function [t, x, u] = hw5_cvutID()
    % Discrete system dynamics
    f = @(x, u) x - 0.4*x^2 + u;

    % Cost Functions
    % !Choose appropriate cost functions!
    L = ;
    phi = ;

    % Quantization the state and input variable
    xb = -1:.2:1;
    ub = -.5:0.1:.5;

    % Time vector
    t = 0:5;

    % Initialize the table containing the optimal control policy and optimal
    % value function. Rows in matrices uopt and J correspond to time and
    % columns to quantized state values. For instance, u(i,j) correspond to
    % optimal control action for a system at state xb(j) and at time t(i).
    uopt = zeros(numel(t)-1, numel(xb));
    J = zeros(numel(t), numel(xb));

    % Initialize the value function at the final time
    for i = 1:numel(xb)
        J(numel(t), i) = phi(xb(i));
    end

    %% Run the DP algorithm to find an optimal control policy
    for k = (numel(t)-1):-1:1
        for i = 1:numel(xb)
            for j = 1:numel(ub)
                % Your code goes here. ...
            end
            % ...here, 
            J(k, i) = [];
            uopt(k, i) = [];
        end
    end

    %% Simulation
    x = zeros(numel(t), 1);
    x(1) = .9;
    u = zeros(numel(t)-1, 1);

    for i = 2:numel(t)
        % ... and also here
        u(i-1) = 0;
        x(i) = f(x(i-1), u(i-1));
    end

    figure(1)
    clf
    subplot(211)
    stairs(t, x)
    title('State variable')
    ylabel('x[k]')
    xlabel('Time index k')
    grid on

    subplot(212)
    stairs(t(1:end-1), u)
    title('Control variable')
    ylabel('u[k]')
    xlabel('Time index k')
    grid on

end