Trust-region method of `filtersqp` does not converge for this specific NMPC problem

[franckgaga]

Following discussion at #584, here's a specific problem with MPC.jl v2.1.2, in which the trust-region method of filtersqp does not converge:

using ModelPredictiveControl, JuMP
using UnoSolver

function f!(ẋ, x, u, _ , p)
    g, L, K, m = p          # [m/s²], [m], [kg/s], [kg]
    θ, ω = x[1], x[2]       # [rad], [rad/s]
    τ  = u[1]               # [Nm]
    ẋ[1] = ω
    ẋ[2] = -g/L*sin(θ) - K/m*ω + τ/m/L^2
    return nothing
end
h!(y, x, _ , _ ) = (y[1] = 180/π*x[1]; nothing) # [°]
p = [9.8, 0.4, 1.2, 0.3]
nu, nx, ny, Ts = 1, 2, 1, 0.1
model = NonLinModel(f!, h!, Ts, nu, nx, ny; p)
p_plant = copy(p); p_plant[3] = p[3]*1.25
plant = NonLinModel(f!, h!, Ts, nu, nx, ny; p=p_plant)
Hp, Hc, Mwt, Nwt = 20, 2, [0.5], [2.5]
α=0.01; σQ=[0.1, 1.0]; σR=[5.0]; nint_u=[1]; σQint_u=[0.1]
σQint_ym = zeros(0)
umin, umax = [-1.5], [+1.5]
transcription = MultipleShooting()
optim = Model(()->UnoSolver.Optimizer(
    preset="filtersqp"
))
hessian = false
nmpc = NonLinMPC(ManualEstimator(model; nint_u); 
    Hp, Hc, Mwt, Nwt, Cwt=Inf, transcription, hessian, optim,
)
nmpc = setconstraint!(nmpc; umin, umax)
unset_time_limit_sec(nmpc.optim)
unset_silent(nmpc.optim)

lastu = [0.014154762243809182]
x̂ = [2.9752971537433544, 1.3081343123447584, -0.11156581408839139]
setstate!(nmpc, x̂)

using Logging
debuglogger = ConsoleLogger(stderr, Logging.Debug)
with_logger(debuglogger) do 
    moveinput!(nmpc, [180.0]; lastu)
end
nothing

giving:

Original model C model
62 variables, 100 constraints (60 equality, 40 inequality)
Problem type: NLP
An exact Hessian (matrix or operator) was not provided, setting an L-BFGS Hessian instead

