Search

Many real-world dynamics can be modeled as nonlinear time-delay systems. In order to capture a more realistic model for system dynamics, the exact values of time-delay should be taken into account. For nonlinear time-delay systems, the estimation of delays in both state and output equations is discussed. A cost function is defined based on least-square error between actual and estimated values of the output measurement. The value of time-delays in the nonlinear system are then derived using a gradient-based optimization method. Because of the implicit description of the cost function with respect to the delay value, its gradients cannot be obtained by standard analytical differentiation rules. In this case, the optimal computational methods are utilized to derive two formulas for computing the gradient. An optimization scheme is then formulated to estimate both state and output delays. The effectiveness of the proposed estimation method is finally demonstrated using the simulation results on a benchmark chemical process. [ABSTRACT FROM AUTHOR]

The stability problem of nonlinear time-delay systems is addressed. A quadratic constraint is employed to exploit the structure of nonlinearity in dynamical systems via a set of multiplier matrices. This yields less conservative results concerning stability analysis. By employing a Wirtinger-based inequality, a delay-dependent stability criterion is derived in terms of linear matrix inequalities for the nominal and uncertain systems. A numerical example is used to demonstrate the effectiveness of the proposed stability conditions in dealing with some larger class of nonlinearities. [ABSTRACT FROM AUTHOR]

An observer-based controller for Lipschitz nonlinear systems is presented. The necessary and sufficient condition to ensure stability of state-observer as well as nonlinear system with state-feedback control law is derived. According to the separation principle, the closed-loop stability is guaranteed based on dual problems concerning stability of state-observer and stability of state-feedback parts. Also, the stability region for locally Lipschitz nonlinearities is obtained. A practical synthesis approach to achieve controller parameters is then given which yields the closed-loop convergence with less conservative results. The effectiveness of the proposed synthesis method is finally demonstrated by simulation results. [ABSTRACT FROM AUTHOR]

The problem of designing an observer for nonlinear Lipschitz systems affected by system and sensor noises is addressed. Related to the system nonlinearity, the stability of observer dynamic with static and dynamic gain is considered. The advantage of using dynamic gain to deal with large Lipschitz nonlinearity is discussed and it is proved that no dynamic gain can stabilise the observer for a larger Lipschitz constant as compared with the static gain. However, a nonlinear observer with dynamic gain has some additional degrees of freedom which can be utilised to attenuate noise effect on the observer behaviour. Using mixedandcriteria, this article introduces a method to obtain a dynamic gain which can deal with system nonlinearity and noise simultaneously. The effectiveness of the proposed method is finally demonstrated by some simulation results. [ABSTRACT FROM AUTHOR]

The problem of designing Luenberger-like observer for non-linear Lipschitz systems is addressed. Based on using the coordinate transformation, the author classify many practical approaches of observer synthesis into direct and indirect methods. A generalised Lipschitz condition and the related stability condition are then employed to establish a general framework in designing the Luenberger-like observer dealing with both methods. Moreover, the proposed framework is interpreted in terms of some linear matrix inequalities (LMIs) which allows using numerical techniques to obtain a reduced order observer. Finally, some simulation examples are given to exhibit the effectiveness of the proposed observer synthesis approach. [ABSTRACT FROM AUTHOR]

The problem of designing Luenberger‐like observer for non‐linear Lipschitz systems is addressed. Based on using the coordinate transformation, the author classify many practical approaches of observer synthesis into direct and indirect methods. A generalised Lipschitz condition and the related stability condition are then employed to establish a general framework in designing the Luenberger‐like observer dealing with both methods. Moreover, the proposed framework is interpreted in terms of some linear matrix inequalities (LMIs) which allows using numerical techniques to obtain a reduced order observer. Finally, some simulation examples are given to exhibit the effectiveness of the proposed observer synthesis approach. [ABSTRACT FROM AUTHOR]

