This paper deals with the robust stabilization and passivity of general nonlinear systems with structural uncertainty. By using Lyapunov function, it verifies that under some conditions the robust passivity implies th...This paper deals with the robust stabilization and passivity of general nonlinear systems with structural uncertainty. By using Lyapunov function, it verifies that under some conditions the robust passivity implies the zero-state detectability, Furthermore, it also implies the robust stabilization for such nonlinear systems. We then establish a stabilization method for the nonlinear systems with structural uncertainty. The smooth state feedback law can be constructed with the solution of an equation. Finally, it is worth noting that the main contribution of the paper establishes the relation between robust passivity and feedback stabilization for the general nonlinear systems with structural uncertainty. The simulation shows the effectiveness of the method.展开更多
The local robust stabilization for a class of nonlinear uncertain systems is studied. The robustness concept of Lyapunov type stabilizability for nonlinear uncertain systems is defined. Under the norm bounded struct...The local robust stabilization for a class of nonlinear uncertain systems is studied. The robustness concept of Lyapunov type stabilizability for nonlinear uncertain systems is defined. Under the norm bounded structured condition, two cases for uncertainty in control matrix are taken to discuss Lyapunov type stabilizability of systems. The sufficient conditions of Lyapunov type stabilization are given from differential geometry and nonlinear H ∞ control of view, respectively.展开更多
In this paper, we study the robust fault detection problem of nonlinear systems. Based on the Lyapunov method, a robust fault detection approach for a general class of nonlinear systems is proposed. A nonlinear observ...In this paper, we study the robust fault detection problem of nonlinear systems. Based on the Lyapunov method, a robust fault detection approach for a general class of nonlinear systems is proposed. A nonlinear observer is first provided, and a sufficient condition is given to make the observer locally stable. Then, a practical algorithm is presented to facilitate the realization of the proposed observer for robust fault detection. Finally, a numerical example is provided to show the effectiveness of the proposed approach.展开更多
This paper studies the global robust stabilization problem for a class of feedforward systems that is subject to both dynamic and time-varying static uncertainties. A small gain theorem-based bottom-up recursive desig...This paper studies the global robust stabilization problem for a class of feedforward systems that is subject to both dynamic and time-varying static uncertainties. A small gain theorem-based bottom-up recursive design is developed for constructing a nested saturation control law. At each recursion, two versions of small gain theorem with restrictions are employed to establish the global attractiveness and local stability of the closed-loop system at the equilibrium point, respectively.展开更多
In this paper, Lyapunov function method is used to study the robust absolute stability of general interval Lur'e type nonlinear control systems. As a result, algebraically sufficient conditions with interval matri...In this paper, Lyapunov function method is used to study the robust absolute stability of general interval Lur'e type nonlinear control systems. As a result, algebraically sufficient conditions with interval matrix inequality form are obtained for the general interval Lur'e type nonlinear control systems, thus the relationship between the stability of symmetrical interval matrix and the robust absolute stability of general interval Lur'e type nonlinear control systems is established.展开更多
This paper investigates the problem of delay-dependent robust stability analysis for a class of neutral systems with interval time-varying delays and nonlinear perturbations. Such nonlinear perturbations are with time...This paper investigates the problem of delay-dependent robust stability analysis for a class of neutral systems with interval time-varying delays and nonlinear perturbations. Such nonlinear perturbations are with time-varying but norm-bounded characteristics. Based on a new Lyapunov-Krasovskii functional, together ,sith a free-weighting matrices technique, improved delay-dependent stability criteria are established. It is shown that less conservative results can be obtained in terms of linear matrix inequalities （LMIs）. Numerical examples are provided to demonstrate the effectiveness and less conservatism of the proposed approach.展开更多
The purpose of this paper is the design of neural network-based adaptive sliding mode controller for uncertain unknown nonlinear systems. A special architecture adaptive neural network, with hyperbolic tangent activat...The purpose of this paper is the design of neural network-based adaptive sliding mode controller for uncertain unknown nonlinear systems. A special architecture adaptive neural network, with hyperbolic tangent activation functions, is used to emulate the equivalent and switching control terms of the classic sliding mode control （SMC）. Lyapunov stability theory is used to guarantee a uniform ultimate boundedness property for the tracking error, as well as of all other signals in the closed loop. In addition to keeping the stability and robustness properties of the SMC, the neural network-based adaptive sliding mode controller exhibits perfect rejection of faults arising during the system operating. Simulation studies are used to illustrate and clarify the theoretical results.展开更多
