Nonlinear Parameter Perturbations Research Articles

Integral sliding mode control for offshore steel jacket platforms

This paper is concerned with robust integral sliding mode control for an offshore steel jacket platforms subject to nonlinear wave-induced force and parameter perturbations. A robust integral sliding mode controller is designed to stabilize the dynamic model of the offshore steel jacket platform. It is shown through simulation results that the robust integral sliding mode control scheme can reduce the internal oscillations of the offshore steel jacket platform dramatically; and the performance of the offshore steel jacket platform under the robust integral sliding mode control scheme is better than the ones under the nonlinear control scheme and the dynamic output feedback control scheme.

Application of the conditional nonlinear optimal perturbation method to the predictability study of the Kuroshio large meander

A reduced-gravity barotropic shallow-water model was used to simulate the Kuroshio path variations. The results show that the model was able to capture the essential features of these path variations. We used one simulation of the model as the reference state and investigated the effects of errors in model parameters on the prediction of the transition to the Kuroshio large meander (KLM) state using the conditional nonlinear optimal parameter perturbation (CNOP-P) method. Because of their relatively large uncertainties, three model parameters were considered: the interfacial friction coefficient, the wind-stress amplitude, and the lateral friction coefficient. We determined the CNOP-Ps optimized for each of these three parameters independently, and we optimized all three parameters simultaneously using the Spectral Projected Gradient 2 (SPG2) algorithm. Similarly, the impacts caused by errors in initial conditions were examined using the conditional nonlinear optimal initial perturbation (CNOP-I) method. Both the CNOP-I and CNOP-Ps can result in significant prediction errors of the KLM over a lead time of 240 days. But the prediction error caused by CNOP-I is greater than that caused by CNOP-P. The results of this study indicate not only that initial condition errors have greater effects on the prediction of the KLM than errors in model parameters but also that the latter cannot be ignored. Hence, to enhance the forecast skill of the KLM in this model, the initial conditions should first be improved, the model parameters should use the best possible estimates.

Improved results on robust stability of neutral systems with mixed time-varying delays and nonlinear perturbations

This paper considers the problem of robust stability of neutral systems with mixed time-varying delays and nonlinear perturbations. Two type uncertainties such as nonlinear time-varying parameter perturbations and norm-bounded uncertainties have been discussed. Based on the new Lyapunov–Krasovskii functional with triple integral terms, some integral inequalities and convex combination technique, a new delay-dependent stability criterion for the system is established in terms of linear matrix inequalities (LMIs). Finally, four numerical examples are given to illustrate the effectiveness and an improvement over some existing results in the literature with the proposed results.

Non-linear robust control of a voltage-controlled magnetic levitation system with a feedback linearization approach

The magnetic levitation system's control problem is of considerable scientific interest because the system is open-loop unstable and highly non-linear, and the system's parameters are uncertain. In this paper, the system is formulated by a third-order non-linear differential equation. Based on this third-order non-linear system, the system is first linearized by applying the feedback linearization method. Then, the controller is designed based on a global sliding mode technique, which is able to stabilize a linearized system. Experimental results show that, compared with the classic proportional—integral—derivative (PID) controller, the proposed controller provides excellent transient response performance and the system is robust against the non-linear parameter perturbation. Further experiments show that the sampling period is an important parameter to the system robustness. The reason is explained theoretically, and the analysis shows that in the practical global sliding mode control (GSMC) system the smaller the sampling period is, the more robust the controller will be.

Delay dependent stability analysis of neutral systems with mixed time-varying delays and nonlinear perturbations

This paper is concerned with the problem of stability of neutral systems with interval time-varying delays and nonlinear perturbations. The uncertainties under consideration are nonlinear time-varying parameter perturbations and norm-bounded uncertainties. A new delay-dependent stability condition is derived in terms of linear matrix inequality by constructing a new Lyapunov functional and using some integral inequalities without introducing any free-weighting matrices. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.

