Nonlinear state feedback design for continuous polynomial systems

Jemai, Wiem Jebri; Jerbi, Houssem; Abdelkrim, Mohamed Naceur

doi:10.1007/s12555-011-0317-x

Cited by 14 publications

(5 citation statements)

References 16 publications

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“…Singular models and time-delay phenomena are general enough to enable some fundamental results from the theory of state-space systems to be extended to this class of systems (see for instance [3,5,10,15,17,45]). On the other hand, the research on nonlinear systems [9] is an extremely hard issue due to their inherent complexity. Due to its rigorous mathematical structure, the T-S fuzzy model [14] has recently been applied to handle nonlinear complex systems, since this model has been known for its powerful approximation of smoothly nonlinear systems.…”

Section: Literature Reviewmentioning

confidence: 99%

Observer-based feedback control of interval-valued fuzzy singular system with time-varying delay and stochastic faults

Jerbi

Kchaou

Alshammari

et al. 2022

INT J COMPUT COMMUN, Int. J. Comput. Commun. Control

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There are countless applications of non-linear systems that incorporate delay and algebraic equations. Despite current improvements in control theory, stochastic actuator defects still pose challenges when it comes to these systems. Furthermore, when it is not possible to measure the states of the system, and when uncertainties affect the system under investigation, the problem becomes even more complex. This paper is concerned with fault-tolerant observer-based controller synthesis for non-linear delayed singular systems with uncertainties and stochastic actuator failures. On the basis of interval valued models, a new Lyapunov-Krasovskii functional is built to develop a less conservative criterion to ensure that the closed-loop system is admissible in the mean-square sense. In addition, as these matrices are coupled with multiple variables, finding the parametric matrices of the observer and controller in terms of the obtained condition is more complex and challenging. The proposed method employs the matrix inequality decoupling technique to resolve this issue. Eventually, simulations are carried out to demonstrate the applicability of the proposed method.

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Section: Literature Reviewmentioning

confidence: 99%

Observer-based feedback control of interval-valued fuzzy singular system with time-varying delay and stochastic faults

Jerbi

Kchaou

Alshammari

et al. 2022

INT J COMPUT COMMUN, Int. J. Comput. Commun. Control

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“…where u servo is the control signal to design to track the desired trajectory, u fz is the compensation signal executed by the fuzzy logic controller, and κ is the robustification signal with design constant ρ = ρ 1 ρ 2 T ∈ R 2 . β(χ) is invertible knowing that the system is feedback-linearizable as described in [33] and [35].…”

Section: Adaptive Fuzzy-based Gain Scheduling Control Designmentioning

confidence: 99%

“…A linear control design is devised in these areas and further explored by using the same system structure interpolation. Nevertheless, instead of interpolating controllable linear systems, through [8] (but not limited to the precise feedback form), the study is concentrated on utilizing fuzzy PID feedback controllers as the ''parts'' to form the ''universal'' nonlinear system through interpolation [33].…”

Section: Introductionmentioning

confidence: 99%

An Advanced PID Based Control Technique With Adaptive Parameter Scheduling for A Nonlinear CSTR Plant

2019

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The continuous stirred tank reactor (CSTR) tends to reveal unstable severe nonlinear behavior when the operating level changes. As investigated in an earlier work, the hard nonlinearity nature of the CSTR originates from multiple probable sets of states for the same reaction in the same CSTR under identical ongoing inlet conditions. The previous work concluded, and this paper will discuss, that nonlinear processes with dynamic trajectories will involve a degrading control performance whenever the measured process variable evolves away from the designed level of the desired output trajectory. In this work, this problem will be examined for temperature tracking control on a CSTR with an adaptive fuzzy gain-scheduling proportional-integral-derivative (AFGS-PID) controller scheduled for a dynamic output trajectory. It will be proven that the AFGS-PID has better tracking performance than the fuzzy gain scheduling (FGS-PID) and conventional PID. Although all three controllers demonstrate the same level of control efforts, AFGS-PID has the smallest IAE and ISE. The lowest settling time being exhibited by AFGS-PID also proves that the intended regulator can rapidly track the desired coolant jacket temperature. A Lyapunov analysis is presented to prove the stability of the closed-loop and support the simulated result in the comparative study.

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“…DA approximation is also performed using the non-Lyapunov trajectory inversion technique that relies on topological aspects. However, computational complexity is one challenge associated with this technique; this can be addressed by integrating the approach with Lyapunov techniques [53,54]. Formulating reachable sets is a different approach sometimes used for evaluation of DA.…”

Section: Introductionmentioning

confidence: 99%

A Chaotic Krill Herd Optimization Algorithm for Global Numerical Estimation of the Attraction Domain for Nonlinear Systems

et al. 2021

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Nowadays, solving constrained engineering problems related to optimization approaches is an attractive research topic. The chaotic krill herd approach is considered as one of most advanced optimization techniques. An advanced hybrid technique is exploited in this paper to solve the challenging problem of estimating the largest domain of attraction for nonlinear systems. Indeed, an intelligent methodology for the estimation of the largest stable equilibrium domain of attraction established on quadratic Lyapunov functions is developed. The designed technique aims at computing and characterizing a largest level set of a Lyapunov function that is included in a particular region, satisfying some hard and delicate algebraic constraints. The formulated optimization problem searches to solve a tangency constraint between the LF derivative sign and constraints on the level sets. Such formulation avoids possible dummy solutions for the nonlinear optimization solver. The analytical development of the solution exploits the Chebyshev chaotic map function that ensures high search space capabilities. The accuracy and efficiency of the chaotic krill herd technique has been evaluated by benchmark models of nonlinear systems. The optimization solution shows that the chaotic krill herd approach is effective in determining the largest estimate of the attraction domain. Moreover, since global optimality is needed for proper estimation, a bound type meta-heuristic optimization solver is implemented. In contrast to existing strategies, the synthesized technique can be exploited for both rational and polynomial Lyapunov functions. Moreover, it permits the exploitation of a chaotic operative optimization algorithm which guarantees converging to an expanded domain of attraction in an essentially restricted running time. The synthesized methodology is discussed, with several examples to illustrate the advantageous aspects of the designed approach.

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Nonlinear state feedback design for continuous polynomial systems

Cited by 14 publications

References 16 publications

Observer-based feedback control of interval-valued fuzzy singular system with time-varying delay and stochastic faults

Observer-based feedback control of interval-valued fuzzy singular system with time-varying delay and stochastic faults

An Advanced PID Based Control Technique With Adaptive Parameter Scheduling for A Nonlinear CSTR Plant

A Chaotic Krill Herd Optimization Algorithm for Global Numerical Estimation of the Attraction Domain for Nonlinear Systems

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