Non-default options:
QP_solver = BQPD
hessian_model = LBFGS

──────────────────────────────────────────────────────────────────────────────────────────────────────────────────
  Iterations
 Major  Minor  Penalty   Radius    Phase |BFGS|  ||Step||  Objective  Infeas    Statio    Compl     Status        
──────────────────────────────────────────────────────────────────────────────────────────────────────────────────
 0      -      -         1.00e+01  OPT   0       -         3.240e+05  4.12e+00  4.61e+04  0.00e+00  initial point 
 1      1      -         1.00e+01  OPT   0       6.25e+00  1.118e+05  2.78e+01  2.37e+04  0.00e+00  ✔ (f-type)    
 2      1      -         1.00e+01  OPT   0       1.00e+01  6.194e+04  3.62e+01  3.84e+04  0.00e+00  ✔ (f-type)    
 3      1      -         2.00e+01  OPT   -       2.00e+01  3.524e+05  6.79e+01  -         -         ✘ (current)   
 -      2      -         1.00e+01  OPT   0       1.00e+01  3.453e+04  3.29e+01  2.72e+04  0.00e+00  ✔ (f-type)    
 4      1      -         2.00e+01  OPT   -       2.00e+01  3.080e+05  5.15e+01  -         -         ✘ (current)   
 -      2      -         1.00e+01  OPT   1       1.00e+01  2.845e+04  2.12e+01  3.08e+04  0.00e+00  ✔ (f-type)    
 5      1      -         2.00e+01  OPT   1       1.45e+01  1.116e+04  4.79e+00  2.26e+05  0.00e+00  ✔ (h-type)    
 6      1      -         2.00e+01  OPT   2       1.11e+00  1.149e+04  1.67e-01  9.53e+03  0.00e+00  ✔ (h-type)    
 7      1      -         2.00e+01  OPT   3       3.84e-01  7.770e+03  1.34e-01  6.27e+03  0.00e+00  ✔ (f-type)    
 8      1      -         2.00e+01  OPT   4       1.54e+00  5.419e+02  1.26e+00  2.20e+03  0.00e+00  ✔ (f-type)    
 9      1      -         2.00e+01  OPT   5       4.95e-01  4.811e+02  3.42e-03  1.33e+03  0.00e+00  ✔ (h-type)    
 10     1      -         2.00e+01  OPT   6       1.45e-01  4.120e+02  1.09e-03  4.63e+02  0.00e+00  ✔ (f-type)    
 11     1      -         2.00e+01  OPT   6       4.44e-01  2.728e+02  4.63e-03  6.29e+02  0.00e+00  ✔ (f-type)    
 12     1      -         2.00e+01  OPT   6       3.45e-01  1.147e+02  1.85e-03  6.36e+02  0.00e+00  ✔ (f-type)    
 13     1      -         2.00e+01  OPT   6       5.14e-01  1.331e+01  2.05e-03  1.91e+02  0.00e+00  ✔ (f-type)    
 14     1      -         2.00e+01  OPT   6       6.08e-02  1.198e+01  2.93e-06  2.21e+01  0.00e+00  ✔ (f-type)    
 15     1      -         2.00e+01  OPT   6       7.02e-03  1.196e+01  4.89e-08  2.49e+00  0.00e+00  ✔ (f-type)    
 16     1      -         2.00e+01  OPT   6       9.12e-04  1.196e+01  8.69e-10  1.34e-02  0.00e+00  ✔ (f-type)    
 17     1      -         2.00e+01  OPT   6       1.57e-06  1.196e+01  9.68e-15  7.09e-04  0.00e+00  ✔ (h-type)    
 18     1      -         2.00e+01  OPT   6       9.86e-08  1.196e+01  8.00e-15  1.88e-05  0.00e+00  ✔ (f-type)    
 19     1      -         2.00e+01  OPT   -       8.12e-10  1.196e+01  8.41e-15  -         -         ✘ (current)   
 -      -      -         -         -     -       -         -          -         -         -         Small radius  
──────────────────────────────────────────────────────────────────────────────────────────────────────────────────
  Iterations
 Major  Minor  Penalty   Radius    Phase |BFGS|  ||Step||  Objective  Infeas    Statio    Compl     Status        
──────────────────────────────────────────────────────────────────────────────────────────────────────────────────

