Optimizing the end-point state-weighting matrix in model-based predictive control

Bloemen, H.H.J.; Boom, T.J.J. van den; Verbruggen, H.B.

doi:10.1016/s0005-1098(01)00296-5

Cited by 46 publications

(29 citation statements)

References 19 publications

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“…It is appropriate to use a finite-horizon cost function to approximate J i (k) and, for the neighbors, apply the assumed control trajectories as in [1,2]. The MPC with N free control moves (N is named switching horizon), as in [7], will be applied. Define…”

Section: Remarkmentioning

confidence: 99%

“…In solving problem (11), a symmetric positive-definite matrix P i (k) is introduced and the following is imposed for achieving closed-loop stability (as in [7,8]):…”

Section: Design Of Local Control Lawsmentioning

confidence: 99%

“…Lemma 1 (A generalization of the result in [7]) Suppose there exist a scalar i > 0, symmetric matrices S i , Z i , i and a matrix Y i satisfying (14)-(16). Then the state feedback controller (6) exponentially stabilizes the system x i ( j +1|k) = A i x i ( j|k)+ B i u i ( j|k) for any x i (N |k) ∈ E S i , while satisfying the constraints in (3) for all j N , and the resultant state trajectory x i ( j|k), j N always remains in the region E S i .…”

Section: Design Of Local Control Lawsmentioning

confidence: 99%

“…where, for optimization, x i ( j|k) and x i (N |k) should be properly expressed as functions of u i ( j|k), j ∈ N. For N a = 1, (24) reduces to the technique in [7].…”

Section: Remarkmentioning

confidence: 99%

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Distributed model predictive control for constrained linear systems

Ding¹,

Xie²,

Cai³

2010

Intl J Robust & Nonlinear

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SUMMARYWe address the distributed model predictive control (MPC) for a set of linear local systems with decoupled dynamics and a coupled global cost function. By the decomposition of the global cost function, the distributed control problem is converted to the MPC for each local system associated with a cost involving neighboring system states and inputs. For each local controller, the infinite horizon control moves are parameterized as N free control moves followed by a single state feedback law. An interacting compatibility condition is derived, disassembled and incorporated into the design of each local control so as to achieve the stability of the global closed-loop system. Each local system exchanges with its neighbors the current states and the previous optimal control strategies. The global closed-loop system is shown to be exponentially stable provided that all the local optimizers are feasible at the initial time.

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Section: Remarkmentioning

confidence: 99%

“…In solving problem (11), a symmetric positive-definite matrix P i (k) is introduced and the following is imposed for achieving closed-loop stability (as in [7,8]):…”

Section: Design Of Local Control Lawsmentioning

confidence: 99%

Section: Design Of Local Control Lawsmentioning

confidence: 99%

“…where, for optimization, x i ( j|k) and x i (N |k) should be properly expressed as functions of u i ( j|k), j ∈ N. For N a = 1, (24) reduces to the technique in [7].…”

Section: Remarkmentioning

confidence: 99%

See 2 more Smart Citations

Distributed model predictive control for constrained linear systems

Ding¹,

Xie²,

Cai³

2010

Intl J Robust & Nonlinear

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“…Sufficient conditions for stabilizing the finite horizon MPC with terminal cost have been discussed in (Bloemen, et al, 2002), where the inequality relation between the terminal weighting matrix and the linear static state feedback law has been established. Here, a simple sufficient condition for stability of single MPC without local linear static state feedback law is derived first to be the base for further discussions on stability of SS-MPC.…”

Section: Stability Of Ss-mpcmentioning

confidence: 99%

Analysis and Design of Softly Switched Model Predictive Control

Wang

Brdyś

2005

IFAC Proceedings Volumes

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This paper presents a new approach to soft switching between two model predictive controllers. The motivation for this work comes from the control of large scale hierarchical systems where different operating scenario asking for different control objective makes a single model predictive controller (MPC) unsuitable. The proposed soft switching approach shows much better switching performance both in system output and control input than the traditional hard switching. The stability of the designed soft switching process is analysed and sufficient conditions for stability are derived. Numerical examples with simulation results show that the proposed approach can be useful in practical applications.

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References

2024

Model Predictive Control

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Optimizing the end-point state-weighting matrix in model-based predictive control

Cited by 46 publications

References 19 publications

Distributed model predictive control for constrained linear systems

Distributed model predictive control for constrained linear systems

Analysis and Design of Softly Switched Model Predictive Control

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