Robust delay-dependent guaranteed cost controller design for uncertain neutral systems

In this paper, a novel robust delay-dependent guaranteed cost controller is introduced for a class of uncertain nonlinear neutral systems with both norm-bounded uncertainties and nonlinear parameter perturbations. A neutral memory state-feedback control law is chosen such that a quadratic cost function is minimized. On the basis of a descriptor type model transformation, an augmented descriptor form Lyapunov–Krasovskii functional is proposed in order to derive a linear matrix inequality (LMI) condition of the synthesis of a robust stabilizing guaranteed cost controller for uncertain nonlinear neutral systems. The descriptor approach is applied for both the delay-differential equation and the neutral difference operator allowing to introduce several additional free weighting matrices in order to obtain further relaxation in the synthesis process. The proposed method of introducing some relaxation into design problem also leads to develop LMI conditions which can be easily solved using interior point algorithms. Two numerical examples have been introduced to show the application of the theoretical results which indicate that the proposed approach improves the guaranteed cost performance.

Robust delay‐dependent guaranteed cost controller design for uncertain nonlinear neutral systems with time‐varying state delays

AbstractIn this paper, the problem of robust delay‐dependent guaranteed cost control for uncertain nonlinear neutral systems with time‐varying state delay is investigated. The control law is chosen to be a memoryless type one. Neither any model transformation nor bounding of any cross terms are utilized. The system under consideration may be subjected to both norm‐bounded uncertainties and nonlinear parameter perturbations. A delay‐dependent sufficient condition is obtained in terms of a matrix inequality for which a cone complementarity problem is introduced to provide a feasible solution set. Two numerical examples have been demonstrated to show the effective application of the proposed method. Copyright © 2009 John Wiley & Sons, Ltd.

Further results on robust stability of neutral system with mixed time-varying delays and nonlinear perturbations

This paper studies delay-dependent robust stability problem for neutral system with mixed time-varying delays. The uncertainties under consideration are nonlinear time-varying parameter perturbations and norm-bounded uncertainties, respectively. Based on Lyapunov functional approach and linear matrix inequality technology, some improved delay-dependent stability conditions are derived by introducing free-weighting matrices. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.

New Delay‐Dependent Stability Criteria for Uncertain Neutral Systems with Mixed Time‐Varying Delays and Nonlinear Perturbations

The problem of stability analysis for a class of neutral systems with mixed time‐varying neutral, discrete and distributed delays and nonlinear parameter perturbations is addressed. By introducing a novel Lyapunov‐Krasovskii functional and combining the descriptor model transformation, the Leibniz‐Newton formula, some free‐weighting matrices, and a suitable change of variables, new sufficient conditions are established for the stability of the considered system, which are neutral‐delay‐dependent, discrete‐delay‐range‐dependent, and distributed‐delay‐dependent. The conditions are presented in terms of linear matrix inequalities (LMIs) and can be efficiently solved using convex programming techniques. Two numerical examples are given to illustrate the efficiency of the proposed method.

DESIGN OF ROBUST DELAY-DEPENDENT GUARANTEED COST CONTROLLER FOR UNCERTAIN NONLINEAR NEUTRAL SYSTEMS: AN LMI DESCRIPTOR APPROACH

Abstract In this paper, a novel robust delay-dependent guaranteed cost controller is introduced for a class of uncertain nonlinear neutral systems with both norm-bounded uncertainties and nonlinear parameter perturbations. A neutral memory state-feedback control law is chosen such that a quadratic cost function is minimized. On the basis of a descriptor type model transformation, an augmented descriptor form Lyapunov-Krasovskii functional is proposed. A linear matrix inequality (LMI) of synthesis condition is derived. Two numerical examples have been introduced to show the application of the theoretical results.

Delay‐Dependent Robust Stability Criteria For Uncertain Neutral Systems With Mixed Time‐Varying Discrete And Neutral Delays

ABSTRACTIn this paper, a new class of augmented quasi full size Lypunov‐Krasovskii functional is introduced for the robust stability of uncertain neutral systems with mixed time‐varying discrete and neutral delays. The nonlinear parameter perturbations and norm‐bounded uncertainties are taken into consideration separately. Delay‐dependent robust stability criteria are derived in the form of linear matrix inequalities. Numerical examples are presented to illustrate the significant improvement on the conservativeness of the delay bound over some reported results in the literature.

Delay-dependent Robust Stability of Neutral Systems with Mixed Delays and Nonlinear Perturbations

Abstract This paper concerns the delay-dependent robust stability problem of uncertain neutral systems with mixed neutral and discrete delays. Nonlinear time-varying parameter perturbations are considered. Based on the newly established integral inequalities, the neutral-delay-dependent and discrete-delay-dependent stability criterion is derived without using a fixed model transformation. The condition is presented in terms of linear matrix inequality and can be easily solved by existing convex optimization techniques. A numerical example is given to demonstrate the less conservatism of the proposed results.