This paper deals with the problem of the stabilization for multi-input polytopic nonlinear systems. Based on the robust control Lyapunov function, a sufficient condition for the existence of time-invariant, continuous...This paper deals with the problem of the stabilization for multi-input polytopic nonlinear systems. Based on the robust control Lyapunov function, a sufficient condition for the existence of time-invariant, continuous, asymptotically stabilizing state feedback controller is derived. It is shown that the obtained sufficient condition is also necessary if there exists a state feedback controller such that the closed-loop system has a robust Lyapunov function for all possible uncertainties. Moreover, a universal formula for constructing stabilizing controller is proposed and the existence of the corresponding Lyapunov function is proven. Particularly, a Lyapunov function is constructed for the polytopic nonlinear system in canonical form. Finally, the feasibility of the proposed control law is verified by a numerical example.展开更多
The relationship between the technique by state- dependent Riccati equations （SDRE） and Hamilton-Jacobi-lsaacs （HJI） equations for nonlinear H∞ control design is investigated. By establishing the Lyapunov matrix ...The relationship between the technique by state- dependent Riccati equations （SDRE） and Hamilton-Jacobi-lsaacs （HJI） equations for nonlinear H∞ control design is investigated. By establishing the Lyapunov matrix equations for partial derivates of the solution of the SDREs and introducing symmetry measure for some related matrices, a method is proposed for examining whether the SDRE method admits a global optimal control equiva- lent to that solved by the HJI equation method. Two examples with simulation are given to illustrate the method is effective.展开更多
This paper studies simultaneous stabilization of a class of nonlinear descriptor systems via the Hamiltonian function method. Firstly, based on the Hamiltonian realization of the nonlinear descriptor systems and a sui...This paper studies simultaneous stabilization of a class of nonlinear descriptor systems via the Hamiltonian function method. Firstly, based on the Hamiltonian realization of the nonlinear descriptor systems and a suitable output feedback, two nonlinear descriptor systems are equivalently transformed into two nonlinear Hamiltonian differential-algebraic systems by a nonsingular transformation, and a sufficient condition for two closed-loop systems to be impulse-free is given. The two systems are then combined to generate an augmented dissipative Hamiltonian differential-algebraic system by using the system-augmentation technique, based on which a simultaneous stabilization controller and a robust simultaneous stabilization controller are designed for the two systems. Secondly, the case of more than two nonlinear descriptor systems is investigated, and two new results are proposed for the simultaneous stabilization and robust simultaneous stabilization, respectively. Finally, an illustrative example is studied by using the results proposed in this paper, and simulations show that the simultaneous stabilization controllers obtained in this paper work very well.展开更多
The paper shows that a control strategy with disturbance rejection is able to reduce the control effort to a minimum, ensuring at the same time a desired performance level. The disturbance to be rejected is completely...The paper shows that a control strategy with disturbance rejection is able to reduce the control effort to a minimum, ensuring at the same time a desired performance level. The disturbance to be rejected is completely unknown, except for a sectorial bound. The control unit is endowed with an extended state observer which includes a disturbance dynamics, whose state tracks the unknown disturbance to be rejected. In summary, the novel contributions of the paper are the following. First, we derive a robust stability condition for the proposed control scheme, holding for all the nonlinearities that are bounded by a known （or estimated） maximum slope. Second, we propose a novel approach for designing the observer and state feedback gains, which guarantee robust closed-loop stability. Third, we show that the designed control system yields, with a minimum control effort, the same control performance as a robust state feedback control, which on the contrary may require a larger command activity. Two simulated case studies are presented to show the effectiveness of the proposed approach.展开更多
We discuss the delay dependent robust dissipative problem for a class of time-delay systems with nonlinear perturbations. And the sufficient conditions for the delay dependent robust dissipation and quadratic stabilit...We discuss the delay dependent robust dissipative problem for a class of time-delay systems with nonlinear perturbations. And the sufficient conditions for the delay dependent robust dissipation and quadratic stability are given by the linear matrix inequalities （LMIs）, then the time-delay bound and the delay dependent robust dissipative state feedback controller are presented.展开更多
基金Sponsored by the Natural Science of Foundation of Fujian Province(Grant No.A0510025).
