This repository implements the dual mode MPC and LQR control system architecture as described in the accompanying paper, and also implements an openAI gym interface so that it can be integrated with reinforcement learning libraries. The MPC and simulator is implemented based on the do-mpc python library and the CasADi optimization software.
This environment uses the python function eval to run code provided by the json configuration file, and as such could run arbitrary code on your system, the consequences of which the author takes no responsibility for. Please ensure that any json configuration files used does not contain any malicious code.
git clone https://github.com/eivindeb/gym-letMPC
cd gym-letMPC
pip install -e .An example configuration file defining a cart pendulum system is provided, where the MPCs cost functions defines the objective of stabilizing the pendulum to the upright position and the LQR is based on a linearized model of the true system. The real system is subject to process noise affecting the angular velocity of the pendulum.
from gym_let_mpc.let_mpc import LetMPCEnv
env = LetMPCEnv("configs/cart_pendulum.json")
env.seed(0)
obs = env.reset(state={"theta": 0.5})
done = False
while not done:
obs, rew, done, info = env.step([env.steps_count % 5 == 0]) # Recompute MPC every 5 time steps.
env.render()Running this scenario simulates the cart pendulum system with an initial pendulum angle of 0.5 radians, a control law
where the MPC is computed every 5 time steps while the LQR is employed to account for prediction errors in-between MPC computations.
The scenario is then rendered producing the following output, where crosses correspond to computation of MPC solution, and the
dashed lines are the MPC predictions.
Episode conditions can be specified through the keyword arguments to the environment reset function, overriding the defaults and randomization specified in the configuration file and the randomization, for e.g. evaluation purposes or for testing specific scenarios, see reset docstring.
The control system and the environment are configured using the json config file supplied to the environment class. The json file has four main entries:
Sets variables of the gym environment.
- max_steps: Integer. Sets the maximum episode length in number of time steps, after which the episode is ended.
- observation: List of dictionaries. Defines the observation vector of the environment. Each dictionary defines
one entry in the observation vector and has the following attributes:
- name String. Name of variable, e.g. name of state, input or parameter as defined in simulator.
- type String. Type of variable, one of ["state", "input", "reference", "tvp", "error", "epsilon", "constraint", "action", "time", "parameter"]. Where "error" is defined as state reference minus current value, "epsilon" is MPC prediction minus current value, "action" refers to inputs to the environment step function (as opposed to MPC and LQR control inputs), "time" refers to the number of steps since last MPC computation. The resultant value is further defined by value_type.
- value_type String. Augments the value of the variable, see LetMPCEnv._get_variable_value function.
- limits List of Floats. List of two floats defining the minimum and maximum value of the variable, respectively. Its actual value is clipped to fit into the provided limits.
- transform List of Strings. List of transformations to apply to the variable value, for which one entry is added to the observation vector for each transformation. One of ["none", "absolute", "square"].
- action Dictionary. Defines the action space of the environment.
- variables List of dictionaries. Defines the variables of the action space, which have the following attributes:
- name String. Name of action space variable.
- variables List of dictionaries. Defines the variables of the action space, which have the following attributes:
- reward Dictionary. Defines the reward function.
- variables List of dictionaries. List of the variables that are included in the reward function.
- name String. Name of variable.
- type String. Type of variable, see observation variable type.
- value_type String. String. Augments the value of the variable, see LetMPCEnv._get_variable_value function.
- expression String. String representation of the python code used to evaluate the reward function using the variables as defined above.
- variables List of dictionaries. List of the variables that are included in the reward function.
- randomize Dictionary. The entries defined here have their values randomized in each episode, as opposed to the
fixed defaults provided in the other sections of the configuration file.
- reference Dictionary of dictionaries. Name of state references as keys with randomization attributes as value.
- type String. The distribution random values are drawn from, see numpy.random distributions for the available options.
- kw Dictionary. Dictionary of keywords provided to the numpy.random distribution function, see numpy documentation for parameters.
- state Dictionary of dictionaries. States defined here have their initial value randomized. Same attributes as reference.
- constraints Dictionary of dictionaries. Keys are names of constraints on the format "c-{state name}-{u/l}" where u is for upper bound and l is for lower bound. Same attributes as reference.
- model Dictionary. Attributes defined here are randomized in the models (i.e. system dynamics).
- apply List of Strings. The models to which these randomized values are applied, valid values ["plant", "mpc", "lqr"].
- states Dictionary of dictionary. State names as keys with factors in the state's dynamics (rhs in DE) as values. For each factor provide numpy.random distrbution and kw as defined for "randomize reference" above.
- reference Dictionary of dictionaries. Name of state references as keys with randomization attributes as value.
- render Dictionary of environment properties to be included in render figure. Valid keys ["plot_action", "plot_reward"], with value true/false.
