Improved exponential observer design for one‐sided Lipschitz nonlinear systems

This paper investigates the exponential observer design problem for one‐sided Lipschitz nonlinear systems. A unified framework for designing both full‐order and reduced‐order exponential state observers is proposed. The developed design approach requires neither scaling of the one‐sided Lipschitz constant nor the additional quadratically inner‐bounded condition. It is shown that the synthesis conditions established include some known existing results as special cases and can reduce the intrinsic conservatism. For design purposes, we also formulate the observer synthesis conditions in a tractable LMI form or a Riccati‐type inequality with equality constraints. Simulation results on a numerical example are given to illustrate the advantages and effectiveness of the proposed design scheme. Copyright © 2016 John Wiley & Sons, Ltd.     

Separation principle for quasi‐one‐sided Lipschitz nonlinear systems with time delay

In this article, we address the problem of output stabilization for a class of nonlinear time‐delay systems. First, an observer is designed for estimating the state of nonlinear time‐delay systems by means of quasi‐one‐sided Lipschitz condition, which is less conservative than the one‐sided Lipschitz condition. Then, a state feedback controller is designed to stabilize the nonlinear systems in terms of weak quasi‐one‐sided Lipschitz condition. Furthermore, it is shown that the separation principle holds for stabilization of the systems based on the observer‐based controller. Under the quasi‐one‐sided Lipschitz condition, state observer and feedback controller can be designed separately even though the parameter (A,C) of nonlinear time‐delay systems is not detectable and parameter (A,B) is not stabilizable. Finally, a numerical example is provided to verify the efficiency of the main results.     

D‐type iterative learning control for one‐sided Lipschitz nonlinear systems

In this paper, the problem of iterative learning control for a class of nonlinear systems is studied. Here, the nonlinear functions satisfy the one‐sided Lipschitz and quadratically inner‐bounded conditions. For such nonlinear systems, open‐loop and closed‐loop D‐type learning algorithms are adopted, respectively, and furthermore, the convergence conditions of the D‐type learning algorithms are established. It is shown that both algorithms can ensure that the system output converges to the desired trajectory on the whole time interval. Finally, the validity of the presented D‐type learning algorithms is verified by a numerical example.     

Robust observer design for uncertain one‐sided Lipschitz systems with disturbances

In this paper, we study the robust observer design problem for a class of uncertain one‐sided Lipschitz systems with disturbances. Not only the system matrices but also the nonlinear functions are assumed to be uncertain. The nominal models of nonlinearities are assumed to satisfy both the one‐sided Lipschitz condition and the quadratically inner‐bounded condition. By utilizing a novel approach, our observer designs are robust against unknown nonlinear uncertainties and system and measurement noises. The new approach also relaxes some conservativeness in related existing results, ie, less conservative observer design conditions are obtained. Furthermore, the problem of designing reduced‐order observers is considered in case the output measurement is not subject to uncertainty and disturbance. Two examples are provided to show the efficiency and advantages of our results over existing works.     

H∞ control for uncertain one‐sided Lipschitz nonlinear systems in finite frequency domain

The current article discusses the H_∞ disturbance attenuation control design problem for one‐sided Lipschitz systems in finite frequency domain. Models containing norm‐bounded parameter uncertainties, disturbances, and input nonlinearities are considered. By contrast to existing full frequency methods, the H_∞ controller is computed depending on the frequency ranges of disturbances. The finite frequency disturbance attenuation index is initially defined. Thanks to Finsler's lemma, sufficient and less conservative analysis conditions are also derived for the closed‐loop system. Then, synthesis conditions in the low, middle, and high frequency ranges as well as the whole frequency range, are formulated in terms of linear matrix inequalities. At last, to prove the effectiveness and the superiority of the proposed approach, a physical example is used and a comparative study is done.     

