Functions: Generic Functions

Functions: Generic Functions

This page contains the documentation of functions that are generic to SimModel, StateEstimator and PredictiveController types.

Set Constraint

ModelPredictiveControl.setconstraint! — Function

setconstraint!(estim::MovingHorizonEstimator; <keyword arguments>) -> estim

Set the constraint parameters of the MovingHorizonEstimator estim.

It supports both soft and hard constraints on the estimated state $\mathbf{x̂}$, process noise $\mathbf{ŵ}$ and sensor noise $\mathbf{v̂}$:

\[\begin{alignat*}{3} \mathbf{x̂_{min} - c_{x̂_{min}}} ϵ ≤&&\ \mathbf{x̂}_k(k-j+p) &≤ \mathbf{x̂_{max} + c_{x̂_{max}}} ϵ &&\qquad j = N_k, N_k - 1, ... , 0 \\ \mathbf{ŵ_{min} - c_{ŵ_{min}}} ϵ ≤&&\ \mathbf{ŵ}(k-j+p) &≤ \mathbf{ŵ_{max} + c_{ŵ_{max}}} ϵ &&\qquad j = N_k, N_k - 1, ... , 1 \\ \mathbf{v̂_{min} - c_{v̂_{min}}} ϵ ≤&&\ \mathbf{v̂}(k-j+1) &≤ \mathbf{v̂_{max} + c_{v̂_{max}}} ϵ &&\qquad j = N_k, N_k - 1, ... , 1 \end{alignat*}\]

and also $ϵ ≥ 0$. All the constraint parameters are vector. Use ±Inf values when there is no bound. The constraint softness parameters $\mathbf{c}$, also called equal concern for relaxation, are non-negative values that specify the softness of the associated bound. Use 0.0 values for hard constraints (default for all of them). Notice that constraining the estimated sensor noises is equivalent to bounding the innovation term, since $\mathbf{v̂}(k) = \mathbf{y^m}(k) - \mathbf{ŷ^m}(k)$. See Extended Help for details on the constant $p$, on model augmentation and on time-varying constraints.

Arguments

Info

All the keyword arguments have non-Unicode alternatives e.g. xhatmin or Vhatmax.

The default constraints are mentioned here for clarity but omitting a keyword argument will not re-assign to its default value (defaults are set at construction only).

estim::MovingHorizonEstimator : moving horizon estimator to set constraints
x̂min=fill(-Inf,nx̂) / x̂max=fill(+Inf,nx̂) : estimated state bound $\mathbf{x̂_{min/max}}$
ŵmin=fill(-Inf,nx̂) / ŵmax=fill(+Inf,nx̂) : estimated process noise bound $\mathbf{ŵ_{min/max}}$
v̂min=fill(-Inf,nym) / v̂max=fill(+Inf,nym) : estimated sensor noise bound $\mathbf{v̂_{min/max}}$
c_x̂min=fill(0.0,nx̂) / c_x̂max=fill(0.0,nx̂) : x̂min / x̂max softness weight $\mathbf{c_{x̂_{min/max}}}$
c_ŵmin=fill(0.0,nx̂) / c_ŵmax=fill(0.0,nx̂) : ŵmin / ŵmax softness weight $\mathbf{c_{ŵ_{min/max}}}$
c_v̂min=fill(0.0,nym) / c_v̂max=fill(0.0,nym) : v̂min / v̂max softness weight $\mathbf{c_{v̂_{min/max}}}$
all the keyword arguments above but with a first capital letter, e.g. X̂max or C_ŵmax: for time-varying constraints (see Extended Help)

Examples

julia> estim = MovingHorizonEstimator(LinModel(ss(0.5,1,1,0,1)), He=3);

julia> estim = setconstraint!(estim, x̂min=[-50, -50], x̂max=[50, 50])
MovingHorizonEstimator estimator with a sample time Ts = 1.0 s, OSQP optimizer, LinModel and:
 3 estimation steps He
 0 slack variable ϵ (estimation constraints)
 1 manipulated inputs u (0 integrating states)
 2 estimated states x̂
 1 measured outputs ym (1 integrating states)
 0 unmeasured outputs yu
 0 measured disturbances d

Extended Help

Extended Help

The constant $p=0$ if estim.direct==true (current form), else $p=1$ (prediction form). Note that the state $\mathbf{x̂}$ and process noise $\mathbf{ŵ}$ constraints are applied on the augmented model, detailed in SteadyKalmanFilter Extended Help. For variable constraints, the bounds can be modified after calling updatestate!, that is, at runtime, except for ±Inf bounds. Time-varying constraints over the estimation horizon $H_e$ are also possible, mathematically defined as:

\[\begin{alignat*}{3} \mathbf{X̂_{min} - C_{x̂_{min}}} ϵ ≤&&\ \mathbf{X̂} &≤ \mathbf{X̂_{max} + C_{x̂_{max}}} ϵ \\ \mathbf{Ŵ_{min} - C_{ŵ_{min}}} ϵ ≤&&\ \mathbf{Ŵ} &≤ \mathbf{Ŵ_{max} + C_{ŵ_{max}}} ϵ \\ \mathbf{V̂_{min} - C_{v̂_{min}}} ϵ ≤&&\ \mathbf{V̂} &≤ \mathbf{V̂_{max} + C_{v̂_{max}}} ϵ \end{alignat*}\]

For this, use the same keyword arguments as above but with a first capital letter:

X̂min / X̂max / C_x̂min / C_x̂max : $\mathbf{X̂}$ constraints (nx̂*(He+1),).
Ŵmin / Ŵmax / C_ŵmin / C_ŵmax : $\mathbf{Ŵ}$ constraints (nx̂*He,).
V̂min / V̂max / C_v̂min / C_v̂max : $\mathbf{V̂}$ constraints (nym*He,).