Uno 2.4.2 (TR Fletcher-filter restoration inequality-constrained method with L-BFGS Hessian and no regularization)
Fri Mar 13 11:36:20 2026
────────────────────────────────────────
Optimization status:                    Algorithmic error
Solution status:                        Suboptimal point
Objective value:                        11.9586
Primal feasibility:                     7.995232e-15
┌ Stationarity residual:                1.876023e-05
│ Primal feasibility:                   7.995232e-15
└ Complementarity residual:             0
CPU time:                               20.87466s
Iterations:                             19
Objective evaluations:                  22
Constraints evaluations:                22
Objective gradient evaluations:         22
Jacobian evaluations:                   22
Hessian evaluations:                    0
Number of subproblems solved:           21
┌ Error: MPC terminated without solution: returning last solution shifted (more info in debug log)
│   status = OTHER_ERROR::TerminationStatusCode = 24
└ @ ModelPredictiveControl ~/.julia/dev/ModelPredictiveControl/src/controller/execute.jl:510
┌ Debug: Content of getinfo dictionary:
│   :x̂ => [2.9752971537433544, 1.3081343123447584, -0.11156581408839139]
│   :ΔU => [0.0, 0.0]
│   :gc => Float64[]
│   :Ŷs => [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
│   :∇g => sparse(Int64[], Int64[], Float64[], 0, 62)
│   :R̂y => [180.0, 180.0, 180.0, 180.0, 180.0, 180.0, 180.0, 180.0, 180.0, 180.0, 180.0, 180.0, 180.0, 180.0, 180.0, 180.0, 180.0, 180.0, 180.0, 180.0]
│   :JE => 0.0
│   :R̂u => [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
│   :d => Float64[]
│   :∇geq => sparse([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 1, 3, 4, 2, 3, 4, 3, 4, 3, 5, 6, 4, 5, 6, 5, 6, 5, 7, 8, 6, 7, 8, 7, 8, 7, 9, 10, 8, 9, 10, 9, 10, 9, 11, 12, 10, 11, 12, 11, 12, 11, 13, 14, 12, 13, 14, 13, 14, 13, 15, 16, 14, 15, 16, 15, 16, 15, 17, 18, 16, 17, 18, 17, 18, 17, 19, 20, 18, 19, 20, 19, 20, 19, 21, 22, 20, 21, 22, 21, 22, 21, 23, 24, 22, 23, 24, 23, 24, 23, 25, 26, 24, 25, 26, 25, 26, 25, 27, 28, 26, 27, 28, 27, 28, 27, 29, 30, 28, 29, 30, 29, 30, 29, 31, 32, 30, 31, 32, 31, 32, 31, 33, 34, 32, 33, 34, 33, 34, 33, 35, 36, 34, 35, 36, 35, 36, 35, 37, 38, 36, 37, 38, 37, 38, 37, 39, 40, 38, 39, 40, 39, 40, 39, 40], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 18, 18, 18, 19, 19, 19, 20, 20, 21, 21, 21, 22, 22, 22, 23, 23, 24, 24, 24, 25, 25, 25, 26, 26, 27, 27, 27, 28, 28, 28, 29, 29, 30, 30, 30, 31, 31, 31, 32, 32, 33, 33, 33, 34, 34, 34, 35, 35, 36, 36, 36, 37, 37, 37, 38, 38, 39, 39, 39, 40, 40, 40, 41, 41, 42, 42, 42, 43, 43, 43, 44, 44, 45, 45, 45, 46, 46, 46, 47, 47, 48, 48, 48, 49, 49, 49, 50, 50, 51, 51, 51, 52, 52, 52, 53, 53, 54, 54, 54, 55, 55, 55, 56, 56, 57, 57, 57, 58, 58, 58, 59, 59, 60, 61], [0.09377568187489765, 1.7843485264107242, 0.08953993113350024, 1.6486111440308397, 0.08953993113350024, 1.6486111440308397, 0.08953993113350024, 1.6486111440308397, 0.08953993113350024, 