scholarly journals Automatic Offline Formulation of Robust Model Predictive Control Based on Linear Matrix Inequalities Method

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Longge Zhang
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Control Strategies ◽  
Linear Matrix ◽  
Feedback Controllers ◽  
Robust Model Predictive Control ◽  
Online Computation ◽  
Robust Model ◽  
Output Constraints ◽  
Geometric Proportion

Two automatic robust model predictive control strategies are presented for uncertain polytopic linear plants with input and output constraints. A sequence of nested geometric proportion asymptotically stable ellipsoids and controllers is constructed offline first. Then the feedback controllers are automatically selected with the receding horizon online in the first strategy. Finally, a modified automatic offline robust MPC approach is constructed to improve the closed system's performance. The new proposed strategies not only reduce the conservatism but also decrease the online computation. Numerical examples are given to illustrate their effectiveness.

scholarly journals Robust Model Predictive Control with Almost Zero Online Computation

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 242
Author(s):  
Yan Yan ◽  
Longge Zhang
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Linear Matrix ◽  
Robust Model Predictive Control ◽  
Online Computation ◽  
Discrete Time Systems ◽  
Robust Model ◽  
Control Scheme ◽  
Geometric Proportion ◽  
Time Systems

This paper provides a strategy for the problem of robust model predictive control of constrained, discrete-time systems with state and output disturbances. Using the linear matrix inequality (LMI) method, the nested geometric proportion asymptotically stable ellipsoid (GPASE) strategy is designed off-line, and then the designed shrinking ellipsoids strategy assures the system converges on the equivalent with an exponential convergence velocity. The biggest advantage of this method is the online computation is almost reduced to zero, which makes it possible to apply the designed control scheme not only to plants with slowly varying parameters, but also to fast ones. Finally, a simulation example shows the validity of the proposed technique.

scholarly journals Robust Model Predictive Control Using Linear Matrix Inequalities for the Treatment of Asymmetric Output Constraints

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Mariana Santos Matos Cavalca ◽  
Roberto Kawakami Harrop Galvão ◽  
Takashi Yoneyama
Keyword(s):  
Model Predictive Control ◽  
Linear Matrix Inequalities ◽  
Predictive Control ◽  
Constraint Satisfaction ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Robust Model Predictive Control ◽  
Robust Model ◽  
Output Constraints

One of the main advantages of predictive control approaches is the capability of dealing explicitly with constraints on the manipulated and output variables. However, if the predictive control formulation does not consider model uncertainties, then the constraint satisfaction may be compromised. A solution for this inconvenience is to use robust model predictive control (RMPC) strategies based on linear matrix inequalities (LMIs). However, LMI-based RMPC formulations typically consider only symmetric constraints. This paper proposes a method based on pseudoreferences to treat asymmetric output constraints in integrating SISO systems. Such technique guarantees robust constraint satisfaction and convergence of the state to the desired equilibrium point. A case study using numerical simulation indicates that satisfactory results can be achieved.

scholarly journals Robust Model Predictive Control Schemes for Tracking Setpoints

2010 ◽  
Vol 2010 ◽  
pp. 1-9 ◽  
Author(s):  
Vu Trieu Minh ◽  
Fakhruldin Bin Mohd Hashim
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Uncertain Systems ◽  
State Constraints ◽  
Weighting Factor ◽  
The State ◽  
Future Research ◽  
Linear Matrix ◽  
Robust Model Predictive Control ◽  
Robust Model

This paper briefly reviews the development of nontracking robust model predictive control (RMPC) schemes for uncertain systems using linear matrix inequalities (LMIs) subject to input saturated and softened state constraints. Then we develop two new tracking setpoint RMPC schemes with common Lyapunov function and with zero terminal equality subject to input saturated and softened state constraints. The novel tracking setpoint RMPC schemes are able to stabilize uncertain systems once the output setpoints lead to the violation of the state constraints. The state violation can be regulated by changing the value of the weighting factor. A brief comparative simulation study of the two tracking setpoint RMPC schemes is done via simple examples to demonstrate the ability of the softened state constraint schemes. Finally, some features of future research from this study are discussed.

Stabilization of uncertain nonlinear discrete-time switched systems with state delays: A constrained robust model predictive control approach

2019 ◽  
Vol 25 (14) ◽  
pp. 2079-2090 ◽  
Author(s):  
Maryam Aminsafaee ◽  
Mohammad Hossein Shafiei
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Discrete Time ◽  
Switched Systems ◽  
Control Method ◽  
Sufficient Conditions ◽  
Switched System ◽  
Linear Matrix ◽  
Robust Model Predictive Control ◽  
Robust Model

This paper studies the problem of robust stabilization for a class of nonlinear discrete-time switched systems with polytopic uncertainties and unknown state delay. Moreover, the control signal is assumed to be constrained. The objective of the proposed controller is to stabilize the switched system under arbitrary switching signals based on the switched Lyapunov function approach. Therefore, based on the constrained robust model predictive control method and an appropriate Lyapunov–Krasovskii functional, the sufficient conditions to guarantee the asymptotical stability of the switched system are developed as linear matrix inequalities. Through online solving an optimization problem, the predictive state-feedback controller is designed. Furthermore, in this delay-dependent approach, only the upper bound of time-delay should be known. Appropriate transient response, ability to handle constraints, and nonconstrained switching signal are the other advantages of the proposed method. Finally, the performance of the proposed approach is compared with a similar approach through a numerical example. As well as, to show the applicability of the proposed controller, it is applied to a drinking water supply network, as an application example.

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