文摘This paper deals with the robust stabilization and passivity of general nonlinear systems with structural uncertainty. By using Lyapunov function, it verifies that under some conditions the robust passivity implies the zero-state detectability, Furthermore, it also implies the robust stabilization for such nonlinear systems. We then establish a stabilization method for the nonlinear systems with structural uncertainty. The smooth state feedback law can be constructed with the solution of an equation. Finally, it is worth noting that the main contribution of the paper establishes the relation between robust passivity and feedback stabilization for the general nonlinear systems with structural uncertainty. The simulation shows the effectiveness of the method.
文摘The local robust stabilization for a class of nonlinear uncertain systems is studied. The robustness concept of Lyapunov type stabilizability for nonlinear uncertain systems is defined. Under the norm bounded structured condition, two cases for uncertainty in control matrix are taken to discuss Lyapunov type stabilizability of systems. The sufficient conditions of Lyapunov type stabilization are given from differential geometry and nonlinear H ∞ control of view, respectively.
基金This work was mainly supported by NSFC (No.60234010) and also partially supported by the Field Bus Technology & Automation Key Lab of Beijing in North China, and the national 973 program of China (No.2002CB312200).
文摘In this paper, we study the robust fault detection problem of nonlinear systems. Based on the Lyapunov method, a robust fault detection approach for a general class of nonlinear systems is proposed. A nonlinear observer is first provided, and a sufficient condition is given to make the observer locally stable. Then, a practical algorithm is presented to facilitate the realization of the proposed observer for robust fault detection. Finally, a numerical example is provided to show the effectiveness of the proposed approach.
基金supported by the Research Grants Council of the Hong Kong Special Administration Region (No.412006)
文摘This paper studies the global robust stabilization problem for a class of feedforward systems that is subject to both dynamic and time-varying static uncertainties. A small gain theorem-based bottom-up recursive design is developed for constructing a nested saturation control law. At each recursion, two versions of small gain theorem with restrictions are employed to establish the global attractiveness and local stability of the closed-loop system at the equilibrium point, respectively.
基金This project was supported by the National Natural Science Foundation of China (No. 69934030)the Foundation for University
文摘In this paper, Lyapunov function method is used to study the robust absolute stability of general interval Lur'e type nonlinear control systems. As a result, algebraically sufficient conditions with interval matrix inequality form are obtained for the general interval Lur'e type nonlinear control systems, thus the relationship between the stability of symmetrical interval matrix and the robust absolute stability of general interval Lur'e type nonlinear control systems is established.
基金Sponsored by the National Natural Science Foundation of China(Grant No.61004038)
文摘This paper investigates the problem of delay-dependent robust stability analysis for a class of neutral systems with interval time-varying delays and nonlinear perturbations. Such nonlinear perturbations are with time-varying but norm-bounded characteristics. Based on a new Lyapunov-Krasovskii functional, together ,sith a free-weighting matrices technique, improved delay-dependent stability criteria are established. It is shown that less conservative results can be obtained in terms of linear matrix inequalities （LMIs）. Numerical examples are provided to demonstrate the effectiveness and less conservatism of the proposed approach.