1.6486111440308397, 0.08953993113350024, 1.6486111440308397, 0.08953993113350024, 1.6486111440308397, 0.08953993113350024, 1.6486111440308397, 0.08953993113350024, 1.6486111440308397, 0.08953993113350024, 1.6486111440308397, 0.08953993113350024, 1.6486111440308397, 0.08953993113350024, 1.6486111440308397, 0.08953993113350024, 1.6486111440308397, 0.08953993113350024, 1.6486111440308397, 0.08953993113350024, 1.6486111440308397, 0.08953993113350024, 1.6486111440308397, 0.08953993113350024, 1.6486111440308397, 0.08953993113350024, 1.6486111440308397, 0.08953993113350024, 1.6486111440308397, 0.08953993113350024, 1.6486111440308397, 0.08953993113350024, 1.6486111440308397, 0.08953993113350024, 1.6486111440308397, 0.08953993113350024, 1.6486111440308397, 0.08953993113350024, 1.6486111440308397, 0.08953993113350024, 1.6486111440308397, 0.08953993113350024, 1.6486111440308397, 0.08953993113350024, 1.6486111440308397, 0.08953993113350024, 1.6486111440308397, 0.08953993113350024, 1.6486111440308397, 0.08953993113350024, 1.6486111440308397, 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0.5781677375571752, 0.08953993113350024, 1.6486111440308397, -1.0, 0.8947010520835421, -1.9387662437642916, -1.0, 0.07913333377719486, 0.5781677375571752, 0.08953993113350024, 1.6486111440308397, -1.0, 0.8947010520835421, -1.9387662437642916, -1.0, 0.07913333377719486, 0.5781677375571752, 0.08953993113350024, 1.6486111440308397, -1.0, 0.8947010520835421, -1.9387662437642916, -1.0, 0.07913333377719486, 0.5781677375571752, 0.08953993113350024, 1.6486111440308397, -1.0, 0.8947010520835421, -1.9387662437642916, -1.0, 0.07913333377719486, 0.5781677375571752, 0.08953993113350024, 1.6486111440308397, -1.0, 0.8947010520835421, -1.9387662437642916, -1.0, 0.07913333377719486, 0.5781677375571752, 0.08953993113350024, 1.6486111440308397, -1.0, 0.8947010520835421, -1.9387662437642916, -1.0, 0.07913333377719486, 0.5781677375571752, 0.08953993113350024, 1.6486111440308397, -1.0, 0.8947010520835421, -1.9387662437642916, -1.0, 0.07913333377719486, 0.5781677375571752, 0.08953993113350024, 1.6486111440308397, -1.0, 0.8947010520835421, -1.9387662437642916, -1.0, 0.07913333377719486, 0.5781677375571752, 0.08953993113350024, 1.6486111440308397, -1.0, 0.8947010520835421, -1.9387662437642916, -1.0, 0.07913333377719486, 0.5781677375571752, 0.08953993113350024, 1.6486111440308397, -1.0, 0.8947010520835421, -1.9387662437642916, -1.0, 0.07913333377719486, 0.5781677375571752, 0.08953993113350024, 1.6486111440308397, -1.0, 0.8947010520835421, -1.9387662437642916, -1.0, 0.07913333377719486, 0.5781677375571752, 0.08953993113350024, 1.6486111440308397, -1.0, 0.8947010520835421, -1.9387662437642916, -1.0, 0.07913333377719486, 0.5781677375571752, 0.08953993113350024, 1.6486111440308397, -1.0, 0.8947010520835421, -1.9387662437642916, -1.0, 0.07913333377719486, 0.5781677375571752, 0.08953993113350024, 1.6486111440308397, -1.0, 0.8947010520835421, -1.9387662437642916, -1.0, 0.07913333377719486, 0.5781677375571752, 0.08953993113350024, 1.6486111440308397, -1.0, -1.0], 40, 62)
