1,647 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
An Improved Constraint-Tightening Approach for Stochastic MPC
The problem of achieving a good trade-off in Stochastic Model Predictive
Control between the competing goals of improving the average performance and
reducing conservativeness, while still guaranteeing recursive feasibility and
low computational complexity, is addressed. We propose a novel, less
restrictive scheme which is based on considering stability and recursive
feasibility separately. Through an explicit first step constraint we guarantee
recursive feasibility. In particular we guarantee the existence of a feasible
input trajectory at each time instant, but we only require that the input
sequence computed at time remains feasible at time for most
disturbances but not necessarily for all, which suffices for stability. To
overcome the computational complexity of probabilistic constraints, we propose
an offline constraint-tightening procedure, which can be efficiently solved via
a sampling approach to the desired accuracy. The online computational
complexity of the resulting Model Predictive Control (MPC) algorithm is similar
to that of a nominal MPC with terminal region. A numerical example, which
provides a comparison with classical, recursively feasible Stochastic MPC and
Robust MPC, shows the efficacy of the proposed approach.Comment: Paper has been submitted to ACC 201
On feasibility, stability and performance in distributed model predictive control
In distributed model predictive control (DMPC), where a centralized
optimization problem is solved in distributed fashion using dual decomposition,
it is important to keep the number of iterations in the solution algorithm,
i.e. the amount of communication between subsystems, as small as possible. At
the same time, the number of iterations must be enough to give a feasible
solution to the optimization problem and to guarantee stability of the closed
loop system. In this paper, a stopping condition to the distributed
optimization algorithm that guarantees these properties, is presented. The
stopping condition is based on two theoretical contributions. First, since the
optimization problem is solved using dual decomposition, standard techniques to
prove stability in model predictive control (MPC), i.e. with a terminal cost
and a terminal constraint set that involve all state variables, do not apply.
For the case without a terminal cost or a terminal constraint set, we present a
new method to quantify the control horizon needed to ensure stability and a
prespecified performance. Second, the stopping condition is based on a novel
adaptive constraint tightening approach. Using this adaptive constraint
tightening approach, we guarantee that a primal feasible solution to the
optimization problem is found and that closed loop stability and performance is
obtained. Numerical examples show that the number of iterations needed to
guarantee feasibility of the optimization problem, stability and a prespecified
performance of the closed-loop system can be reduced significantly using the
proposed stopping condition
- …