710 research outputs found
Stochastic MPC with Dynamic Feedback Gain Selection and Discounted Probabilistic Constraints
This paper considers linear discrete-time systems with additive disturbances,
and designs a Model Predictive Control (MPC) law incorporating a dynamic
feedback gain to minimise a quadratic cost function subject to a single chance
constraint. The feedback gain is selected from a set of candidates generated by
solutions of multiobjective optimisation problems solved by Dynamic Programming
(DP). We provide two methods for gain selection based on minimising upper
bounds on predicted costs. The chance constraint is defined as a discounted sum
of violation probabilities on an infinite horizon. By penalising violation
probabilities close to the initial time and ignoring violation probabilities in
the far future, this form of constraint allows for an MPC law with guarantees
of recursive feasibility without an assumption of boundedness of the
disturbance. A computationally convenient MPC optimisation problem is
formulated using Chebyshev's inequality and we introduce an online
constraint-tightening technique to ensure recursive feasibility. The closed
loop system is guaranteed to satisfy the chance constraint and a quadratic
stability condition. With dynamic feedback gain selection, the conservativeness
of Chebyshev's inequality is mitigated and closed loop cost is reduced with a
larger set of feasible initial conditions. A numerical example is given to show
these properties.Comment: 14 page
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Reconfigurable predictive control for redundantly actuated systems with parameterised input constraints
A method is proposed for on-line recon guration of the terminal constraint used to provide theoretical nominal stability
guarantees in linear model predictive control (MPC). By parameterising the terminal constraint, its complete reconstruction
is avoided when input constraints are modi ed to accommodate faults. To enlarge the region of feasibility of the
terminal control law for a certain class of input faults with redundantly actuated plants, the linear terminal controller
is de ned in terms of virtual commands. A suitable terminal cost weighting for the recon gurable MPC is obtained by
means of an upper bound on the cost for all feasible realisations of the virtual commands from the terminal controller.
Conditions are proposed that guarantee feasibility recovery for a de ned subset of faults. The proposed method is
demonstrated by means of a numerical example.The research leading to these results has received function
from the European Union Seventh Framework Programme
FP7/2007{2013 under grant agreement no. 314 544.This is the accepted manuscript. The final version is available from Elsevier at http://www.sciencedirect.com/science/article/pii/S0167691114000127
Multiobjective economic MPC of constrained nonâlinear systems
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/166264/1/cth2bf00058.pd
Data-driven distributed MPC of dynamically coupled linear systems
In this paper, we present a data-driven distributed model predictive control (MPC) scheme to stabilise the origin of dynamically coupled discrete-time linear systems subject to decoupled input constraints. The local optimisation problems solved by the subsystems rely on a distributed adaptation of the Fundamental Lemma by Willems et al., allowing to parametrise system trajectories using only measured input-output data without explicit model knowledge. For the local predictions, the subsystems rely on communicated assumed trajectories of neighbours. Each subsystem guarantees a small deviation from these trajectories via a consistency constraint. We provide a theoretical analysis of the resulting non-iterative distributed MPC scheme, including proofs of recursive feasibility and (practical) stability. Finally, the approach is successfully applied to a numerical example
Stabilising Model Predictive Control for Discrete-time Fractional-order Systems
In this paper we propose a model predictive control scheme for constrained
fractional-order discrete-time systems. We prove that all constraints are
satisfied at all time instants and we prescribe conditions for the origin to be
an asymptotically stable equilibrium point of the controlled system. We employ
a finite-dimensional approximation of the original infinite-dimensional
dynamics for which the approximation error can become arbitrarily small. We use
the approximate dynamics to design a tube-based model predictive controller
which steers the system state to a neighbourhood of the origin of controlled
size. We finally derive stability conditions for the MPC-controlled system
which are computationally tractable and account for the infinite dimensional
nature of the fractional-order system and the state and input constraints. The
proposed control methodology guarantees asymptotic stability of the
discrete-time fractional order system, satisfaction of the prescribed
constraints and recursive feasibility
A general dissipativity constraint for feedback system design, with emphasis on MPC
A âGeneral Dissipativity Constraintâ (GDC) is introduced to facilitate the design of stable feedback systems. A primary application is to MPC controllers when it is preferred to avoid the use of âstabilising ingredientsâ such as terminal constraint sets or long prediction horizons. Some very general convergence results are proved under mild conditions. The use of quadratic functions, replacing GDC by âQuadratic Dissipation Constraintâ (QDC), is introduced to allow implementation using linear matrix inequalities. The use of QDC is illustrated for several scenarios: state feedback for a linear time-invariant system, MPC of a linear system, MPC of an input-affine system, and MPC with persistent disturbances. The stability that is guaranteed by GDC is weaker than Lyapunov stability, being âLagrange stability plus convergenceâ. Input-to-state stability is obtained if the control law is continuous in the state. An example involving an open-loop unstable helicopter illustrates the efficacy of the approach in practice.National Research Foundation Singapor
Stability and performance in MPC using a finite-tail cost
In this paper, we provide a stability and performance analysis of model
predictive control (MPC) schemes based on finite-tail costs. We study the MPC
formulation originally proposed by Magni et al. (2001) wherein the standard
terminal penalty is replaced by a finite-horizon cost of some stabilizing
control law. In order to analyse the closed loop, we leverage the more recent
technical machinery developed for MPC without terminal ingredients. For a
specified set of initial conditions, we obtain sufficient conditions for
stability and a performance bound in dependence of the prediction horizon and
the extended horizon used for the terminal penalty. The main practical benefit
of the considered finite-tail cost MPC formulation is the simpler offline
design in combination with typically significantly less restrictive bounds on
the prediction horizon to ensure stability. We demonstrate the benefits of the
considered MPC formulation using the classical example of a four tank system
Model Predictive Control with and without Terminal Weight: Stability and Algorithms
This paper presents stability analysis tools for model predictive control
(MPC) with and without terminal weight. Stability analysis of MPC with a
limited horizon but without terminal weight is a long-standing open problem. By
using a modified value function as an Lyapunov function candidate and the
principle of optimality, this paper establishes stability conditions for this
type of widely spread MPC algorithms. A new stability guaranteed MPC algorithm
without terminal weight (MPCS) is presented. With the help of designing a new
sublevel set defined by the value function of one-step ahead stage cost,
conditions for checking its recursive feasibility and stability of the proposed
MPC algorithm are presented. The new stability condition and the derived MPCS
overcome the difficulties arising in the existing terminal weight based MPC
framework, including the need of searching a suitable terminal weight and
possible poor performance caused by an inappropriate terminal weight. This work
is further extended to MPC with a terminal weight for the completeness.
Numerical examples are presented to demonstrate the effectiveness of the
proposed tool, whereas the existing stability analysis tools are either not
applicable or lead to quite conservative results. It shows that the proposed
tools offer a number of mechanisms to achieve stability: adjusting state and/or
control weights, extending the length of horizon, and adding a simple extra
constraint on the first or second state in the optimisation
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