TuneMPC

TuneMPC is a Python package for economic tuning of nonlinear model predictive control (NMPC) problems.

More precisely, it implements a formal procedure that tunes a tracking (N)MPC scheme so that it is locally first-order equivalent to economic NMPC. For user-provided system dynamics, constraints and economic objective, TuneMPC enables automated computation of optimal steady states and periodic trajectories, and spits out corresponding tuned stage cost matrices.

Installation

TuneMPC requires Python 3.5/3.6/3.7.

1. Get a local copy of tunempc:

   git clone https://github.com/jdeschut/tunempc.git
   

2. Install the package with dependencies:

   pip3 install <path_to_installation_folder>/tunempc
   

Installation (optional)

The following features enable additional features and enhance reliability and performance.

1. Install MOSEK SDP solver (free academic licenses available)

   pip3 install -f https://download.mosek.com/stable/wheel/index.html Mosek==9.0.98
   

2. Install the acados software package for generating fast and embedded TuneMPC solvers.

   git submodule update --init --recursive
   cd external/acados
   mkdir build && cd build
   cmake -DACADOS_WITH_QPOASES=ON ..
   make install -j4 && cd ..
   pip3 install interfaces/acados_template
   export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:"<tunempc_root>/external/acados/lib"
   

   More detailed instructions can be found here.

3. It is recommended to use HSL linear solvers as a plugin with IPOPT. In order to get the HSL solvers and render them visible to CasADi, follow these instructions.

Using TuneMPC

The interface of TuneMPC is based on the symbolic modeling framework CasADi.
Input functions should be given as CasADi Function objects.

User-defined inputs:

import casadi as ca

x = ca.MX.sym('x',<insert state dimension>) # states
u = ca.MX.sym('u',<insert control dimension>) # controls

f = ca.Function('f',[x,u],[<insert dynamics expr>],['x','u'],['xf']) # discrete system dynamics
l = ca.Function('l',[x,u],[<insert cost expr>]) # economic stage cost
h = ca.Function('h',[x,u],[<insert constraints expr>]) # constraints >= 0

p = <insert period of interest> # choose p=1 for steady-state

Basic application of TuneMPC with a few lines of code:

import tunempc

tuner  = tunempc.Tuner(f, l, h, p) # construct optimal control problem
w_opt  = tuner.solve_ocp() # compute optimal p-periodic trajectory
[H, q] = tuner.convexify() # compute economically tuned stage cost matrices

Create a tracking MPC controller (terminal point constraint) based on the tuned stage cost matrices:

ctrl = tuner.create_mpc('tuned', N = <insert MPC horizon>)
u0 = ctrl.step(x0)  # compute feedback law

(optional) Code-generate a fast and embeddable solver for this MPC controller using acados (see installation instructions):

ode = <insert ode expr based on x,u> # ode or dae expression
acados_ocp_solver, _ = ctrl.generate(ode) # generate solver
u0 = ctrl.step_acados(x0) # solver can be called through python interface

For a more complete overview of the available functionality, have a look at the different application examples.

Acknowledgments

This project has received funding by DFG via Research Unit FOR 2401 and by an industrial project with the company Kiteswarms Ltd.

Literature

Software

TuneMPC - A Tool for Economic Tuning of Tracking (N)MPC Problems
J. De Schutter, M. Zanon, M. Diehl
IEEE Control Systems Letters 2020

Theory

A Periodic Tracking MPC that is Locally Equivalent to Periodic Economic MPC
M. Zanon, S. Gros, M. Diehl
IFAC 2017 World Congress

A tracking MPC formulation that is locally equivalent to economic MPC
M. Zanon, S. Gros, M. Diehl
Journal of Process Control 2016

CasADi

CasADi - A software framework for nonlinear optimization and optimal control
J.A.E. Andersson, J. Gillis, G. Horn, J.B. Rawlings, M. Diehl
Mathematical Programming Computation, 2018