│   :lastu => [0.014154762243809182]
│   :g => Float64[]
│   :u => [0.014154762243809182]
│   :∇²J => nothing
│   :geq => [3.0599299938287636, 0.48190787323866113, 0.001267416431067964, 0.023335698465603513, 0.001267416431067964, 0.023335698465603513, 0.001267416431067964, 0.023335698465603513, 0.001267416431067964, 0.023335698465603513, 0.001267416431067964, 0.023335698465603513, 0.001267416431067964, 0.023335698465603513, 0.001267416431067964, 0.023335698465603513, 0.001267416431067964, 0.023335698465603513, 0.001267416431067964, 0.023335698465603513, 0.001267416431067964, 0.023335698465603513, 0.001267416431067964, 0.023335698465603513, 0.001267416431067964, 0.023335698465603513, 0.001267416431067964, 0.023335698465603513, 0.001267416431067964, 0.023335698465603513, 0.001267416431067964, 0.023335698465603513, 0.001267416431067964, 0.023335698465603513, 0.001267416431067964, 0.023335698465603513, 0.001267416431067964, 0.023335698465603513, 0.001267416431067964, 0.023335698465603513]
│   :Ŷ => [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
│   :U => [0.014154762243809182, 0.014154762243809182, 0.014154762243809182, 0.014154762243809182, 0.014154762243809182, 0.014154762243809182, 0.014154762243809182, 0.014154762243809182, 0.014154762243809182, 0.014154762243809182, 0.014154762243809182, 0.014154762243809182, 0.014154762243809182, 0.014154762243809182, 0.014154762243809182, 0.014154762243809182, 0.014154762243809182, 0.014154762243809182, 0.014154762243809182, 0.014154762243809182]
│   :x̂end => [0.0, 0.0, 0.0]
│   :J => 324000.0
│   :∇²ℓgeq => nothing
│   :D̂ => Float64[]
│   :∇J => [0.0, 0.0, -10313.240312354817, 0.0, 0.0, -10313.240312354817, 0.0, 0.0, -10313.240312354817, 0.0, 0.0, -10313.240312354817, 0.0, 0.0, -10313.240312354817, 0.0, 0.0, -10313.240312354817, 0.0, 0.0, -10313.240312354817, 0.0, 0.0, -10313.240312354817, 0.0, 0.0, -10313.240312354817, 0.0, 0.0, -10313.240312354817, 0.0, 0.0, -10313.240312354817, 0.0, 0.0, -10313.240312354817, 0.0, 0.0, -10313.240312354817, 0.0, 0.0, -10313.240312354817, 0.0, 0.0, -10313.240312354817, 0.0, 0.0, -10313.240312354817, 0.0, 0.0, -10313.240312354817, 0.0, 0.0, -10313.240312354817, 0.0, 0.0, -10313.240312354817, 0.0, 0.0, -10313.240312354817, 0.0, 0.0]
│   :ŷ => [170.47196970678064]
│   :∇²ℓg => nothing
│   :sol => 
│    solution_summary(; result = 1, verbose = true)
│    ├ solver_name          : Uno
│    ├ Termination
│    │ ├ termination_status : OTHER_ERROR
│    │ ├ result_count       : 1
│    │ └ raw_status         : 4
│    ├ Solution (result = 1)
│    │ ├ primal_status        : FEASIBLE_POINT
│    │ ├ dual_status          : UNKNOWN_RESULT_STATUS
│    │ ├ objective_value      : 1.19586e+01
│    │ ├ dual_objective_value : 1.31807e-02
│    │ ├ value
│    │ │ ├ Z̃var[10] : 1.39137e-01
│    │ │ ├ Z̃var[11] : -1.11566e-01
│    │ │ ├ Z̃var[12] : 3.13878e+00
│    │ │ ├ Z̃var[13] : 6.69001e-02
│    │ │ ├ Z̃var[14] : -1.11566e-01
│    │ │ ├ Z̃var[15] : 3.14349e+00
│    │ │ ├ Z̃var[16] : 3.20639e-02
