Time Optimal Control Laws for Bilinear Systems

Bichiou, Salim; Bouafoura, Mohamed Karim; Braïek, Naceur Benhadj

doi:10.1155/2018/5217427

Cited by 13 publications

(5 citation statements)

References 27 publications

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“…First, we give a brief overview to specify our strict framework, that is to say, the BPFs parameterization technique. Then, the challenging tasks investigated in this section will concern the extension of the direct approach (BPFs) to decentralized optimal control with observers of interconnected systems (Bichiou et al, 2018; Dadkhah and Farahi, 2015; Ghali et al, 2017a, b; Hosseinpour and Nazemi, 2016; Marzban, 2016; Tang et al, 2017; Warrad et al, 2018; Xie and Huang, 2016; Ziari et al, 2019).…”

Section: Proposed Approach For Decentralized Observer-based Optimal Cmentioning

confidence: 99%

A decentralized observer-based optimal control for interconnected systems using the block pulse functions

Ghali

Benallègue²,

Elloumi

2020

Transactions of the Institute of Measurement and Control

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The paper proposes a method to integrate numerically an interconnected system, based on an idea of orthogonal approximation of functions. Here, block pulse functions (BPFs) are chosen as the orthogonal set. The main advantage of using this technique is its ability to transform the original optimal control problem to a mathematical programming problem relatively easier to solve. The primary focus of this paper is to exploit and rigorously develop the BPFs parametrization technique for the synthesis of a decentralized observer-based optimal control for large-scale interconnected systems. In addition, we develop a mathematical model of a double-parallel inverted pendulum coupled by a spring, taking into account all possible changes of the connecting position of the elastic spring. In so doing, we conducted advanced simulations applying the new optimal control method to the studied interconnected system. Our results demonstrate the validity and the effectiveness of the developed decentralized observer-based optimal control approach.

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Section: Proposed Approach For Decentralized Observer-based Optimal Cmentioning

confidence: 99%

A decentralized observer-based optimal control for interconnected systems using the block pulse functions

Ghali

Benallègue²,

Elloumi

2020

Transactions of the Institute of Measurement and Control

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“…It should be pointed out that generally many controllers can be designed to achieve the stabilizability of bilinear systems, 22,23 but maybe more work needs to be done to improve the close‐loop performance by utilizing the remaining degrees of freedom. For bilinear systems, optimal control problems have attracted much attention 10,24‐26 . However, to the best knowledge of the authors, for state‐based SBLSs few results exist focusing on the performance optimization of the controller.…”

Section: Introductionmentioning

confidence: 99%

Optimizing the performance of the feedback controller for state‐based switching bilinear systems

Lin

Schutter

2020

Optim Control Appl Methods

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Summary This article is concerned with the design and performance optimization of feedback controllers for state‐based switching bilinear systems (SBLSs), where subsystems take the form of bilinear systems in different state space polyhedra. First, by further dividing the subregions into smaller regions and designing region‐dependent feedback controllers in the resulting regions, the SBLSs can be transformed into corresponding switching linear systems (SLSs). Then, for these SLSs, by imposing contractility conditions on the Lyapunov functions, an upper bound on the infinite horizon quadratic cost can be obtained. Optimizing this upper bound yields the controller design. The optimization problem is formulated as a linear matrix inequalities optimization problem, which can be solved efficiently. Finally, the stability of the close‐loop system under the proposed controller is established step by step through a decreasing overall Lyapunov function.

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“…Among them, some results were concerned with continuous-time bilinear systems with only multiplicative control [3,4]. For bilinear systems with both additive and multiplicative control inputs, there were some control designs, such as bang-bang control law with a nonlinear switching function [5], quadratic feedback control [6], and optimal control [7][8][9]. Since the exact system models are not always available, the model uncertainties may occur in the bilinear systems.…”

Section: Introductionmentioning

confidence: 99%

Combined Constrained Robust Least Squares Approach and Block-Pulse Functions Technique for Tracking Control Synthesis of Uncertain Bilinear Systems with Multiple Time-Delayed States under Bounded Input Control

Warrad

Bouafoura

Braïek

2020

Mathematical Problems in Engineering

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The present study tackles the tracking control problem for unstructured uncertain bilinear systems with multiple time-delayed states subject to control input constraints. First, a new method is introduced to design memory state feedback controllers with compensator gain based on the use of operational properties of block-pulse functions basis. The proposed technique permits transformation of the posed control problem into a constrained and robust optimization problem. The constrained robust least squares approach is then used for determination of the control gains. Second, new sufficient conditions are proposed for the practical stability analysis of the closed-loop system, where a domain of attraction is estimated. A real-world example, the headbox control of a paper machine, demonstrates the efficiency of the proposed method.

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Time Optimal Control Laws for Bilinear Systems

Cited by 13 publications

References 27 publications

A decentralized observer-based optimal control for interconnected systems using the block pulse functions

A decentralized observer-based optimal control for interconnected systems using the block pulse functions

Optimizing the performance of the feedback controller for state‐based switching bilinear systems

Combined Constrained Robust Least Squares Approach and Block-Pulse Functions Technique for Tracking Control Synthesis of Uncertain Bilinear Systems with Multiple Time-Delayed States under Bounded Input Control

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