diff options
| -rw-r--r-- | templates/MPC.m | 44 | ||||
| -rw-r--r-- | templates/lqr_maxPI.m | 37 | ||||
| -rw-r--r-- | 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 |