- info Dictionary of dictionaries. Values here are processed at each call to environment.step() and returned in the
info dictionary.
- reward Dictionary of String -> String. Key is name of reward component while value is python code expression as for reward above. Can be used to monitor sub-compoments of the reward function or other quantities not included in the reward function. Any variables needed here must be defined in the variables list of the reward entry above.
Sets variables of the simulated (real) system.
- render Dictionary of plant variables to be included in render figure. Valid keys are ["process_noise"].
- params Dictionary of key-value pairs used in model creation, see do-mpc documentation.
- model Dictionary of model attributes.
- type String. Type of model, one of ["continuous", "discrete"].
- class String. The class of the system dynamics, one of ["linear", "nonlinear"].
- states Dictionary of state names as keys and state properties dictionary as value. If class is linear, entries for a and b must be defined, any entries not included are assumed to be 0, see included double integrator configuration file. If class is nonlinear, the rhs of the DE must be provided as python code expression. The expression can include other states, inputs and parameters as defined here, see included cart pendulum configuration file.
- inputs Dictionary of input names as keys and input properties dictionary as value. All control inputs used by plant must be defined here. Properties are unused as of now.
- tvps Dictionary of time-varying parameter names and attributes. Time-varying parameters are simulated by the
plant simulator as defined by the distributions here, the true value is used applied to the plant. Forecasts are
generated with length equal to the MPC horizon for any tvps used by the MPC. The first value in the forecast is the
true value, while subsequent forecasted values are the sum of true and forecast (noise), where the strength of the
forecast noise is linearly scaled with forecast length up to 1. For tvps exclusive to the MPC (e.g. only used in
cost function) need only be defined in the MPC model definition. For tvps used by both the MPC model definition should
be of the form {tvp-name}: "sim".
- true List of distribution dictionaries. These are distributions that summed constitute the true
value of the tvp.
- type String. Either distribution from numpy.random or "OU" for Ornstein-Uhelenbeck process.
- forecast_aware Boolean. Whether the forecast predicts changes in this distribution (true), or the fixed value at the start of forecast generation is assumed to be constant over the forecast length (false). Defaults to true.
- redraw_probability The probability (in [0, 1]) with which the value of the tvp is drawn at every time step or the last value is kept for the current time step. Defaults to 1 (i.e. always redraw).
- kw Dictionary. Keyword arguments passed to distribution.
- forecast List of distribution dictionaries. These are distributions that summed consitute the noise applied to the forecasted tvps. See definition of true above.
- true List of distribution dictionaries. These are distributions that summed constitute the true
value of the tvp.
- parameters Dictionary of string parameter name as key and float values as value. These are parameters with fixed value, used for convenience and readability of dynamics expressions, e.g. physical constants.
Sets variables of the MPC model, constraints, cost function etc.
- params Dictionary of key-value pairs used in model creation, see do-mpc documentation. Note that store_full_solution must be set to true.
- model See plant model definition. Can also have the special value of "plant", for which the model definition is copied from the plant model.
- reference Dictionary of control references. Reference is key which must be on the form {variable_name}_r. Values is dictionary which must include "type" e.g. "_x" for state variable (see do-mpc documentation). The attribute value sets the fixed reference value.
- constraints List of constraint dictionaries.
- var_name String. Name of state/input variable.
- var_type String. Either "_x" for state constraint or "_u" for input constraint.
- constraint_type String. Either "lower" for lower bound constraint or "upper" for upper bound.
- value Float. Value of constraint.
- objective Dictionary that defines the objective function of the MPC. Both lterm (stage cost) and
mterm (end of horizon cost) must be defined, although they can be set to constant 0.
- lterm Dictionary with variables and expression entries. See definition of reward function above. Can depend on states, inputs, parameters and time-varying parameters.
- mterm Same as lterm, although it can only depend states.
- R_delta Dictionary of input name and cost of changing the input setpoint from time step to time step.
Sets variables of the LQR.
- model Dictionary of model attributes. See definition of plant model above. Note that model class nonlinear is not supported, and model class must then be set to a provided fixed linear model or model class set to linearization, where the supplied model is that of the Jacobians of A and B and values for states and inputs are inserted from the current values of the plant. Can also be "plant"/"mpc" for which the model definition is copied from the plant or mpc, respectively.
- objective Dictionary containing the two required entries Q and R, as list of lists for matrices or lists of one element for scalar values in single state/input systems.
Tests can be run with pytest:
pip install pytest
cd tests
python -m pytestIf you use this software in your work, please consider citing:
@misc{bohn2020optimization,
title={Optimization of the Model Predictive Control Update Interval Using Reinforcement Learning},
author={Eivind Bøhn and Sebastien Gros and Signe Moe and Tor Arne Johansen},
year={2020},
eprint={2011.13365},
archivePrefix={arXiv},
primaryClass={eess.SY}
}