E.K. Boukas

Shandong Jianzhu (Architecture and Engineering) University, Chi-nan-shih, Shandong Sheng, China

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Publications (209)170.17 Total impact

  • M. D. S. Aliyu, E. K. Boukas
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    ABSTRACT: In Section 5 of Aliyu and Boukas (Int. J. Robust Nonlinear Control 2009; 19:394–417), the authors have presented certainty-equivalent filters for the mixed ℋ2/ℋ∞ filtering problem for affine nonlinear systems. Sufficient conditions for the solvability of the problem with a finite-dimensional filter are given in terms of a pair of coupled Hamilton–Jacobi–Isaacs equations (HJIEs). In this note, we supply a correction to these HJIEs. Moreover, for linear systems this correction is not necessary. Copyright © 2011 John Wiley & Sons, Ltd.
    International Journal of Robust and Nonlinear Control 06/2012; 22(9). · 1.90 Impact Factor
  • M.D.S. Aliyu, E.K. Boukas
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    ABSTRACT: In this study, the authors consider the H<sub>2</sub> (or Kalman)-filtering problem for singularly perturbed (two-timescale) non-linear systems. Two types of filters, namely (i) decomposition and (ii) aggregate, are discussed, and sufficient conditions for the solvability of the problem in terms of Hamilton-Jacobi-Bellman equations (HJBEs) are presented. The results are also specialised to linear systems in which case the HJBEs reduce to a system of bilinear-matrix-inequalities.
    IET Control Theory and Applications 12/2011; · 1.72 Impact Factor
  • M.D.S. Aliyu, E.K. Boukas
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    ABSTRACT: In this article, we introduce, formulate and solve the W 1,2 and W 1,∞ estimation problems. We propose proportional, proportional-derivative and proportional-integral (PI) filters for each problem, and we derive sufficient conditions for the existence of optimal filter gains in terms of new Hamilton–Jacobi–Bellman and Hamilton–Jacobi–Isaacs equations. The output-feedback W 1,2 and W 1,∞ control problems are also re-solved using the separation principle. We show that, by combining an optimal estimator with state-feedback control, a viable optimal output-feedback controller can be synthesised.
    International Journal of Systems Science 05/2011; 42(5):907-920. · 1.31 Impact Factor
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    ABSTRACT: In this technical note, constructive control techniques have been proposed for controlling feedforward nonlinear time-delay systems. The nonlinear terms admit an incremental rate depending on the input or delayed input. Based on the Lyapunov-Razumikhin theorem and Lyapunov-Krasovskii theorem, the delay-independent feedback controllers are explicitly constructed such that the closed-loop systems are globally asymptotically stable. An example is given to demonstrate the effectiveness of the proposed design procedure.
    IEEE Transactions on Automatic Control 04/2011; · 2.72 Impact Factor
  • M. D. S. Aliyu, E. K. Boukas
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    ABSTRACT: In this paper, we consider the (or Kalman)-fil- tering problem for discrete-time singularly-perturbed (two time-scale) nonlinear systems. Two types of filters, namely, i) decomposition and ii) aggregate, are discussed, and sufficient conditions for the solvability of the problem in terms of new discrete-time Hamilton-Jacobi-Bellman equations (DHJBEs) are presented. For each type of filter above, first-order approximate filters are derived, and reduced-order filters are also derived in each case. The results are also specialized to linear systems, in which case the DHJBEs reduce to a system of linear-matrix-in- equalities (LMIs) which are efficient to solve. Examples are also presented to illustrate the results. Index Terms—Discrete-time nonlinear filtering, -norm, dis- crete-time singularly perturbed nonlinear system, decomposition filters, aggregate filters, discrete-time Hamilton-Jacobi-Bellman equations.
    IEEE Transactions on Circuits and Systems I-regular Papers - IEEE TRANS CIRCUIT SYST-I. 01/2011; 58(8):1854-1864.
  • M. D. S. Aliyu, E. K. Boukas
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    ABSTRACT: In this paper, we consider the Kalman (or H2\mathcal{H}_{2})-filtering problem for affine nonlinear descriptor systems. Two types of filters are discussed, namely, (i) singular; (ii) normal, and sufficient conditions for the solvability of the problem in terms of Hamilton–Jacobi–Bellman equations (HJBEs) are presented. The results are also specialized to linear systems in which case the HJBEs reduce to a system of linear-matrix-inequalities (LMIs). Examples are also presented to illustrate the results. KeywordsNonlinear filtering- H2\mathcal{H}_{2}-norm-Descriptor nonlinear system-Singular filter-Normal filter-Hamilton–Jacobi–Bellman equations
    Circuits Systems and Signal Processing 01/2011; 30(1):125-142. · 0.98 Impact Factor
  • M. D. S. Aliyu, E. K. Boukas
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    ABSTRACT: In this article, we introduce, formulate and solve the W1,2, W1,∞ nonlinear optimal control problems as extensions of H2, H∞ optimal control problems, respectively. As these spaces contain less smooth functions, a larger number of problems could be solved in this framework, and by a suitable choice of weighting functions, additional design objectives could be achieved using the present formulation. Moreover, any solution of the W1, p, p = 2, ∞ problem, is automatically a solution of the corresponding Hp-problem. Sufficient conditions for the solvability of the problems are given in terms of new Hamilton-Jacobi equations (HJEs). These new HJEs may also be easier to solve because of the additional degrees of freedom offered by the current norms. Both the state-feedback and output-feedback problems are discussed. The results are then specialised to linear systems, in which case the solutions are characterised in terms of new algebraic-Riccati equations.
