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1

An observer design for Takagi-Sugeno fuzzy bilinear control systems

Delmotte François, Hadj Taieb Nizar, Hammami Mohamed Ali, Meghnafi Houria

Archives of Control Sciences

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2023

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Vol. 33, No. 3

631--649

EN

In this paper, the observer design problem for a T-S fuzzy bilinear control system is investigated. First, an observer of Kalman type is designed to estimate the system states for the linear case. Then, some new sufficient conditions are derived to show the exponential convergence of the solutions of the error equation for fuzzy bilinear systems. Furthermore, we consider some uncertainties of the system that are bounded and satisfy a certain condition where an observer is designed. Moreover, an application to Van de Vusse system is given.

2

Ideal observability for bilinear discrete-time systems with and without delays in observation

Lhous M., Rachik M., Magri E. M.

Archives of Control Sciences

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2018

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Vol. 28, No. 4

601--616

EN

An ideal observability subspace expression is stated for bilinear abstract system with bounded operator in Hilbert spaces. The case of finite dimentional space is also treated. However, it’s noticed that the state ideal observability can never be fulfilled within an infinite dimensional phase space in the case of scalar output. The case of bilinear discrete-time system with delays in observation is also described. To illustrate this work some examples are presented.

3

A goal oriented approach to model identification of an industrial furnace system combining a priori knowledge and optimal estimation

Vinsonneau B., Martineau S., Goodall D. P., Burnham K. J.

Systems Science

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2007

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Vol. 33, no 4

103-110

EN

Prompted by the need to determine a unique tuning parameter, the paper proposes a conceptual model for a high temperature industrial furnace in which the notion of an unmeasurable "global temperature" plays a key role. The developed approach is designed to accommodate a priori knowledge of system nonlinearities, as well as the effects of an externally triggered burner firing cycle which gives rise to an oscillatory response present on the locally measured zone temperature. It is assumed that the variation in the global temperature is lower than that observed at the locally measured temperature at a point. The developed model is able to accommodate, and effectively separate, the effects of the combustion burner firing cycle and the underlying bilinear characteristic behaviour relating fuel combustion and temperature of each zone. It is assumed that these physical phenomena can be represented by a linear model, modelling the effects of the combustion burner firing cycle, cascaded with a bilinear model, where an intermediate variable is the global temperature. The result of employing a regularisation technique together with the cascade multiple model produces an optimal value for the tuning parameter of a four-term bilinear PID control system.

4

Using control theory to make cancer chemotherapy beneficial from phase dependence and resistant to drug resistance

Kimmel M., Świerniak A.

Archives of Control Sciences

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2004

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Vol. 14, no. 2

105-145

EN

Two major obstacles against successful chemotheraphy of cancer are (1) the cell-cycle-phase dependence of treatment, and (2) the emergence of resistance of cancer cells to cytotoxic agents. One way to understand and overcome these two problems is to apply optimal control theory to mathematical models of cell cycle dynamics. These models should include division og the cell cycle into subphase and/or the mechanisms of drug resistance. we review our relevant results in mathematical modelling and control of the cell cycle and the mechanisms of gene amplification, and estimation of parameters of the constructed models.

5

Separation Principle for Nonlinear Systems: a Bilinear Approach

Hammani M. A., Jerbi H.

International Journal of Applied Mathematics and Computer Science

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2001

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Vol. 11, no 2

481-492

EN

In this paper we investigate the local stabilizability of single-input nonlinear affine systems by means of an estimated state feedback law given by a bilinear observer. The associated bilinear approximating system is assumed to be observable for any input and stabilizable by a homogeneous feedback law of degree zero. Furthermore, we discuss the case of planar systems which admit bad inputs (i.e. the ones that make bilinear systems unobservable). A separation principle for such systems is given.

6

Optimal control for bilinear systems with delay on control

Eljai A., Karrakchou J., Rachik M., Lhous M.

Archives of Control Sciences

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2001

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Vol. 11, no. 1/2

23-55

EN

The quadratic optimal control for bilinear distributed systems with delays in the control is considered. A semigroup model which involves no explicit delays in control is introduced. In the case of continuous delay, the control operator is bounded and the classical results can be applied. The case of general delays can be considered as a distributed system with boundary control. With the aid of a family of approximating systems, it is shown that the optimal control is obtained as a limit of sequence which is solution of classical control problems.

7

Observer design for distributed-parameter dissipative bilinear systems

Bounit H., Hammouri H.

Applied Mathematics and Computer Science

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1998

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Vol. 8, no 2

381-402

EN

This paper deals with the problem of observer synthesis for a class of infinitedimensional dissipative bilinear systems working for a class of inputs. First, a simple observer (the estimation error converges strongly asymptotically to zero) for strongly persistent input signals is presented. Next, sufficient conditions are given which guarantee the existence of an exponential observer for skew-adjoint bilinear systems based on the time-varying differential Riccati (or Lyapunov) equations working for strongly regularly persistent inputs. These results are illustrated by means of partial-differential systems.