1,007 research outputs found
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
Learning-based predictive control for linear systems: a unitary approach
A comprehensive approach addressing identification and control for
learningbased Model Predictive Control (MPC) for linear systems is presented.
The design technique yields a data-driven MPC law, based on a dataset collected
from the working plant. The method is indirect, i.e. it relies on a model
learning phase and a model-based control design one, devised in an integrated
manner. In the model learning phase, a twofold outcome is achieved: first,
different optimal p-steps ahead prediction models are obtained, to be used in
the MPC cost function; secondly, a perturbed state-space model is derived, to
be used for robust constraint satisfaction. Resorting to Set Membership
techniques, a characterization of the bounded model uncertainties is obtained,
which is a key feature for a successful application of the robust control
algorithm. In the control design phase, a robust MPC law is proposed, able to
track piece-wise constant reference signals, with guaranteed recursive
feasibility and convergence properties. The controller embeds multistep
predictors in the cost function, it ensures robust constraints satisfaction
thanks to the learnt uncertainty model, and it can deal with possibly
unfeasible reference values. The proposed approach is finally tested in a
numerical example
Recursive Feasibility of Stochastic Model Predictive Control with Mission-Wide Probabilistic Constraints
This paper is concerned with solving chance-constrained finite-horizon
optimal control problems, with a particular focus on the recursive feasibility
issue of stochastic model predictive control (SMPC) in terms of mission-wide
probability of safety (MWPS). MWPS assesses the probability that the entire
state trajectory lies within the constraint set, and the objective of the SMPC
controller is to ensure that it is no less than a threshold value. This differs
from classic SMPC where the probability that the state lies in the constraint
set is enforced independently at each time instant. Unlike robust MPC, where
strict recursive feasibility is satisfied by assuming that the uncertainty is
supported by a compact set, the proposed concept of recursive feasibility for
MWPS is based on the notion of remaining MWPSs, which is conserved in the
expected value sense. We demonstrate the idea of mission-wide SMPC in the
linear SMPC case by deploying a scenario-based algorithm
Stochastic Model Predictive Control with a Safety Guarantee for Automated Driving
Automated vehicles require efficient and safe planning to maneuver in
uncertain environments. Largely this uncertainty is caused by other traffic
participants, e.g., surrounding vehicles. Future motion of surrounding vehicles
is often difficult to predict. Whereas robust control approaches achieve safe,
yet conservative motion planning for automated vehicles, Stochastic Model
Predictive Control (SMPC) provides efficient planning in the presence of
uncertainty. Probabilistic constraints are applied to ensure that the maximal
risk remains below a predefined level. However, safety cannot be ensured as
probabilistic constraints may be violated, which is not acceptable for
automated vehicles. Here, we propose an efficient trajectory planning framework
with safety guarantees for automated vehicles. SMPC is applied to obtain
efficient vehicle trajectories for a finite horizon. Based on the first
optimized SMPC input, a guaranteed safe backup trajectory is planned, using
reachable sets. The SMPC input is only applied to the vehicle if a safe backup
solution can be found. If no new safe backup solution can be found, the
previously calculated, still valid safe backup solution is applied instead of
the SMPC solution. Recursive feasibility of the safe SMPC algorithm is proved.
Highway simulations show the effectiveness of the proposed method regarding
performance and safety
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