Delay-dependent guaranteed cost control for uncertain neutral systems with nonlinear parameter perturbations

The delay-dependent guaranteed cost control problem for uncertain neutral systems with nonlinear time-varying parameter perturbations is studied. By using a newly established integral inequality, the delay-dependent conditions for the existence of memoryless and memory state feedback guaranteed cost controllers are derived in terms of nonlinear matrix inequalities without involving model transformation and bounding technique for cross terms. An iterative algorithm involving convex optimisation is presented to solve these nonlinear matrix inequalities. A numerical example is given to demonstrate the effectiveness and superiority of the proposed results.

DELAY-DEPENDENT ROBUST STABILITY OF UNCERTAIN NEUTRAL SYSTEMS: QUASI FULL SIZE LYAPUNOV FUNCTIONAL APPROACH

In this paper a new class of augmented quasi full size Lypunov-Krasovskii functional is introduced for the robust stability of linear uncertain neutral systems. The nonlinear parameter perturbations and norm bounded uncertainties are taken into consideration separately. Delay-dependent robust stability criteria are derived in the form of linear matrix inequalities. Numerical examples are presented to illustrate the significant improvement on the conservativeness of the delay bound over some reported results in the literature.

Improved results for neutral systems with nonlinear perturbations

In this paper, a simple robust stability problem for uncertain neutral systems is considered. The uncertainty under consideration is nonlinear parameter perturbations and does not require a matching condition. Based on the constructive use of the Lyapunov functional approach and linear matrix inequality (LMI) technique, a new delay‐dependent criterion is proposed to guarantee robust stability for such systems. Finally, less conservative than previous results are illustrated by the five examples.

Robust stability of linear neutral systems with nonlinear parameter perturbations

The robust stability of uncertain linear neutral systems with time-varying discrete and neutral delays is investigated. The uncertainties under consideration are nonlinear time-varying parameter perturbations and norm-bounded uncertainties, respectively. Both delay-dependent and delay-derivative-dependent stability criteria are proposed and are formulated in the form of linear matrix inequalities (LMIs). The results in this paper contain some existing results as their special cases. A numerical example is also given to indicate significant improvements over some existing results.

Robust stability of predictor-based control systems with delayed control

This article deals with the delay-dependent robust stability of predictor-based control systems with a delayed control and non-linear parameter perturbations. The uncertainty terms do not require the matching condition but are norm-bounded. The predictor-based controller includes a predictor to compensate for time delay. The problem treated here is to determine an allowable delay bound to ensure the robust stability of the delayed control systems under the predictor-based control. A delay bound for memoryless state feedback control systems is also derived for comparisons of their delay bounds. It is shown that the predictor-based control can maximize the allowable delay bound to a greater degree than the memoryless state feedback via an illustrative example.

Sliding mode control with uncertainty adaptation for uncertain input-delay systems

This paper deals with a sliding mode control with uncertainty adaptation for the robust stabilization of uncertain input delay systems. The types of uncertainties comprise unknown time-varying non-linear parameter perturbations and external disturbance. A sliding surface including a state predictor is employed to compensate for the input delay. The proposed method does not need a priori knowledge of upper bounds on the norm of the uncertainties, but estimates them by using the adaptation scheme based on the sliding surface. Then, a robust control law with uncertainty adaptation is derived to ensure the existence of the sliding mode.

Robust stabilization of uncertain input-delay systems by sliding mode control with delay compensation

In this paper, a sliding mode control is proposed for the robust stabilization of uncertain linear input-delay systems with nonlinear parametric perturbations. The proposed sliding surface includes a predictor to compensate for the input delay of the system. A robust control law is derived to ensure the existence of a sliding mode and to overcome the effects of the delay and uncertainty in the sliding mode. A numerical example is given to illustrate the design procedure and results of the proposed approach.

Function observer-based robust stabilization for delay systems with parameter perturbations

This paper is concerned with the function observer-based stabilization for time-varying delay systems with parameter perturbations. Both nonlinear parameter perturbations and linear structured/unstructured perturbations are discussed respectively. By making use of the linear matrix inequality (LMI) approach, the function observer and the observer state feedback control laws that guarantee to stabilize the mentioned systems are developed. The main feature of the present schemes is that it does not involve any matching conditions. Besides, we propose a parametric approach for function observer-based stabilization design.