+++ b/templates/plot_trajectory_z.m
@@ -0,0 +1,78 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% 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 [fig_time,axes_time,fig_pos,axes_pos] = plot_trajectory_z(x,u,ctrl_info,params)
+    fig_time = figure;
+
+    % check if input is 3-dimensional
+    n_traj = size(x,3);
+    assert(size(u,3) == n_traj);
+    assert(size(ctrl_info,3) == n_traj);
+
+    nx = params.model.nx;
+    assert(nx == size(x,1));
+
+    t = 0:params.model.TimeStep:params.model.TimeStep*params.model.HorizonLength;
+
+    % plot
+    axes_time = cell(4,1);
+    axes_time{1} = subplot(4,1,1);
+    hold on;
+
+    for i = 1:n_traj
+        plot(axes_time{1},t,x(1,:,i),'DisplayName',sprintf('z_%d',i));
+    end
+    legend('Location','EastOutside')
+
+    % max position
+    x_max = params.constraints.MaxAbsPositionXZ; %*T(1);
+    plot(axes_time{1}, [t(1); t(end)],[x_max; x_max],'k--','HandleVisibility','off');
+    plot(axes_time{1}, [t(1); t(end)],[-x_max; -x_max],'k--','HandleVisibility','off');
+    ylabel('Position [Mm]')
+
+    axes_time{2} = subplot(4,1,2);
+    hold on;
+    for i = 1:n_traj
+        plot(axes_time{2},t,x(2,:,i),'DisplayName',sprintf('v_{z%d}',i));
+    end
+    legend('Location','EastOutside')
+    ylabel('Velocity [km/s]')
+
+    axes_time{3} = subplot(4,1,3);
+    hold on;
+    % append one input value for plotting
+    u(:,length(t),:) = u(:,length(t)-1,:);
+    for i = 1:n_traj
+        stairs(axes_time{3},t,u(1,:,i)','DisplayName',sprintf('u_{z%d}',i));
+    end
+
+    % max thrust
+    thrust_max = params.constraints.MaxAbsThrust;
+    plot([t(1); t(end)],[thrust_max; thrust_max],'k--','HandleVisibility','off');
+    plot([t(1); t(end)],[-thrust_max; -thrust_max],'k--','HandleVisibility','off');
+    legend('Location','EastOutside')
+    ylabel('Thrust [N]')
+
+    % feasibility
+    axes_time{4} = subplot(4,1,4);
+    hold on;
+    for i = 1:n_traj
+        % append one input value for plotting
+        ctrl_feas = [ctrl_info(:,:,i).ctrl_feas];
+        ctrl_feas(length(t)) = ctrl_feas(length(t) - 1);
+        stairs(axes_time{4},t,ctrl_feas','DisplayName',sprintf('feas_%d',i));
+    end
+    legend('Location','EastOutside')
+    ylabel('Feasible [0/1]')
+
+    % link axes
+    axes_time = [axes_time{:}];
+    linkaxes(axes_time,'x')
+    xlabel('Time [s]')
+end
\ No newline at end of file
diff --git a/templates/simulate.m b/templates/simulate.m
new file mode 100644
index 0000000..3138cd1
--- /dev/null
+++ b/templates/simulate.m
@@ -0,0 +1,14 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% 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 [Xt,Ut,ctrl_info] = simulate(x0, ctrl, params)
+
+% YOUR CODE HERE
+% Hint: you can access the control command with ctrl.eval(x(:,i))
+
+end
\ No newline at end of file
diff --git a/templates/simulate_uncertain.m b/templates/simulate_uncertain.m
new file mode 100644
index 0000000..dc9df26
--- /dev/null
+++ b/templates/simulate_uncertain.m
@@ -0,0 +1,11 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% 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 [Xt,Ut,ctrl_info] = simulate_uncertain(x0, ctrl, Wt, params)
+	% YOUR CODE HERE
+end
\ No newline at end of file
diff --git a/templates/traj_constraints.m b/templates/traj_constraints.m
new file mode 100644
index 0000000..4b0a081
--- /dev/null
+++ b/templates/traj_constraints.m
@@ -0,0 +1,12 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% 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 [s_max, y_max, u_max, J_u, df_max, vf_max, traj_feas] = traj_constraints(x,u,params)
+    % YOUR CODE HERE
+end
+
diff --git a/templates/traj_cost.m b/templates/traj_cost.m
new file mode 100644
index 0000000..7e0b443
--- /dev/null
+++ b/templates/traj_cost.m
@@ -0,0 +1,11 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% 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 J_Nt = traj_cost(Xt,Ut,Q,R)
+    % YOUR CODE HERE
+end
\ No newline at end of file