param N;
param T;
param q;
param r;
param xf;

var x {j in 0..N};
var v {j in 1..N}   <= 1000, >= -1000;
var a               <= 1000, >= -1000;

minimize trade_off: q*(x[N] - xf)^2 + r* a^2 * T;

subject to x0: x[0] = 0;
subject to v0: v[1] = 0;

subject to v_def {j in 1..N}: N*(x[j] - x[j-1]) = T*v[j];

subject to a_def {j in 1..N-1}: (v[j+1]-v[j])*N = T*a;

let N := 800;
let T := 10;

let q := 1;
let r := 100;
let xf := 100;

solve;

#display x;
display a;
display x[N];
display v[N];
display a^2 * T;