Solving MPC using JuMP and Gurobi

Specific Domains Optimization (Mathematical)
2

I couldn’t run your code so I don’t know the reason for the infeasibility. Shouldn’t the function linear_mps_control return something?

To get the most help out of posts on discourse, it helps to simplify the problem into a minimal reproducible example. Take a read of Please read: make it easier to help you.

You probably have something wrong with your data or there might be a typo somewhere. Try simplifying the problem until you’re confident that it works, then add complexity. For example, just try running linear_mpc_control. Do the outputs match what you expect?

I’d also write your JuMP model slightly differently. Here’s how I would write it:

function linear_mpc_control(xref, xbar, x0, dref)
    model = Model(Gurobi.Optimizer)
    @variable(model, x[1:NX, 1:(T+1)])
    @variable(model, u[1:NU, 1:T])
    for i in 1:NX
        fix(x[i, 1], x0[i])
    end
    for t in 1:(T+1)
        set_upper_bound(x[3, t], MAX_SPEED)
        set_lower_bound(x[3, t], MIN_SPEED)
        set_upper_bound(u[1, t], MAX_ACCEL)
        set_lower_bound(u[1, t], -MAX_ACCEL)
        set_upper_bound(u[2, t], MAX_STEER)
        set_lower_bound(u[2, t], -MAX_STEER)
    end
    for t in 1:T
        A, B, C = get_linear_model_matrix(xbar[3, t], xbar[4, t], dref[1, t])
        @constraint(model, x[:, t + 1] .== A * x[:, t] + B * u[:, t] + C)
    end
    for t in 1:(T-2)
        @constraint(model, u[2, t + 1] - u[2, t] <= MAX_DSTEER * DT)
        @constraint(model, u[2, t + 1] - u[2, t] >= -MAX_DSTEER * DT)
    end
    @objective(
        model, 
        Min, 
        sum(u[:, t]' * R * u[:, t] for t in 1:T) +
        sum((xref[:, t] - x[:, t])' * Q * (xref[:, t] - x[:, t]) for t in 2:T) +
        sum((u[:, t+1] - u[:, t])' * Rd * (u[:, t+1] - u[:, t]) for t in 1:(T-2)) +
        (xref[:, T] - x[:, T])' * Qf * (xref[:, T] - x[:, T]),
    )
    optimize!(model)
    solution_summary(model)
end
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