Functions

MPC controller settings.

Fields

• reference_condensation::Bool = false: Collapse reference trajectory to setpoint
• reference_tracking::Bool = true: Enable reference tracking
• reference_preview::Bool = false: Enable time-varying reference preview
• soft_weight::Float64 = 1e6: Penalty weight for soft constraint violations
• solver_opts::Dict{Symbol,Any}: Additional solver options

add_constraint!(mpc::MPC;
    Ax, Au, Ar, Aw, Ad, Aup,
    ub, lb, ks, soft, binary, prio)
add_constraint!(mpc;Ax,Au,ub,lb,
                ks, soft, binary,prio)

Adds the constraints lb ≤ Ax xₖ + Au uₖ ≤ ub for the time steps k ∈ ks (additional terms Ar rₖ, Aw wₖ, Ad dₖ, Aup u⁻ₖ are possible)

• soft marks if the constraint should be softened (default false)
• binary marks if either the upper or lower bounds should be enforced with equality (default false)
• prio marks the relative priority of the constraint (default 0)

certify(mpc; range, AS0, opts)

Provide certificates on the iteration complexity of DAQP for solving the resulting optimization problems.

• range is the parameter range over which the certification should be done
• AS0 is the starting working set in DAQP (defaults to empty)
• settings the settings used in the certification (see ASCertain.CertSettings())

compute_control(mpc,x;r,uprev)

For a given MPC mpc and state x, compute the optimal control action.

Optional arguments:

• r - reference value. Can be:
  • Vector of length ny for constant reference
  • Matrix of size (ny, Np) for reference preview (when mpc.settings.reference_preview = true)
• uprev - previous control action

All arguments default to zero.

Examples

# Standard reference tracking
u = compute_control(mpc, x; r=[1.0, 0.0])

# Reference preview (requires mpc.settings.reference_preview = true)
r_trajectory = [1.0 1.5 2.0 2.0 2.0;   # ny × Np matrix
                0.0 0.0 0.5 1.0 1.0]
u = compute_control(mpc, x; r=r_trajectory)

condense_reference(mpc, r)

Condense reference trajectory to single setpoint.

constraint_violation(c,xs,us)

evaluates the possible violation of constraint c at state x and control u

set_correct_state!(mpcy)

Correct the state estimated based on measurement u. This updates the state of state_observer

evaluate_cost(mpc,xs,us,rs;Q,Rr,S)

Compute the cost 0.5 ∑ x'*Q x + u' R u + Δu' Rr Δu + x' S u

evaluate_cost(mpc,sim;Q,Rr,S)

Compute the cost 0.5 ∑ x'*Q x + u' R u + Δu' Rr Δu + x' S u

format_reference(mpc, r)

Format reference input for MPC controller. Handles both single reference and reference preview scenarios.

get_reference_preview(rs, k, Np)

Extract reference preview from reference trajectory starting at time step k.

get_state!(mpc)

Get the current state of the observer

move_block!(mpc,block)

Reduce the number of controls by keeping it constant in blocks. For example, block=[2,1,3] keeps the control constant for 2 time-steps, 1 time step, and 3 time steps.

• if sum(block) ≠ mpc.Np, the resulting block will be padded or clipped
• if block is an Int, a vector with constant block size is created

mpc2mpqp(mpc)

For a given MPC structure mpc, form the multi-parametric QP mpQP.

predict_state!(mpc,u)

Predict the state at the next time step if the control u is applied. This updates the state of state_observer

set_binary_controls!(mpc,bin_ids)

Makes the controls in bin_ids to binary controls

set_bounds!(mpc;umin,umax,ymin,umax)

Sets the bounds umin ≤ u ≤ umax and ymin ≤ y ≤ umax

set_disturbance!(mpc,wmin,wmax)

set_horizon!(mpc,Np)

Sets the prediction horizon Np

set_input_bounds!(mpc;umin,umax)

Sets the input bounds umin ≤ u ≤ umax

set_labels!(mpc;x,u,y,d)

Sets the name of the states x, controls u, output u, disturbance d

set_objective!(mpc;Q,R,Rr,S,Qf)

Set the weights in the objective function `xN' C' Qf C xN^T + ∑ (C xₖ - rₖ)' Q (C xₖ - rₖ) + uₖ' R uₖ + Δuₖ' Rr Δuₖ + xₖ' S uₖ

A vector is interpreted as a diagonal matrix.

set_output_bounds!(mpc;ymin,ymax,
                ks, soft, binary,prio)

Adds the constraints lb ≤ C x ≤ ub for the time steps k ∈ ks

• soft marks if the constraint should be softened (default false)
• binary marks if either the upper or lower bounds should be enforced with equality (default false)
• prio marks the relative priority of the constraint (default 0)

set_prestabilizing_feedback!(mpc,K)

Sets the prestabilizing feedback K

set_prestabilizing_feedback!(mpc)

Sets the prestabilizing feedback K to the infinte horizon LQR gain`

set_state!(mpc,x)

Set the state of state_observer to x

set_state_observer!(mpc;F,G,C,Q,R,x0)

Creates a steady-state Kalman filter for estimating the sate. If F,G, and C are not provided, the model used in mpc is used in the filter

set_terminal_cost!(mpc)

Sets the terminal cost Qf to the inifinite horizon LQR cost

settings!(mpc,key1=value1, key2=value2,...)

setup!(mpc)

Sets up the mpc given its current parameters and settings Internally, this means generating an mpQP, and setting up a DAQP workspace.

xdaqp,fval,exitflag,info = solve(mpc,θ)

Solve corresponding QP given the parameter θ