24,600 research outputs found
Asynchronous networked MPC with ISM for uncertain nonlinear systems
A model-based event-triggered control scheme for nonlinear constrained continuous-time uncertain systems in networked configuration is presented in this paper. It is based on the combined use of Model Predictive Control (MPC) and Integral Sliding Mode (ISM) control, and it is oriented to reduce the packets transmission over the network both in the direct path and in the feedback path, in order to avoid network congestion. The key elements of the proposed control scheme are the ISM local control law, the MPC remote controller, a smart sensor and a smart actuator, both containing a copy of the nominal model of the plant. The role of the ISM control law is to compensate matched uncertainties, without amplifying the unmatched ones. The MPC controller with tightened constraints generates the control component oriented to comply with state and control requirements, and is asynchronous since the underlying constrained optimization problem is solved only when a triggering event occurs. In the paper, the robustness properties of the controlled system are theoretically analyzed, proving the regional input-tostate practical stability of the overall control scheme
Robust nonlinear receding horizon control with constraint tightening: off line approximation and application to networked control system
2007/2008Nonlinear Receding Horizon (RH) control, also known as moving horizon control or nonlinear
Model Predictive Control (MPC), refers to a class of algorithms that make explicit use of a
nonlinear process model to optimize the plant behavior, by computing a sequence of future ma-
nipulated variable adjustments. Usually the optimal control sequence is obtained by minimizing
a multi-stage cost functional on the basis of open-loop predictions. The presence of uncertainty
in the model used for the optimization raises the question of robustness, i.e., the maintenance
of certain properties such as stability and performance in the presence of uncertainty.
The need for guaranteeing the closed-loop stability in presence of uncertainties motivates
the conception of robust nonlinear MPC, in which the perturbations are explicitly taken in
account in the design of the controller. When the nature of the uncertainty is know, and it is
assumed to be bounded in some compact set, the robust RH control can be determined, in a
natural way, by solving a min–max optimal control problem, that is, the performance objective
is optimized for the worst-case scenario. However, the use of min-max techniques is limited
by the high computational burden required to solve the optimization problem. In the case of
constrained system, a possibility to ensure the robust constraint satisfaction and the closed-loop
stability without resorting to min-max optimization consists in imposing restricted (tightened)
constraints on the the predicted trajectories during the optimization.
In this framework, an MPC scheme with constraint tightening for discrete-time nonlinear
systems affected by state-dependent and norm bounded uncertainties is proposed and discussed.
A novel method to tighten the constraints relying on the nominal state prediction is described,
leading to less conservative set contractions than in the existing approaches. Moreover, by
imposing a stabilizing state constraint at the end of the control horizon (in place of the usual
terminal one placed at the end of the prediction horizon), less stringent assumptions can be posed on the terminal region, while improving the robust stability properties of the MPC closed-loop
system.
The robust nonlinear MPC formulation with tightened constraints is then used to design off-
line approximate feedback laws able to guarantee the practical stability of the closed-loop system.
By using off-line approximations, the computational burden due to the on-line optimization is
removed, thus allowing for the application of the MPC to systems with fast dynamics. In this
framework, we will also address the problem of approximating possibly discontinuous feedback
functions, thus overcoming the limitation of existent approximation scheme which assume the
continuity of the RH control law (whereas this condition is not always verified in practice, due
to both nonlinearities and constraints).
Finally, the problem of stabilizing constrained systems with networked unreliable (and de-
layed) feedback and command channels is also considered. In order to satisfy the control ob-
jectives for this class of systems, also referenced to as Networked Control Systems (NCS’s), a
control scheme based on the combined use of constraint tightening MPC with a delay compen-
sation strategy will be proposed and analyzed.
The stability properties of all the aforementioned MPC schemes are characterized by using
the regional Input-to-State Stability (ISS) tool. The ISS approach allows to analyze the depen-
dence of state trajectories of nonlinear systems on the magnitude of inputs, which can represent
control variables or disturbances. Typically, in MPC the ISS property is characterized in terms
of Lyapunov functions, both for historical and practical reasons, since the optimal finite horizon
cost of the optimization problem can be easily used for this task. Note that, in order to study
the ISS property of MPC closed-loop systems, global results are in general not useful because,
due to the presence of state and input constraints, it is impossible to establish global bounds for
the multi-stage cost used as Lyapunov function. On the other hand local results do not allow to
analyze the properties of the predictive control law in terms of its region of attraction. There-
fore, regional ISS results have to employed for MPC controlled systems. Moreover, in the case of
NCS, the resulting control strategy yields to a time-varying closed-loop system, whose stability
properties can be analyzed using a novel regional ISS characterization in terms of time-varying
Lyapunov functions.XXI Ciclo198
A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems
This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version
On generalized terminal state constraints for model predictive control
This manuscript contains technical results related to a particular approach
for the design of Model Predictive Control (MPC) laws. The approach, named
"generalized" terminal state constraint, induces the recursive feasibility of
the underlying optimization problem and recursive satisfaction of state and
input constraints, and it can be used for both tracking MPC (i.e. when the
objective is to track a given steady state) and economic MPC (i.e. when the
objective is to minimize a cost function which does not necessarily attains its
minimum at a steady state). It is shown that the proposed technique provides,
in general, a larger feasibility set with respect to existing approaches, given
the same computational complexity. Moreover, a new receding horizon strategy is
introduced, exploiting the generalized terminal state constraint. Under mild
assumptions, the new strategy is guaranteed to converge in finite time, with
arbitrarily good accuracy, to an MPC law with an optimally-chosen terminal
state constraint, while still enjoying a larger feasibility set. The features
of the new technique are illustrated by three examples.Comment: Part of the material in this manuscript is contained in a paper
accepted for publication on Automatica and it is subject to Elsevier
copyright. The copy of record is available on http://www.sciencedirect.com
Explicit Reference Governor for Continuous Time Nonlinear Systems Subject to Convex Constraints
This paper introduces a novel closed-form strategy that dynamically modifies
the reference of a pre-compensated nonlinear system to ensure the satisfaction
of a set of convex constraints. The main idea consists of translating
constraints in the state space into constraints on the Lyapunov function and
then modulating the reference velocity so as to limit the value of the Lyapunov
function. The theory is introduced for general nonlinear systems subject to
convex constraints. In the case of polyhedric constraints, an explicit solution
is provided for the large and highly relevant class of nonlinear systems whose
Lyapunov function is lower-bounded by a quadratic form. In view of improving
performances, further specializations are provided for the relevant cases of
linear systems and robotic manipulators.Comment: Submitted to: IEEE Transactions on Automatic Contro
Model predictive control based on LPV models with parameter-varying delays
© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.This paper presents a Model Predictive Control (MPC) strategy based on Linear Parameter Varying (LPV) models with varying delays affecting states and inputs. The proposed control approach allows the controller to accommodate the scheduling parameters and delay change. By computing the prediction of the state variables and delay along a prediction time horizon, the system model can be modified according to the evaluation of the estimated state and delay at each time instant. Moreover, the solution of the optimization problem associated with the MPC design is achieved by solving a series of Quadratic Programming (QP) problem at each time instant. This iterative approach reduces the computational burden compared to the solution of a non-linear optimization problem. A pasteurization plant system is used as a case study to demonstrate the effectiveness of the proposed approach.Peer ReviewedPostprint (author's final draft
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