Bassem Iben Warrad

Bio: Bassem Iben Warrad is an academic researcher from Carthage University. The author has contributed to research in topics: Nonlinear system & Polynomial. The author has an hindex of 2, co-authored 6 publications receiving 15 citations.

Static output tracking control for non-linear polynomial time-delay systems via block-pulse functions

Abstract: In this paper, a new method is introduced to design static output tracking controllers for a class of non-linear polynomial time-delay systems. The proposed technique is based on the projection of the controlled system and the associated linear reference model that it should follow over a basis of block-pulse functions. The useful properties of these orthogonal functions such as operational matrices jointly used with the Kronecker tensor product may transform the non-linear delay differential equations into linear algebraic equations depending only on parameters of the feedback regulator. The least-squares method is then used for determination of the unknown parameters. Sufficient conditions for the practical stability of the closed-loop system are derived, and a domain of attraction is estimated. The implementation of the proposed method is illustrated on a double inverted pendulums benchmark as well as a two-degree-of- freedom mass-spring-damper system. The simulation results show the effectiven...

Tracking control synthesis of nonlinear polynomial systems

Abstract: In this paper, tracking control of nonlinear polynomial systems is investigated. A nonlinear state feedback is derived using orthogonal functions and Kronecker product. The main objective is to force the controlled system output to follow that of a linear reference model. The useful properties of the considered basis transform the differential equations into algebraic ones depending only on the parameters of the feedback regulator, which can be solved in the least square sense. The efficiency of the proposed control strategy is illustrated by a single-link flexible joint robot.

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

Abstract: 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.

Robust Least Squares Approach for Tracking Control Synthesis of Unstructured Uncertain Bilinear Systems

Abstract: This paper investigates the problem of robust tracking control for unstructured uncertain bilinear system. The control objective is not simply to drive the state to zero but rather that output to track a non zero reference signal. Our work is performed in three steps. Firstly, we built the reference model by taking the linear part of the original system and applying pole placement approach. Secondly, we expanded the controlled uncertain bilinear system and the constructed reference model over block pulse functions basis. Then, we attain to an unstructured linear system of algebraic equations, depending on the parameters of the feedback regulator. Thus, the obtained problem is solved in the robust least square sense. Finally, sufficient conditions for the practical stability of the closed loop system are derived, where a domain of attraction is estimated. Simulation results are provided to demonstrate the merits of the proposed control approach.

Tracking control of nonlinear analytical systems using orthogonal functions

Abstract: This article focuses on the tracking control problem for nonlinear analytical systems. A polynomial state feedback controller is designed to guarantee that the system output tracks those of linear reference model. The parameters of the feedback regulator are derived by solving a linear algebraic problem in the least square sense. The efficiency of the proposed control strategy is illustrated by mass-spring-damper benchmark.

Optimization And Control Of Bilinear Systems Theory Algorithms And Applications

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Static output tracking control for non-linear polynomial time-delay systems via block-pulse functions

Abstract: In this paper, a new method is introduced to design static output tracking controllers for a class of non-linear polynomial time-delay systems. The proposed technique is based on the projection of the controlled system and the associated linear reference model that it should follow over a basis of block-pulse functions. The useful properties of these orthogonal functions such as operational matrices jointly used with the Kronecker tensor product may transform the non-linear delay differential equations into linear algebraic equations depending only on parameters of the feedback regulator. The least-squares method is then used for determination of the unknown parameters. Sufficient conditions for the practical stability of the closed-loop system are derived, and a domain of attraction is estimated. The implementation of the proposed method is illustrated on a double inverted pendulums benchmark as well as a two-degree-of- freedom mass-spring-damper system. The simulation results show the effectiven...

Decentralized Suboptimal State Feedback Integral Tracking Control Design for Coupled Linear Time-Varying Systems

Abstract: In this paper, a suboptimal state feedback integral decentralized tracking control synthesis for interconnected linear time-variant systems is proposed by using orthogonal polynomials. Particularly, the use of operational matrices allows, by expanding the subsystem input states and outputs over a shifted Legendre polynomial basis, the conversion of time-varying parameter differential state equations to a set of time-independent algebraic ones. Hence, optimal open-loop state and control input coefficients are forwardly determined. These data are used to formulate a least-square problem, allowing the synthesis of decentralized state feedback integral control gains. Closed-loop asymptotic stability LMI conditions are given. The proposed approach effectiveness is proved by solving a nonconstant reference tracking problem for coupled inverted pendulums.

Hybrid Functions Direct Approach and State Feedback Optimal Solutions for a Class of Nonlinear Polynomial Time Delay Systems

Abstract: The aim of this paper is to determine the optimal open loop solution and a nonlinear delay-dependent state feedback suboptimal control for a class of nonlinear polynomial time delay systems. The proposed method uses a hybrid of block pulse functions and Legendre polynomials as an orthogonal base for system’s states and input expansion. Hence, the complex dynamic optimization problem is then reduced, with the help of operational properties of the hybrid basis and Kronecker tensor product lemmas, to a nonlinear programming problem that could be solved with available NLP solvers. A practical nonlinear feedback controller gains are deduced with respect to a least square formalism based on the optimal open loop control results. Simulation results show efficiency of the proposed numerical optimal approach.

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

Abstract: 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 orthog...