文摘The purpose of this paper is the design of neural network-based adaptive sliding mode controller for uncertain unknown nonlinear systems. A special architecture adaptive neural network, with hyperbolic tangent activation functions, is used to emulate the equivalent and switching control terms of the classic sliding mode control （SMC）. Lyapunov stability theory is used to guarantee a uniform ultimate boundedness property for the tracking error, as well as of all other signals in the closed loop. In addition to keeping the stability and robustness properties of the SMC, the neural network-based adaptive sliding mode controller exhibits perfect rejection of faults arising during the system operating. Simulation studies are used to illustrate and clarify the theoretical results.
文摘This paper deals with the problem of the stabilization for multi-input polytopic nonlinear systems. Based on the robust control Lyapunov function, a sufficient condition for the existence of time-invariant, continuous, asymptotically stabilizing state feedback controller is derived. It is shown that the obtained sufficient condition is also necessary if there exists a state feedback controller such that the closed-loop system has a robust Lyapunov function for all possible uncertainties. Moreover, a universal formula for constructing stabilizing controller is proposed and the existence of the corresponding Lyapunov function is proven. Particularly, a Lyapunov function is constructed for the polytopic nonlinear system in canonical form. Finally, the feasibility of the proposed control law is verified by a numerical example.
基金supported by the National Natural Science Foundation of China(60874114)
文摘The relationship between the technique by state- dependent Riccati equations （SDRE） and Hamilton-Jacobi-lsaacs （HJI） equations for nonlinear H∞ control design is investigated. By establishing the Lyapunov matrix equations for partial derivates of the solution of the SDREs and introducing symmetry measure for some related matrices, a method is proposed for examining whether the SDRE method admits a global optimal control equiva- lent to that solved by the HJI equation method. Two examples with simulation are given to illustrate the method is effective.
基金Supported by the National Natural Science Foundation of China (Grant No. 60774009)the Natural Science Foundation of Shandong Province(Grant No. Y2006G10)the Research Fund for the Doctoral Program of Chinese Higher Education (Grant No. 200804220028)
文摘This paper studies simultaneous stabilization of a class of nonlinear descriptor systems via the Hamiltonian function method. Firstly, based on the Hamiltonian realization of the nonlinear descriptor systems and a suitable output feedback, two nonlinear descriptor systems are equivalently transformed into two nonlinear Hamiltonian differential-algebraic systems by a nonsingular transformation, and a sufficient condition for two closed-loop systems to be impulse-free is given. The two systems are then combined to generate an augmented dissipative Hamiltonian differential-algebraic system by using the system-augmentation technique, based on which a simultaneous stabilization controller and a robust simultaneous stabilization controller are designed for the two systems. Secondly, the case of more than two nonlinear descriptor systems is investigated, and two new results are proposed for the simultaneous stabilization and robust simultaneous stabilization, respectively. Finally, an illustrative example is studied by using the results proposed in this paper, and simulations show that the simultaneous stabilization controllers obtained in this paper work very well.
文摘The paper shows that a control strategy with disturbance rejection is able to reduce the control effort to a minimum, ensuring at the same time a desired performance level. The disturbance to be rejected is completely unknown, except for a sectorial bound. The control unit is endowed with an extended state observer which includes a disturbance dynamics, whose state tracks the unknown disturbance to be rejected. In summary, the novel contributions of the paper are the following. First, we derive a robust stability condition for the proposed control scheme, holding for all the nonlinearities that are bounded by a known （or estimated） maximum slope. Second, we propose a novel approach for designing the observer and state feedback gains, which guarantee robust closed-loop stability. Third, we show that the designed control system yields, with a minimum control effort, the same control performance as a robust state feedback control, which on the contrary may require a larger command activity. Two simulated case studies are presented to show the effectiveness of the proposed approach.
文摘We discuss the delay dependent robust dissipative problem for a class of time-delay systems with nonlinear perturbations. And the sufficient conditions for the delay dependent robust dissipation and quadratic stability are given by the linear matrix inequalities （LMIs）, then the time-delay bound and the delay dependent robust dissipative state feedback controller are presented.
