Authors:
Ki Baek Kim,
Tae-Woong Yoon,
Volume: 1, Page 148 Paper number 1637
Abstract:
In this paper, new matrix inequality conditions on the terminal weighting
matrices are proposed for linear continuous time-varying systems. Under
these conditions, nonincreasing and nondecreasing monotonicities of
the saddle point value of a dynamic game are shown to be guaranteed.
It is proved that the proposed terminal inequality conditions ensure
the closed-loop stability of the receding horizon H-infinity control
(RHHC). The stabilizing RHHC guarantees an H-infinity norm bound of
the close-loop system. The proposed terminal inequality conditions
for the monotonicity of the saddle point value and the closed-loop
stability include most well-known existing terminal conditions as special
cases. The results for time-invariant systems are obtained correspondingly
from those in the time-varying case.
Authors:
María M. Seron,
José A. De Doná,
Graham C. Goodwin,
Volume: 1, Page 154 Paper number 1817
Abstract:
We derive a closed-form global analytical solution for Model Predictive
Control (MPC) of linear, discrete-time systems, subject to a quadratic
performance index and hard magnitude constraints at the system input.
The solution is shown to be a partition of the state space in regions
for which an analytic expression is given for the corresponding control
law. Both the regions and the control law are characterised in terms
of the parameters of the open-loop optimal control problem that underlies
MPC. The result exploits the geometric properties of quadratic programming.
Authors:
Peter J. Gawthrop,
Volume: 1, Page 160 Paper number 1632
Abstract:
Some of the theoretical properties of predictive-pole-placement control
(a form of model-based predictive control) are given a practical
interpretation and corresponding design rules suggested.
Authors:
Camile Rowe,
Jan M. Maciejowski,
Volume: 1, Page 166 Paper number 1615
Abstract:
In this paper a procedure for obtaining the parameters of a finite
horizon model predictive controller to make it equivalent to an H infinity
normalised left coprime factorisation (NLCF) controller in the unconstrained
case will be considered. The procedure will be based on a Linear Matrix
Inequalities (LMI) approach to the solution of the discrete-time H-infinity
control problem and will be solved by first considering the solution
when the state is available for measurement.
Authors:
David Q. Mayne,
José A. De Doná,
Graham C. Goodwin,
Volume: 1, Page 172 Paper number 1166
Abstract:
It is known that stability of a model predictive control system is
ensured if the terminal conditions of the optimal control problem solved
online satisfy certain criteria. The usual requirement is that the
terminal cost function is a control Lyapunov function defined on the
terminal constraint set. Conventionally the terminal cost function
is chosen, when the system being controlled is linear, to be the value
function for the infinite horizon unconstrained optimal control problem
and the terminal constraint set is chosen to be the output admissible
set for the closed-loop system using the optimal unconstrained controller
u=-Kx. The purpose of this paper is to relax these terminal conditions
thereby facilitating online solution of the optimal control problem.
Using some recent results, we present alternative conditions that employ,
as the terminal cost, the infinite horizon cost resulting from a nonlinear
controller u=-sat(Kx) and, as the terminal constraint set, the set
in which this controller is optimal for the infinite horizon constrained
optimal control problem. It is shown that this solution provides a
considerably larger terminal constraint set.
Authors:
Daniel E. Quevedo,
Mario E. Salgado,
Volume: 1, Page 178 Paper number 1011
Abstract:
A general procedure leading to an enhancement of robustness of existing
Model Predictive Control techniques is proposed. This procedure, which
considers additive modeling errors, is illustrated for the case of
Cautious Stable Predictive Control. The basic idea is the augmentation
of the cost function with an additional term related to a description
of the nominal model uncertainty, leading either to a minimization
or to a min-max optimization problem, depending on the class of error
description being used.
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