│    │ │ ├ Z̃var[17] : -1.11566e-01
│    │ │ ├ Z̃var[18] : 3.14575e+00
│    │ │ ├ Z̃var[19] : 1.52233e-02
│    │ │ ├ Z̃var[1] : 6.62858e-02
│    │ │ ├ Z̃var[20] : -1.11566e-01
│    │ │ ├ Z̃var[21] : 3.14681e+00
│    │ │ ├ Z̃var[22] : 7.02515e-03
│    │ │ ├ Z̃var[23] : -1.11566e-01
│    │ │ ├ Z̃var[24] : 3.14728e+00
│    │ │ ├ Z̃var[25] : 2.95503e-03
│    │ │ ├ Z̃var[26] : -1.11566e-01
│    │ │ ├ Z̃var[27] : 3.14746e+00
│    │ │ ├ Z̃var[28] : 8.24894e-04
│    │ │ ├ Z̃var[29] : -1.11566e-01
│    │ │ ├ Z̃var[2] : 2.36280e-02
│    │ │ ├ Z̃var[30] : 3.14747e+00
│    │ │ ├ Z̃var[31] : -4.38178e-04
│    │ │ ├ Z̃var[32] : -1.11566e-01
│    │ │ ├ Z̃var[33] : 3.14738e+00
│    │ │ ├ Z̃var[34] : -1.37761e-03
│    │ │ ├ Z̃var[35] : -1.11566e-01
│    │ │ ├ Z̃var[36] : 3.14720e+00
│    │ │ ├ Z̃var[37] : -2.29239e-03
│    │ │ ├ Z̃var[38] : -1.11566e-01
│    │ │ ├ Z̃var[39] : 3.14692e+00
│    │ │ ├ Z̃var[3] : 3.06615e+00
│    │ │ ├ Z̃var[40] : -3.37850e-03
│    │ │ ├ Z̃var[41] : -1.11566e-01
│    │ │ ├ Z̃var[42] : 3.14651e+00
│    │ │ ├ Z̃var[43] : -4.80294e-03
│    │ │ ├ Z̃var[44] : -1.11566e-01
│    │ │ ├ Z̃var[45] : 3.14594e+00
│    │ │ ├ Z̃var[46] : -6.74755e-03
│    │ │ ├ Z̃var[47] : -1.11566e-01
│    │ │ ├ Z̃var[48] : 3.14514e+00
│    │ │ ├ Z̃var[49] : -9.44145e-03
│    │ │ ├ Z̃var[4] : 6.00186e-01
│    │ │ ├ Z̃var[50] : -1.11566e-01
│    │ │ ├ Z̃var[51] : 3.14401e+00
│    │ │ ├ Z̃var[52] : -1.31927e-02
│    │ │ ├ Z̃var[53] : -1.11566e-01
│    │ │ ├ Z̃var[54] : 3.14245e+00
│    │ │ ├ Z̃var[55] : -1.84255e-02
│    │ │ ├ Z̃var[56] : -1.11566e-01
│    │ │ ├ Z̃var[57] : 3.14026e+00
│    │ │ ├ Z̃var[58] : -2.57298e-02
│    │ │ ├ Z̃var[59] : -1.11566e-01
│    │ │ ├ Z̃var[5] : -1.11566e-01
│    │ │ ├ Z̃var[60] : 3.13721e+00
│    │ │ ├ Z̃var[61] : -3.59277e-02
│    │ │ ├ Z̃var[62] : -1.11566e-01
│    │ │ ├ Z̃var[6] : 3.10854e+00
│    │ │ ├ Z̃var[7] : 2.89047e-01
│    │ │ ├ Z̃var[8] : -1.11566e-01
│    │ │ └ Z̃var[9] : 3.12895e+00
│    │ └ dual
│    │   ├ linconstraint : multiple constraints with the same name
│    │   ├ linconstrainteq : multiple constraints with the same name
│    │   └ nonlinconstrainteq : [3.31427e-01,1.18143e-01,-2.47677e+02,-3.76467e-06,-2.80728e+01,-1.08501e+02,-1.81263e-06,-3.11065e+01,-4.14886e+01,-8.89138e-07,-2.49934e+01,-9.24433e+00,-4.40573e-07,-1.66392e+01,6.24167e+00,-2.17876e-07,-8.76109e+00,1.36389e+01,-1.05178e-07,-2.23378e+00,1.71160e+01,-4.62739e-08,2.82885e+00,1.86711e+01,-1.29513e-08,6.58797e+00,1.92531e+01,9.51835e-09,9.27019e+00,1.93003e+01,2.94557e-08,1.10836e+01,1.89974e+01,5.23556e-08,1.21888e+01,1.83969e+01,8.28109e-08,1.26931e+01,1.74730e+01,1.25603e-07,1.26528e+01,1.61417e+01,1.86325e-07,1.20793e+01,1.42629e+01,2.71581e-07,1.09494e+01,1.16301e+01,3.88424e-07,9.22588e+00,7.94920e+00,5.42053e-07,6.90305e+00,2.80740e+00,7.29452e-07,4.11138e+00,-4.37316e+00,9.23456e-07,1.35062e+00,-1.43999e+01,1.03541e-06,0.00000e+00]
│    └ Work counters
│      └ solve_time (sec)   : 2.08747e+01
└ @ ModelPredictiveControl ~/.julia/dev/ModelPredictiveControl/src/controller/execute.jl:522