    International Journal of Systems Science 01/2011; 42(5). · 1.31 Impact Factor
  • J. P. Kenne, A. Gharbi, E.K. Boukas
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    ABSTRACT: This paper deals with the production planning problem of a flexible manufacturing system (FMS). This problem is within the class of problems which are usually faced during the life cycle of FMS. There are basically two approaches used to solve this problem: analytical and simulation. The objective of this paper is to develop a methodology for determine the control policy for a given FMS by using the combination of both analytical and simulation approaches. The production rate control of a one-machine one-product system is presented to illustrate our approach. The contribution of the analytical part of the proposed model consists of generating a near-optimal controller based on the concept of an age-dependent hedging point policy. This sub-optimal policy is used as input of the simulation part and the improvement of operating conditions (control policies) achieved with a constant demand rate. The proposed model includes also a stochastic demand and lot sizes in production which consists of similar products batches with bulk arrivals. The robustness of the controller against both demand rates and production types has been validated.
    International Journal of Production Research 11/2010; 35(5):1431-1445. · 1.46 Impact Factor
  • E. K. Boukas, P. Shi, K. Benjelloun
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    ABSTRACT: In this paper, we study the problem of robust stabilizability of the class of uncertain linear systems with Markovian jumping parameters. Under the assumption of complete access to the continuous state, the stochastic stabilizability of the nominal system and the boundedness of the system's uncertainties, sufficient conditions which guarantee the robust stability of the uncertain systems are presented, which are in terms of a set of coupled algebraic Riccati equations. A numerical example is given to illustrate the potential of the proposed technique.
    International Journal of Control 11/2010; 72(9):842-850. · 1.01 Impact Factor
  • Source
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    ABSTRACT: This paper deals with the state feedback controller design for a class of high-order feedforward (upper-triangular) nonlinear systems with delayed inputs. The uncertainties in the systems are assumed to be dominated by higher-order nonlinearities multiplying by a constant growth rate. The designed controller, which is a continuous but not smooth feedback, could achieve global asymptotical stability. Based on the appropriate state transformation of time-delay systems, the problem of controller design can be converted into the problem of finding a parameter, which can be obtained by appraising the nonlinear terms of the systems. The nonlinear systems considered here are more general than conventional feedforward systems and they could be viewed as generalized feedforward systems. Two examples are given to show the effectiveness of the proposed design procedure. Copyright © 2009 John Wiley & Sons, Ltd.
    International Journal of Robust and Nonlinear Control 07/2010; 20(12):1395 - 1406. · 1.90 Impact Factor
  • M. D. S. Aliyu, E. K. Boukas
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    ABSTRACT: In this paper, we consider the ∞-filtering problem for singularly perturbed (two time-scale) nonlinear systems. Two types of filters are discussed, namely, (i) decomposition and (ii) aggregate, and sufficient conditions for the solvability of the problem in terms of Hamilton–Jacobi–Isaac's equations (HJIEs) are presented. Reduced-order filters are also derived in each case, and the results are specialized to linear systems, in which case the HJIEs reduce to a system of linear-matrix-inequalities (LMIs). Based on the linearization of the nonlinear models, upper bounds ε* of the singular parameter ε that guarantee the asymptotic stability of the nonlinear filters can also be obtained. The mixed 2/∞-filtering problem is also discussed. Copyright © 2010 John Wiley & Sons, Ltd.
    International Journal of Robust and Nonlinear Control 05/2010; 21(2):218 - 236. · 1.90 Impact Factor
  • M.D.S. Aliyu, E.-K. Boukas, Y. Chinniah
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    ABSTRACT: In this technical note, exact and approximate solutions of the discrete-time suboptimal proportional-integral- H <sub>∞</sub>-estimation problem for affine nonlinear systems using finite-dimensional estimators (filters) are presented. Sufficient conditions for the solvability of the problem are given in terms of discrete-time Hamilton-Jacobi-Isaac's equations. For linear systems, it is shown that, these equations reduce to a system of linear-matrix inequalities. Simulation results are also presented to show the benefit of the new approach.
    IEEE Transactions on Automatic Control 04/2010; · 2.72 Impact Factor
  • Source
    Shuping Ma, E.-K. Boukas
