7,883 research outputs found
Learning an Approximate Model Predictive Controller with Guarantees
A supervised learning framework is proposed to approximate a model predictive
controller (MPC) with reduced computational complexity and guarantees on
stability and constraint satisfaction. The framework can be used for a wide
class of nonlinear systems. Any standard supervised learning technique (e.g.
neural networks) can be employed to approximate the MPC from samples. In order
to obtain closed-loop guarantees for the learned MPC, a robust MPC design is
combined with statistical learning bounds. The MPC design ensures robustness to
inaccurate inputs within given bounds, and Hoeffding's Inequality is used to
validate that the learned MPC satisfies these bounds with high confidence. The
result is a closed-loop statistical guarantee on stability and constraint
satisfaction for the learned MPC. The proposed learning-based MPC framework is
illustrated on a nonlinear benchmark problem, for which we learn a neural
network controller with guarantees.Comment: 6 pages, 3 figures, to appear in IEEE Control Systems Letter
Learning an approximate model predictive controller with guarantees
In this thesis, a supervised learning framework to approximate a model predictive controller (MPC) with guarantees on stability and constraint satisfaction is proposed. The approximate controller has a reduced computational complexity in comparison to standard MPC which makes it possible to implement the resulting controller for systems with a high sampling rate on a cheap hardware. The framework can be used for a wide class of nonlinear systems.
In order to obtain closed-loop guarantees for the approximate MPC, a robust MPC (RMPC) with robustness to bounded input disturbances is used which guarantees stability and constraint satisfaction if the input is approximated with a bound on the approximation error.
The RMPC can be sampled offline and hence, any standard supervised learning technique can be used to approximate the MPC from samples. Neural networks (NN) are discussed in this thesis as one suitable approximation method.
To guarantee a bound on the approximation error, statistical learning bounds are used. A method based on Hoeffding’s Inequality is proposed to validate that the approximate MPC satisfies these bounds with high confidence. This validation method is suited for any approximation method. The result is a closed-loop statistical guarantee on stability and constraint satisfaction for the approximated MPC.
Within this thesis, an algorithm to obtain automatically an approximate controller is proposed. The proposed learning-based MPC framework is illustrated on a nonlinear benchmark problem for which we learn a neural network controller that guarantees stability and constraint satisfaction.
The combination of robust control and statistical validation can also be used for other learning based control methods to obtain guarantees on stability and constraint satisfaction
Differentiable Predictive Control with Safety Guarantees: A Control Barrier Function Approach
We develop a novel form of differentiable predictive control (DPC) with
safety and robustness guarantees based on control barrier functions. DPC is an
unsupervised learning-based method for obtaining approximate solutions to
explicit model predictive control (MPC) problems. In DPC, the predictive
control policy parametrized by a neural network is optimized offline via direct
policy gradients obtained by automatic differentiation of the MPC problem. The
proposed approach exploits a new form of sampled-data barrier function to
enforce offline and online safety requirements in DPC settings while only
interrupting the neural network-based controller near the boundary of the safe
set. The effectiveness of the proposed approach is demonstrated in simulation.Comment: Accepted to IEEE Conference on Decision and Control Conference 202
Learning Robustness with Bounded Failure: An Iterative MPC Approach
We propose an approach to design a Model Predictive Controller (MPC) for
constrained Linear Time Invariant systems performing an iterative task. The
system is subject to an additive disturbance, and the goal is to learn to
satisfy state and input constraints robustly. Using disturbance measurements
after each iteration, we construct Confidence Support sets, which contain the
true support of the disturbance distribution with a given probability. As more
data is collected, the Confidence Supports converge to the true support of the
disturbance. This enables design of an MPC controller that avoids conservative
estimate of the disturbance support, while simultaneously bounding the
probability of constraint violation. The efficacy of the proposed approach is
then demonstrated with a detailed numerical example.Comment: Added GitHub link to all source code
Bayesian model predictive control: Efficient model exploration and regret bounds using posterior sampling
Tight performance specifications in combination with operational constraints
make model predictive control (MPC) the method of choice in various industries.
As the performance of an MPC controller depends on a sufficiently accurate
objective and prediction model of the process, a significant effort in the MPC
design procedure is dedicated to modeling and identification. Driven by the
increasing amount of available system data and advances in the field of machine
learning, data-driven MPC techniques have been developed to facilitate the MPC
controller design. While these methods are able to leverage available data,
they typically do not provide principled mechanisms to automatically trade off
exploitation of available data and exploration to improve and update the
objective and prediction model. To this end, we present a learning-based MPC
formulation using posterior sampling techniques, which provides finite-time
regret bounds on the learning performance while being simple to implement using
off-the-shelf MPC software and algorithms. The performance analysis of the
method is based on posterior sampling theory and its practical efficiency is
illustrated using a numerical example of a highly nonlinear dynamical
car-trailer system
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