Many thanks for your work!

[cvanaret]

Hi @franckgaga,
(note to myself: I see that the point at which Uno terminates is feasible, so I should at least report that in Solution status)
The trick here is to allow the trust-region radius to decrease below $10^{-7}$, which is the default value of the option TR_min_radius. If you set the option TR_min_radius=1e-12, it should work. Admittedly, this should be the new default value!

[franckgaga]

Oh thanks for the tips!

It seems to be a better default indeed, but maybe the new value should be tested on a collocation of problem, that you may already have. There is the Hock & Schittkowski collection, for example.

[cvanaret]

Good news: since $10^{-12}$ is smaller than the default $10^{-7}$, decreasing the value won't interfere with successful runs. You can only potentially solve instances that you couldn't solve :)
(I tested on our 3000+ CI instances here, doesn't make a difference: #592)

[cvanaret]

@franckgaga OK to close?

[franckgaga]

Forgot to answer you, sorry for the delay.

Using the TR_min_radius=1e-12 setting, there is still two control periods in which the solver fail to converge. It does work with 1e-13:

using ModelPredictiveControl, JuMP
using UnoSolver

N = 35
function f!(ẋ, x, u, _ , p)
    g, L, K, m = p          # [m/s²], [m], [kg/s], [kg]
    θ, ω = x[1], x[2]       # [rad], [rad/s]
    τ  = u[1]               # [Nm]
    ẋ[1] = ω
    ẋ[2] = -g/L*sin(θ) - K/m*ω + τ/m/L^2
    return nothing
end
h!(y, x, _ , _ ) = (y[1] = 180/π*x[1]; nothing) # [°]
p = [9.8, 0.4, 1.2, 0.3]
nu, nx, ny, Ts = 1, 2, 1, 0.1
model = NonLinModel(f!, h!, Ts, nu, nx, ny; p)
p_plant = copy(p); p_plant[3] = p[3]*1.25
plant = NonLinModel(f!, h!, Ts, nu, nx, ny; p=p_plant)
Hp, Hc, Mwt, Nwt = 20, 2, [0.5], [2.5]
α=0.01; σQ=[0.1, 1.0]; σR=[5.0]; nint_u=[1]; σQint_u=[0.1]
σQint_ym = zeros(0)
umin, umax = [-1.5], [+1.5]
transcription = MultipleShooting()
optim = Model(()->UnoSolver.Optimizer(
    preset="filtersqp", TR_min_radius=1e-13
))
hessian = false
nmpc = NonLinMPC(model; 
    Hp, Hc, Mwt, Nwt, Cwt=Inf, transcription, hessian, optim,
    σQ, σR, nint_u, σQint_u
)
nmpc = setconstraint!(nmpc; umin, umax)
unset_time_limit_sec(nmpc.optim)
#unset_silent(nmpc.optim)

res = sim!(nmpc, N, [180.0]; plant, x_0=[0, 0], x̂_0=[0, 0, 0], progress=false)
using Plots
#theme(:default)
theme(:dark)
default(fontfamily="Computer Modern"); scalefontsizes(1.1)
plot(res) |> display

@time sim!(nmpc, N, [180.0]; plant, x_0=[0, 0], x̂_0=[0, 0, 0], progress=false)

Note that this is an inherently hard problem (unstable dynamical system), so I'm not sure you want to reduce the default value to a value as small as that. Still, the line-search method work on this problem without any modification of the settings.

[cvanaret]

@leyffer can you weigh in on this? What would be the typical minimum trust-region radius? Something as small as the machine epsilon? Uno's is set at $10^{-12}$ at the moment.

[franckgaga]

Just a quick follow-up. I was doing some more serious benchmark with UnoSolver V.S. Ipopt V.S. KNITRO SQP solver.

The current default settings of filtersqp seems to struggle on this specific problem without a Hessian matrix (that is, using the internal LBFGS with default settings). However, using the funnelsqp preset with a LS globalization mechanism works very well and is also very fast! The filtersqp with LS does work well on the MRE above, but I have some specific problems that the solver does not converge anymore (I can send it to you if you are interested). This is not the case with funnelsqp and LS, it just always work on the inverted pendulum. So maybe it might be worth it to make this preset more official and documented ? And maybe this preset should default to LS if there is no exact Hessian ?