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    ABSTRACT: The stability and stabilization problems for discrete-time piecewise affine singular systems are discussed. A basic linear matrix inequality (LMI) sufficient condition for the systems to be regular, causal and stable is given. With this condition and some inequalities, a LMI stability condition that makes easier the design of the state feedback controller is proposed, and then the state feedback stabilization problem is solved in terms of LMIs. Finally, a numerical example to illustrate the effectiveness of the method is given.
    Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on; 01/2010
  • M. D. S. Aliyu, E. K. Boukas
    [Show abstract] [Hide abstract]
    ABSTRACT: In this paper, we consider the discrete-time mixed ℋ2/ℋ∞ filtering problem for affine nonlinear systems. Necessary and sufficient conditions for the solvability of this problem with a finite-dimensional filter are given in terms of a pair of coupled discrete-time Hamilton–Jacobi-Isaac's equations (DHJIE) with some side-conditions. For linear systems, it is shown that these conditions reduce to a pair of coupled discrete-time algebraic-Riccati-equations (DAREs) or a system of linear matrix inequalities (LMIs) similar to the ones for the control case. Both the finite-horizon and infinite-horizon problems are discussed. Moreover, sufficient conditions for approximate solvability of the problem are also derived. These solutions are especially useful for computational purposes, considering the difficulty of solving the coupled DHJIEs. An example is also presented to demonstrate the approach. Copyright © 2010 John Wiley & Sons, Ltd.
    International Journal of Robust and Nonlinear Control 01/2010; · 1.90 Impact Factor
  • M. D. S. Aliyu, E. K. Boukas
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    ABSTRACT: In this paper, a new theory of two-degrees-of-freedom (2-DOF)-∞ and certainty-equivalent filters is presented. Exact and approximate solutions to the nonlinear ∞ filtering problem using this class of filters are derived in terms of discrete-time Hamilton–Jacobi–Isaacs equations. The expressions for the filter gains are determined as functions of the filter state and the system's output in contrast to earlier results. Hence, it is shown that coupled with the additional degree-of-freedom, these filters are a substantial improvement over the earlier 1-DOF case. The theory presented is also generalized to n-DOF filters, which bore strong connections to linear infinite-impulse response filters and hence are generalizations of this class of filters to the nonlinear setting. Simulation results are also given to show the usefulness of the new approach. Copyright © 2009 John Wiley & Sons, Ltd.
    International Journal of Robust and Nonlinear Control 01/2010; 20(7):818-833. · 1.90 Impact Factor
  • Source
    Xianfu Zhang, E.K. Boukas, L. Baron
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    ABSTRACT: This paper deals with the asymptotical stability problem for a class of feedforward nonlinear systems with delays in the state and input. The uncertainties in the systems are assumed to be dominated by upper polynomial functions multiplying by an incremental rate depending on the input or delayed input. Based on the state transformation of nonlinear systems and the Lyapunov method, both linear state feedback and linear output feedback controllers with dynamic low gains are provided. The theoretical results are illustrated with an academic example.
    Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on; 12/2009
  • Source
    S. Ma, E.K. Boukas
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    ABSTRACT: The stochastic stability and robust stochastic stabilisation for time-delay discrete Markovian jump singular systems with parameter uncertainties are discussed. Based on stochastic Lyapunov functional, a delay-dependent linear matrix inequalities (LMIs) condition for the time-delay discrete Markovian jump singular systems to be regular, causal and stochastically stable is given. With this condition, the problem of robust stochastic stabilisation is solved. A numerical example to illustrate the effectiveness of the method is given.
    IET Control Theory and Applications 10/2009; · 1.72 Impact Factor
  • Source
    A. Haidar, E.K. Boukas, S. Xu, J. Lam
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    ABSTRACT: This study deals with the class of continuous-time singular linear systems with time-varying delays. The stability and stabilisation problems of this class of systems are addressed. Delay-range-dependent sufficient conditions such that the system is regular, impulse free and ¿-stable are developed in the linear matrix inequality (LMI) setting and an estimate of the convergence rate of such stable systems is also presented. An iterative LMI (ILMI) algorithm to compute a static output feedback controller gains is proposed. Some numerical examples are employed to show the usefulness of the proposed results.
    IET Control Theory and Applications 10/2009; · 1.72 Impact Factor
  • Shuping Ma, E.-K. Boukas
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    ABSTRACT: The robust sliding mode control for Markov jump systems with parameter uncertainties and an unknown nonlinear function is discussed. Based on a descriptor system approach and linear matrix inequality (LMI), a sufficient condition which guarantees the existence of linear switching surface and the stochastic stability of sliding mode dynamics is given. A sliding mode controller is designed such that the closed-loop system is convergent to the switching surface in finite time. A numerical example is given to show the effectiveness of the proposed method.
    Asian Control Conference, 2009. ASCC 2009. 7th; 09/2009
  • Xianfu Zhang, E. K. Boukas, Luc Baron
    7th Asian Control Conference, Hong Kong; 09/2009

