Authors:
Alberto Bemporad,
Francesco Borrelli,
Manfred Morari,
Volume: 1, Page 632 Paper number 1681
Abstract:
For discrete-time linear time-invariant systems with constraints on
inputs and states, we develop an algorithm to determine explicitly,
as a function of the initial state, the solution to optimal control
problems that can be formulated using a linear program. In particular,
we focus our attention on a receding horizon control scheme where the
performance criterion is based on a mixed 1/infinity-norm (i.e., 1-norm
with respect to time and infinity-norm with respect to space). We show
that the optimal control profile is a piecewise linear and continuous
function of the initial state. Thus, when the optimal control problem
is solved at each time step according to a moving horizon scheme, the
on-line computation of the resultant MPC controller is reduced to a
simple linear function evaluation, instead of the typical expensive
linear program required up to now. The technique proposed has both
theoretical and practical advantages. From a theoretical point of view,
the explicit solution gives insight on the action of the controller
in different regions of the state space, and highlights conditions
of degeneracy. From a practical point of view, the proposed technique
is attractive for a wide range of applications where the simplicity
of the on-line computational complexity is a crucial requirement.
Authors:
Zongli Lin,
Tingshu Hu,
Volume: 1, Page 638 Paper number 1228
Abstract:
It is established that a SISO linear system subject to output saturation
can be semi-globally stabilized by linear output feedback if all its
invariant zeros are in the closed left-half plane, no matter where
the open loop poles are. This result can be viewed as dual to a well-known
result: a linear system subject to input saturation can be semi-globally
stabilized by linear output feedback if all its poles are in the open
left-half plane, no matter where the invariant zeros are.
Authors:
Johan Löfberg,
Volume: 1, Page 644 Paper number 1607
Abstract:
We present a method to increase feasibility in MPC algorithms that
use ellipsoidal terminal state constraints and performance bounds
from nominal controllers. The method is based on estimating a bound
on the achievable performance with a saturated nominal controller
and using this bound in the MPC algorithm. The resulting MPC controller
can be implemented efficiently with Second Order Cone Programming.
Authors:
Yong-Yan Cao,
Lisheng Hu,
Paul M. Frank,
Volume: 1, Page 650 Paper number 1107
Abstract:
In this paper, we consider the model predictive control for continuous-time
systems by multirate sampled-data approach. A output feedback multirate
MPC algorithm is proposed for LTI continuous-time systems based on
the so-called periodic piecewise output feedback approach. First the
multirate receding horizon optimal control is derived for discrete-time
systems. It is shown that the multirate receding horizon control design
of the LTI continuous-time systems can be reduced to that of a LTI
discrete-time systems. Then the multirate sampled-data design of the
LTI continuous-time systems is developed.
Authors:
Young Il Lee,
Basil Kouvaritakis,
Volume: 1, Page 656 Paper number 1069
Abstract:
In this paper, a constrained receding horizon output feedback control
method which is based on a state observer is suggested. The proposed
method adopts the receding horizon dual-mode paradigm which consists
of a `feasible invariant set' and `free control moves'. Polyhedral
feasible invariant sets of estimated state are derived along with guaranteed
bounds on state estimation errors. The guaranteed bounds on the state
estimation error are developed by considering invariant sets of state
estimation errors which include possible initial estimation errors.
Predictions of future states are made based on estimated current state
and bounds on current estimation error. The free control moves are
determined so that the predicted future state belongs to the polyhedral
feasible invariant set, despite input constraints and measurement noise.
Authors:
Tor Arne Johansen,
Idar Petersen,
Olav Slupphaug,
Volume: 1, Page 662 Paper number 1412
Abstract:
Optimal feedback solutions to the infinite-horizon LQR problem with
state and input constraints based on receding horizon real-time quadratic
programming are well known. In this paper we develop an explicit solution
to the same problem, eliminating the need for real-time optimization.
A suboptimal strategy, based on a suboptimal choice of a finite horizon
and imposing additional limitations on the allowed switching between
active constraint sets on the horizon, is suggested in order to address
the computer memory and processing capacity requirements of the explicit
solution. It is shown that the resulting feedback controller is piecewise
linear, and the piecewise linear structure is exploited for computational
analysis of stability and performance as well as efficient real-time
implementation.
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