Take deliverables for MPC with theoretical closed-loop guarantees

According to table 8

  - MPC_TE
  - MPC_TE/eval (contained in MPC_TE.m)
  - MPC_TS
  - MPC_TS/eval (contained in MPC_TE.m)

2 files changed, 55 insertions, 3 deletions

diff --git a/templates/MPC_TE.m b/templates/MPC_TE.m
index e0b55d2..747c7ee 100644
--- a/templates/MPC_TE.m
+++ b/templates/MPC_TE.m
@@ -15,7 +15,33 @@ classdef MPC_TE
         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});
+
+            % Create yalmip variables
+            U = sdpvar(repmat(params.model.nu,N,1),ones(1,N));
+            X = sdpvar(repmat(params.model.nx,N+1,1),ones(1,N+1));
+
+            % Build cost function and constraints
+            objective = 0;
+            constraints = [];
+            for k=1:N+1
+                if k <= N
+                    % These constraints are for the index in 1, ..., N
+                    objective = objective + X{k}' * Q * X{k} + U{k}' * R * U{k};
+                    constraints = [constraints, ...
+                        X{k+1} == params.model.A * X{k} + params.model.B * U{k}, ...
+                        params.constraints.InputMatrix * U{k} <= params.constraints.InputRHS, ...
+                    ];
+                end
+
+                % These contrains are for 1, ..., N+1
+                constraints = [constraints, ...
+                    params.constraints.StateMatrix * X{k} <= params.constraints.StateRHS, ...
+                ];
+            end
+            % Terminal constraint
+            constraints = [constraints, X{N+1} == zeros(size(X{N+1}))];
+
+            obj.yalmip_optimizer = optimizer(constraints,objective,opts,X{1},{U{1} objective});
         end
 
         function [u, ctrl_info] = eval(obj,x)
diff --git a/templates/MPC_TS.m b/templates/MPC_TS.m
index 05f92ff..cbe7b45 100644
--- a/templates/MPC_TS.m
+++ b/templates/MPC_TS.m
@@ -15,8 +15,34 @@ classdef MPC_TS
         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
+
+            % Create yalmip optimization variables
+            U = sdpvar(repmat(params.model.nu,N,1),ones(1,N));
+            X = sdpvar(repmat(params.model.nx,N+1,1),ones(1,N+1));
+
+            % Build cost function and constraints
+            Pinf = idare(params.model.A, params.model.B, Q, R);
+            objective = X{N+1}' * Pinf * X{N+1};
+            constraints = [];
+            for k=1:N+1
+                if k <= N
+                    % These constraints are for the index in 1, ..., N
+                    objective = objective + X{k}' * Q * X{k} + U{k}' * R * U{k};
+                    constraints = [constraints, ...
+                        X{k+1} == params.model.A * X{k} + params.model.B * U{k}, ...
+                        params.constraints.InputMatrix * U{k} <= params.constraints.InputRHS, ...
+                    ];
+                end
+
+                % These contrains are for 1, ..., N+1
+                constraints = [constraints, ...
+                    params.constraints.StateMatrix * X{k} <= params.constraints.StateRHS, ...
+                ];
+            end
+            % Terminal constraint
+            constraints = [constraints, H*X{N+1} <= h];
+
+            obj.yalmip_optimizer = optimizer(constraints,objective,opts,X{1},{U{1} objective});        end
 
         function [u, ctrl_info] = eval(obj,x)
             %% evaluate control action by solving MPC problem, e.g.