Nonlinear observer design for one‐sided Lipschitz systems with time‐varying delay and uncertainties

This paper investigates the problem of state observer design for a class of nonlinear uncertain dynamical systems with interval time‐varying delay and the one‐sided Lipschitz condition. By constructing the novel Lyapunov–Krasovskii functional while utilizing the free‐weighting matrices approach, the one‐sided Lipschitz condition and the quadratic inner‐bounded condition, novel sufficient conditions, which guarantee the observer error converge asymptotically to zero, are established for a class of nonlinear dynamical systems with interval time‐varying delay in terms of the linear matrix inequalities. The computing method for observer gain matrix is given. Finally, two examples illustrate the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

Nonlinear H∞ observer design for one‐sided Lipschitz discrete‐time singular systems with time‐varying delay

This paper investigates the H_∞ observer design problem for a class of nonlinear discrete‐time singular systems with time‐varying delays and disturbance inputs. The nonlinear systems can be rectangular and the nonlinearities satisfy the one‐sided Lipschitz condition and quadratically inner‐bounded condition, which are more general than the traditional Lipschitz condition. By appropriately dealing with these two conditions and applying several important inequalities, a linear matrix inequality–based approach for the nonlinear observer design is proposed. The resulting nonlinear H_∞ observer guarantees asymptotic stability of the estimation error dynamics with a prescribed performance γ. The synthesis condition of H_∞ observer design for nonlinear discrete‐time singular systems without time delays is also presented. The design is first addressed for one‐sided Lipschitz discrete‐time singular systems. Finally, two numerical examples are given to show the effectiveness of the present approach.     

Fault tolerant control using virtual actuator for continuous‐time Lipschitz nonlinear systems

In this brief, we extend the existing results on fault tolerant control via virtual actuator approach to a class of systems with Lipschitz nonlinearities to maintain the closed‐loop stability after actuator faults. This generalization is established by relying on the input‐to‐state stability properties of cascaded systems. The virtual actuator block, placed between faulty plant and nominal controller, generates useful input signals for faulty plant by using output signals of the nominal controller to guarantee the closed‐loop stability in the presence of actuator faults. This design problem is reduced to a matrix inequality that can be turned to an LMI by fixing a variable to a constant value and solving the resulting LMI feasibility problem. The proposed fault tolerant control method is successfully evaluated using a nonlinear system. Copyright © 2013 John Wiley & Sons, Ltd.     

Robust H∞ sliding mode observer‐based fault‐tolerant control for One‐sided Lipschitz nonlinear systems

This paper presents fault tolerant controllers for a class of one‐sided Lipschitz nonlinear systems with external disturbances. A sliding mode observer (SMO) is integrated with the H_∞ filtering approach as the fault detection and isolation module. The problem is investigated in the presence of faults and disturbances simultaneously. The H_∞ ‐SMO is capable of approximating faults accurately, while reducing the effect of disturbances in the estimation of the state vector and occurred faults. Accordingly, using only a single SMO, the estimation error of the state vector and faults can be made simultaneously arbitrarily small. In addition, to deal with the weighted bilinear form appearing in the one‐sided Lipschitz condition, the quadratically inner bounded condition presented in the literature is employed in this paper as a useful solution. The proposed method guarantees the stability of the overall closed‐loop system, and after a short transient time, the estimation errors for state vector and fault signal converge to a small neighborhood of the origin. The effectiveness of the presented algorithm is confirmed in two examples including a single arm robot with a flexible joint and a numerical simulation.     

Adaptive fuzzy fault-tolerant output feedback control of uncertain nonlinear systems with actuator faults

This article develops an adaptive fuzzy control method for accommodating actuator faults in a class of unknown nonlinear systems with unmeasured states. The considered faults are modelled as both loss of effectiveness and lock-in-place (stuck at unknown place). With the help of fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy adaptive observer is developed for estimating the unmeasured states. Combining the backstepping technique with the nonlinear tolerant-fault control theory, a novel adaptive fuzzy faults-tolerant control approach is constructed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are bounded and the tracking error between the system output and the reference signal converges to a small neighbourhood of zero by appropriate choice of the design parameters. Simulation results are provided to show the effectiveness of the control approach.