Constrained and Receding Horizon Control

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Author Index
A B C D E F G H I
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S T U V W X Y Z

The Explicit Solution of Constrained LP-Based Receding Horizon Control

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.

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Semi-Global Stabilization Of Linear Systems Subject To Output Saturation

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.

CD001228.PDF (From Author)

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A Stabilizing MPC Algorithm Using Performance Bounds From Saturated Linear Feedback

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.

CD001607.PDF (From Author)

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Model Predictive Control via Piecewise Constant Output Feedback for Multirate Sampled-Data Systems

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.

CD001107.PDF (From Author)

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Receding Horizon Output Feedback Control for Systems with Input Saturation

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.

CD001069.PDF (From Author) CD001069.PDF (Scanned)

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On Explicit Suboptimal LQR With State And Input Constraints

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.

CD001412.PDF (From Author)

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