In this study, stabilisation of input‐delay non‐linear systems in the presence of disturbance based on prediction variable is studied. For both disturbance estimation and delay compensation, an extended prediction variable as well as adaptive sliding mode controller are proposed in which the open‐loop system is not required to be stable. In the proposed prediction variable one needs to estimate disturbance in the future. In order to solve this problem a new non‐linear disturbance observer (NDOB) is proposed. Considering the NDOB in the closed‐loop system, the stability analysis of error dynamic is performed. And the asymptotic stability of non‐linear system with input delay is guaranteed for some class of disturbance. Simulation results finally validate the good performance and robustness of the proposed controller based on disturbance observer. [ABSTRACT FROM AUTHOR]

The mechanical impedance of the human arm can be measured to quantitatively assess the motor function. In this paper, an adaptive least square estimation method is proposed for online measurement of the mechanical impedance of the arm, without force or acceleration sensors, which extremely reduces the expenses and complexity of rehabilitation robots. The proposed strategy may also be used for monitoring the dynamic changes of the mechanical impedance. Estimation of time-varying force is also the other capability of the algorithm. The closed-loop stability of the system is analytically shown using the Lyapunov stability theorem. To show the applications of the proposed scheme, two main scenarios are described which can be used for the rehabilitation robots to assess the motor recovery of the patients undergoing the rehabilitation sessions. To validate the scheme, a 2-DOF manipulator is adopted to illustrate the accuracy of the impedance and force estimations in noiseless and noisy conditions. [ABSTRACT FROM AUTHOR]

This paper proposes a cascade high-gain observer for a class of triangular nonlinear systems with large and diverse time delays at states and output equation. Compared with some existing results in the literature, the main contribution is to consider the simultaneous and diverse delays in both states and output and further, to propose a cascade observer in dealing with arbitrarily large delayed measurements. By choosing a suitable Lyapunov-Krasovskii functional, the sufficient condition is presented that guarantees the exponential convergence of observation error to the origin. Simulation results on a numerical example and a practical case study involving inverted pendulum are finally given to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

A new method is proposed in this article in order to determine a guaranteed interval of time delay in input signal for a class of non-linear control systems with state feedback. This method is based on the stability sufficient condition of a non-linear control system using the Lyapunov direct approach. For this purpose, the dynamic equations of the non-linear input-delayed system are reformulated as a non-linear system without delay, but with delay-dependent coefficients in the state-space description. The control strategy is considered a linear state feedback. Then, by introducing an appropriately related Lyapunov candidate, the stability sufficient condition of the closed-loop system is satisfied, leading to a guaranteed interval of delay according to the state feedback gain. The main results are gathered and proved as a lemma. The effectiveness of this proposed method is investigated by simulating the state feedback control of a non-linear synchronous generator with a delay in input. [ABSTRACT FROM AUTHOR]

In this paper, a finite time control method for an uncertain nonlinear system is proposed. An adaptive sliding mode disturbance observer is designed to estimate the disturbance in finite time. The assumptions on the disturbance are relaxed in the sense that, its first derivative upper bound is considered to be unknown and only the order of its second derivative upper bound is known. Based on the output of proposed disturbance observer, a terminal sliding mode control scheme for the uncertain nonlinear system is presented. The designed control law is continuous and nonsingular. Furthermore, compared with some existing sliding mode controllers, the conditions on the controller parameters bounds are relaxed. It is proved that the disturbance observer error as well as the system states converges to the origin in finite time. Finally, the effectiveness of the proposed method is shown by numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, a novel observer-based force control scheme is proposed to guarantee the position and force tracking in nonlinear teleoperation systems, subject to constant communication time delay. Stability of the teleoperation system is analytically proved using the Lyapunov stability theorem. Enough condition for asymptotic convergence of the force and position are derived. The transparency is also improved by force tracking capability of the system. The teleoperation controller is then applied to a pair of planar 2-DOF robots, connected via a communication channel with constant time delay. The experimental and simulation results demonstrate the effectiveness of the proposed control algorithm, in force estimation and dealing with time delay. [ABSTRACT FROM AUTHOR]