scholarly journals Optimization techniques for tree-structured nonlinear problems

2020 ◽  
Vol 17 (3) ◽  
pp. 409-436
Author(s):  
Jens Hübner ◽  
Martin Schmidt ◽  
Marc C. Steinbach
Keyword(s):  
Predictive Control ◽  
Interior Point Methods ◽  
Optimization Problems ◽  
Nonlinear Problems ◽  
Optimization Techniques ◽  
Active Set ◽  
Robust Model Predictive Control ◽  
Robust Model ◽  
Quasi Newton ◽  
Structured Optimization

Abstract Robust model predictive control approaches and other applications lead to nonlinear optimization problems defined on (scenario) trees. We present structure-preserving Quasi-Newton update formulas as well as structured inertia correction techniques that allow to solve these problems by interior-point methods with specialized KKT solvers for tree-structured optimization problems. The same type of KKT solvers could be used in active-set based SQP methods. The viability of our approach is demonstrated by two robust control problems.

scholarly journals Nonfragile Robust Model Predictive Control for Uncertain Constrained Systems with Time-Delay Compensation

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Wei Jiang ◽  
Hong-li Wang ◽  
Jing-hui Lu ◽  
Wei-wei Qin ◽  
Guang-bin Cai
Keyword(s):  
Time Delay ◽  
Model Predictive Control ◽  
Predictive Control ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Constrained Systems ◽  
Delay Compensation ◽  
Robust Model Predictive Control ◽  
Robust Model ◽  
Time Delay Compensation

This study investigates the problem of asymptotic stabilization for a class of discrete-time linear uncertain time-delayed systems with input constraints. Parametric uncertainty is assumed to be structured, and delay is assumed to be known. In Lyapunov stability theory framework, two synthesis schemes of designing nonfragile robust model predictive control (RMPC) with time-delay compensation are put forward, where the additive and the multiplicative gain perturbations are, respectively, considered. First, by designing appropriate Lyapunov-Krasovskii (L-K) functions, the robust performance index is defined as optimization problems that minimize upper bounds of infinite horizon cost function. Then, to guarantee closed-loop stability, the sufficient conditions for the existence of desired nonfragile RMPC are obtained in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are provided to illustrate the effectiveness of the proposed approaches.

Robust model predictive control with zone control

2009 ◽  
Vol 3 (1) ◽  
pp. 121-135 ◽  
Author(s):  
A.H. González ◽  
D. Odloak ◽  
J.L. Marchetti
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Robust Model Predictive Control ◽  
Zone Control ◽  
Robust Model
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