Sparse Identification of Nonlinear Dynamics for Model Predictive Control in the Low-Data Limit
Sparse identification of nonlinear dynamics with control (SINDYc) is combined with model predictive control (MPC). This framework learns nonlinear dynamical models affected by an exogenous control variable from few measurements. The resulting SINDYc models have the ability to enhance the performance of model predictive control (MPC), based on limited, noisy data. SINDYc models are parsimonious, identifying the fewest terms in the model needed to explain the data, making them interpretable and generalizable. We show that the resulting SINDY-MPC framework has higher performance, requires significantly less data, and is more computationally efficient and robust to noise than neural network models, making it viable for online training and execution in response to rapid system changes. SINDY-MPC also shows improved performance over linear data-driven models, although linear models may provide a stopgap until enough data is available for SINDY. SINDY-MPC is demonstrated on a variety of dynamical systems with different challenges including the Lotka-Volterra system, the chaotic Lorenz system, a simple model for flight control of a F8 aircraft, and an HIV model incorporating drug treatment.
The publication "Sparse identification of nonlinear dynamics for model predictive control in the low-data limit" by E. Kaiser, J. N. Kutz and S. L. Brunton. is available on arXiv.
- Clone this repository to your desktop.
- Add path to
SINDY-MPC/utilsfolder to Matlab search path using
addpath('<path to SINDY-MPC>/SINDY-MPC').
No additional dependencies.
The code for each example
YYYY is in the corresponding example folder
/EX_YYYY. Code used for all examples can be found in
SINDY-MPC/utils, example-specific code, e.g. for plotting, will be in the corresponding example folder.
- Go into an example folder
- Run scripts for SINDYc system identification, e.g.
EX_YYYY_SI_SINDYc.m. To train other models replace
NARXfor a neural network or
DMDcfor a linear system. The trained models are saved in the folder
- Run model predictive control by choosing one of these options:
MPC_YYYY_SINDYc.mto use SINDYc in MPC. b. Run MPC for all models (e.g. SINDYc, neural network, linear system via DMDc) by executing
- Saved figures may be found in
It is easier to get started with the examples
The models for the HIV system are included in the folder
SINDY-MPC/DATA/HIV/. So in order to obtain the control results, one can immediately start by executing
MPC_HIV_ModelComparison.m without prior computation of the models.
The algorithms are in the
SINDY-MPC/ directory. The folder
SINDY-MPC/utils/ contains helper functions. Example specific functions are in the respective folder
SINDY-MPC/EX_YYYY/ for example
YYYY. Each example folder contains a similar set of functions. The most important ones are:
EX_YYYY_SI_SINDYc : SINDYc System Identification (SI) for example YYYY EX_YYYY_SI_DelayDM : (Delay)DMDc System Identification (SI) for example YYYY EX_YYYY_SI_NARX : Neural Network System Identification (SI) for example YYYY getTrainingData : Runs simulation to collect training data getValidationData : Runs simulation to collect validation data getMPCparams : Defines parameters for MPC ConstraintFCN_models : Evaluates MPC constraint functions for different models ObjectiveFCN_models : Computes control objective for different models ConstraintFCN : Evaluates MPC constraint functions using true system model ObjectiveFCN : Computes control objective using true system model MPC_YYYY_ModelComparison : Comparison of all considered models regarding prediction on training and validation data and MPC
See the LICENSE file for details.