Publication Stats

3k Citations
170.17 Total Impact Points

Institutions

  • 2009–2011
    • Shandong Jianzhu (Architecture and Engineering) University
      Chi-nan-shih, Shandong Sheng, China
  • 2009–2010
    • Shandong University
      Chi-nan-shih, Shandong Sheng, China
  • 1990–2010
    • Montreal Polytechnic
      • Département de génie mécanique
      Montréal, Quebec, Canada
    • HEC Paris
      Lutetia Parisorum, Île-de-France, France
  • 2008–2009
    • Harbin Institute of Technology
      Charbin, Heilongjiang Sheng, China
  • 2003–2008
    • Université de Montréal
      Montréal, Quebec, Canada
  • 1998–2002
    • King Fahd University of Petroleum and Minerals
      • Department of Systems Engineering
      Az̧ Z̧ahrān, Eastern Province, Saudi Arabia
    • University of São Paulo
      San Paulo, São Paulo, Brazil
  • 2001
    • University of Georgia
      • Department of Mathematics
      Athens, GA, United States
  • 1996–2001
    • Wayne State University
      • Department of Mathematics
      Detroit, Michigan, United States
  • 1998–1999
    • University of South Australia 
      • School of Information Technology and Mathematical Sciences
      Adelaide, South Australia, Australia
  • 1994
    • University of Kentucky
      • Department of Mathematics
      Lexington, Kentucky, United States