Stabilizing model predictive control: On the enlargement of the terminal set

2014 ◽  
Vol 25 (15) ◽  
pp. 2646-2670 ◽  
Author(s):  
Florian D. Brunner ◽  
Mircea Lazar ◽  
Frank Allgöwer
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Terminal Set

scholarly journals A Nonlinear Model Predictive Control with Enlarged Region of Attraction via the Union of Invariant Sets

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2087
Author(s):  
Ismi Rosyiana Fitri ◽  
Jung-Su Kim
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Convex Combination ◽  
Invariant Sets ◽  
Region Of Attraction ◽  
Control Laws ◽  
Terminal Set ◽  
The One ◽  
The Given ◽  
Regions Of Attraction

In the dual-mode model predictive control (MPC) framework, the size of the stabilizable set, which is also the region of attraction, depends on the terminal constraint set. This paper aims to formulate a larger terminal set for enlarging the region of attraction in a nonlinear MPC. Given several control laws and their corresponding terminal invariant sets, a convex combination of the given sets is used to construct a time-varying terminal set. The resulting region of attraction is the union of the regions of attraction from each invariant set. Simulation results show that the proposed MPC has a larger stabilizable initial set than the one obtained when a fixed terminal set is used.

Multistage Suboptimal Model Predictive Control With Improved Computational Efficiency

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Xiaotao Liu ◽  
Daniela Constantinescu ◽  
Yang Shi
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
The State ◽  
Admissible Set ◽  
Admissible Sets ◽  
Prediction Horizon ◽  
Terminal Set ◽  
Minimum Number ◽  
System States ◽  
The Stability

This paper proposes a multistage suboptimal model predictive control (MPC) strategy which can reduce the prediction horizon without compromising the stability property. The proposed multistage MPC requires a precomputed sequence of j-step admissible sets, where the j-step admissible set is the set of system states that can be steered to the maximum positively invariant set in j control steps. Given the precomputed admissible sets, multistage MPC first determines the minimum number of steps M required to drive the state to the terminal set. Then, it steers the state to the (M – N)-step admissible set if M > N, or to the terminal set otherwise. The paper presents the offline computation of the admissible sets, and shows the feasibility and stability of multistage MPC for systems with and without disturbances. A numerical example illustrates that multistage MPC with N = 5 can be used to stabilize a system which requires MPC with N ≥ 14 in the absence of disturbances, and requires MPC with N ≥ 22 when affected by disturbances.

Model Predictive Control Based Energy Management of Power-Split Hybrid Electric Vehicles in Presence of Uncertainty

2018 ◽  
Author(s):  
Baisravan HomChaudhuri ◽  
Carrie M. Hall
Keyword(s):  
Model Predictive Control ◽  
Energy Management ◽  
Predictive Control ◽  
Electric Vehicles ◽  
Constraint Satisfaction ◽  
Hybrid Electric Vehicles ◽  
Energy Management Strategy ◽  
Terminal Set ◽  
Power Split ◽  
Hybrid Electric

A model predictive control (MPC) based robust energy management strategy for power-split hybrid electric vehicles (HEVs) is proposed in this paper which can guarantee charge sustaining constraint satisfaction in presence of uncertainty in future torque demand and vehicle velocity. The proposed method utilizes robust backward reachability analysis to pre-compute a robust set from where control solutions exist that ensure charge sustaining constraint satisfaction despite the uncertainty. This set is then used as the terminal set constraint of the MPC problem followed by tightening of state constraints for robust constraint satisfaction. An equivalent convex optimal control is then formulated which is solved in a receding horizon fashion. Simulation results show the efficacy of the proposed control strategy in robust constraint satisfaction.

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