3,605 research outputs found
A New Contraction-Based NMPC Formulation Without Stability-Related terminal Constraints
Contraction-Based Nonlinear Model Predictive Control (NMPC) formulations are
attractive because of the generally short prediction horizons they require and
the needless use of terminal set computation that are commonly necessary to
guarantee stability. However, the inclusion of the contraction constraint in
the definition of the underlying optimization problem often leads to non
standard features such as the need for multi-step open-loop application of
control sequences or the use of multi-step memorization of the contraction
level that may induce unfeasibility in presence of unexpected disturbance. This
paper proposes a new formulation of contraction-based NMPC in which no
contraction constraint is explicitly involved. Convergence of the resulting
closed-loop behavior is proved under mild assumptions.Comment: accepted in short version IFAC Nolcos 2016. submitted to Automatica
as a technical communiqu
Stability proof for nonlinear MPC design using monotonically increasing weighting profiles without terminal constraints
In this note, a new formulation of Model Predictive Control (MPC) framework
with no stability-related terminal constraint is proposed and its stability is
proved under mild standard assumptions. The novelty in the formulation lies in
the use of time-varying monotonically increasing stage cost penalty. The main
result is that the -reachability prediction horizon can always be made
stabilizing provided that the increasing rate of the penalty is made
sufficiently high.Comment: Submitted to Automatic
Enlarging the domain of attraction of MPC controllers
This paper presents a method for enlarging the domain of attraction of nonlinear model predictive control (MPC). The usual way of guaranteeing stability of nonlinear MPC is to add a terminal constraint and a terminal cost to the optimization problem such that the terminal region is a positively invariant set for the system and the terminal cost is an associated Lyapunov function. The domain of attraction of the controller depends on the size of the terminal region and the control horizon. By increasing the control horizon, the domain of attraction is enlarged but at the expense of a greater computational burden, while increasing the terminal region produces an enlargement without an extra cost.
In this paper, the MPC formulation with terminal cost and constraint is modified, replacing the terminal constraint by a contractive terminal constraint. This constraint is given by a sequence of sets computed off-line that is based on the positively invariant set. Each set of this sequence does not need to be an invariant set and can be computed by a procedure which provides an inner approximation to the one-step set. This property allows us to use one-step approximations with a trade off between accuracy and computational burden for the computation of the sequence. This strategy guarantees closed loop-stability ensuring the enlargement of the domain of attraction and the local optimality of the controller. Moreover, this idea can be directly translated to robust MPC.Ministerio de Ciencia y TecnologĂa DPI2002-04375-c03-0
Adjoint-based predictor-corrector sequential convex programming for parametric nonlinear optimization
This paper proposes an algorithmic framework for solving parametric
optimization problems which we call adjoint-based predictor-corrector
sequential convex programming. After presenting the algorithm, we prove a
contraction estimate that guarantees the tracking performance of the algorithm.
Two variants of this algorithm are investigated. The first one can be used to
solve nonlinear programming problems while the second variant is aimed to treat
online parametric nonlinear programming problems. The local convergence of
these variants is proved. An application to a large-scale benchmark problem
that originates from nonlinear model predictive control of a hydro power plant
is implemented to examine the performance of the algorithms.Comment: This manuscript consists of 25 pages and 7 figure
Analysis and design of model predictive control frameworks for dynamic operation -- An overview
This article provides an overview of model predictive control (MPC)
frameworks for dynamic operation of nonlinear constrained systems. Dynamic
operation is often an integral part of the control objective, ranging from
tracking of reference signals to the general economic operation of a plant
under online changing time-varying operating conditions. We focus on the
particular challenges that arise when dealing with such more general control
goals and present methods that have emerged in the literature to address these
issues. The goal of this article is to present an overview of the
state-of-the-art techniques, providing a diverse toolkit to apply and further
develop MPC formulations that can handle the challenges intrinsic to dynamic
operation. We also critically assess the applicability of the different
research directions, discussing limitations and opportunities for further
researc
Reinforcement Learning Based on Real-Time Iteration NMPC
Reinforcement Learning (RL) has proven a stunning ability to learn optimal
policies from data without any prior knowledge on the process. The main
drawback of RL is that it is typically very difficult to guarantee stability
and safety. On the other hand, Nonlinear Model Predictive Control (NMPC) is an
advanced model-based control technique which does guarantee safety and
stability, but only yields optimality for the nominal model. Therefore, it has
been recently proposed to use NMPC as a function approximator within RL. While
the ability of this approach to yield good performance has been demonstrated,
the main drawback hindering its applicability is related to the computational
burden of NMPC, which has to be solved to full convergence. In practice,
however, computationally efficient algorithms such as the Real-Time Iteration
(RTI) scheme are deployed in order to return an approximate NMPC solution in
very short time. In this paper we bridge this gap by extending the existing
theoretical framework to also cover RL based on RTI NMPC. We demonstrate the
effectiveness of this new RL approach with a nontrivial example modeling a
challenging nonlinear system subject to stochastic perturbations with the
objective of optimizing an economic cost.Comment: accepted for the IFAC World Congress 202
Robust predictive feedback control for constrained systems
A new method for the design of predictive controllers for SISO systems is presented. The proposed technique allows uncertainties and constraints to be concluded in the design of the control law. The goal is to design, at each sample instant, a predictive feedback control law that minimizes a performance measure and guarantees of constraints are satisfied for a set of models that describes the system to be controlled. The predictive controller consists of a finite horizon parametric-optimization problem with an additional constraint over the manipulated variable behavior. This is an end-constraint based approach that ensures the exponential stability of the closed-loop system. The inclusion of this additional constraint, in the on-line optimization algorithm, enables robust stability properties to be demonstrated for the closed-loop system. This is the case even though constraints and disturbances are present. Finally, simulation results are presented using a nonlinear continuous stirred tank reactor model
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