We propose a new method for robust adaptive backstepping control of nonlinear systems with parametric uncertainties and disturbances in the strict feedback form. The method is called dynamic surface control. Traditio...We propose a new method for robust adaptive backstepping control of nonlinear systems with parametric uncertainties and disturbances in the strict feedback form. The method is called dynamic surface control. Traditional backstepping algorithms require repeated differentiations of the modelled nonlinearities. The addition of n first order low pass filters allows the algorithm to be implemented without differentiating any model nonlinearities, thus ending the complexity arising due to the 'explosion of terms' that makes other methods difficult to implement in practice. The combined robust adaptive backstepping/first order filter system is proved to be semiglobally asymptotically stable for sufficiently fast filters by a singular perturbation approach. The simulation results demonstrate the feasibility and effectiveness of the controller designed by the method.展开更多
This paper presents a sliding mode (SM) based identifier to deal with the parameter identification problem for a class of parameter uncertain nonlinear dynamic systems with input nonlinearity. A sliding mode controlle...This paper presents a sliding mode (SM) based identifier to deal with the parameter identification problem for a class of parameter uncertain nonlinear dynamic systems with input nonlinearity. A sliding mode controller (SMC) is used to ensure the global reaching condition of the sliding mode for the nonlinear system; an identifier is designed to identify the uncertain parameter of the nonlinear system. A numerical example is studied to show the feasibility of the SM controller and the asymptotical convergence of the identifier.展开更多
The problem of robust H∞ control of a class of nonlinear systems with input dynamicaluncertainty is dealt with. By the recursive design approach, a robust controller is constructed suchthat the closed-loop system has...The problem of robust H∞ control of a class of nonlinear systems with input dynamicaluncertainty is dealt with. By the recursive design approach, a robust controller is constructed suchthat the closed-loop system has an arbitrarily small L2 gain from disturbance to output and in theabsence of disturbance, the closed-loop system is globally asymptotically stable.展开更多
This paper proposes a new non-intrusive trigonometric polynomial approximation interval method for the dynamic response analysis of nonlinear systems with uncertain-but-bounded parameters and/or initial conditions.Thi...This paper proposes a new non-intrusive trigonometric polynomial approximation interval method for the dynamic response analysis of nonlinear systems with uncertain-but-bounded parameters and/or initial conditions.This method provides tighter solution ranges compared to the existing approximation interval methods.We consider trigonometric approximation polynomials of three types:both cosine and sine functions,the sine function,and the cosine function.Thus,special interval arithmetic for trigonometric function without overestimation can be used to obtain interval results.The interval method using trigonometric approximation polynomials with a cosine functional form exhibits better performance than the existing Taylor interval method and Chebyshev interval method.Finally,two typical numerical examples with nonlinearity are applied to demonstrate the effectiveness of the proposed method.展开更多
In this paper, we apply the approach of conditional nonlinear optimal perturbation related to the parameter(CNOP-P)to study parameter uncertainties that lead to the stability(maintenance or degradation) of a grassland...In this paper, we apply the approach of conditional nonlinear optimal perturbation related to the parameter(CNOP-P)to study parameter uncertainties that lead to the stability(maintenance or degradation) of a grassland ecosystem. The maintenance of the grassland ecosystem refers to the unchanged or increased quantity of living biomass and wilted biomass in the ecosystem,and the degradation of the grassland ecosystem refers to the reduction in the quantity of living biomass and wilted biomass or its transformation into a desert ecosystem. Based on a theoretical five-variable grassland ecosystem model, 32 physical model parameters are selected for numerical experiments. Two types of parameter uncertainties could be obtained. The first type of parameter uncertainty is the linear combination of each parameter uncertainty that is computed using the CNOP-P method. The second type is the parameter uncertainty from multi-parameter optimization using the CNOP-P method. The results show that for the 32 model parameters, at a given optimization time and with greater parameter uncertainty, the patterns of the two types of parameter uncertainties are different. The different patterns represent physical processes of soil wetness. This implies that the variations in soil wetness(surface layer and root zone) are the primary reasons for uncertainty in the maintenance or degradation of grassland ecosystems, especially for the soil moisture of the surface layer. The above results show that the CNOP-P method is a useful tool for discussing the abovementioned problems.展开更多
In this paper, a new evolutionary algorithm based on a membrane system is proposed to solve the dynamic or uncertain optimization problems. The proposed algorithm employs objects, a dynamical membrane structure and se...In this paper, a new evolutionary algorithm based on a membrane system is proposed to solve the dynamic or uncertain optimization problems. The proposed algorithm employs objects, a dynamical membrane structure and several reaction rules of the membrane systems. The object represents a candidate solution of the optimization problems. The dynamical structure consists of the nested membranes where a skin membrane contains several membranes, which is useful for the proposed algorithm that finds optimal solutions. The reaction rules are designed to locate and track the optimal solutions of the dynamic optimization problems （DOPs）, which are inspired by processing the chemical compounds in the region of cellular membranes. Experimental study is conducted based on the moving peaks benchmark to evaluate the performance of the proposed algorithm in comparison with three state-of-the-art dynamic optimization algorithms. The results indicate the proposed algorithm is effective to solve the DOPs.展开更多
文摘We propose a new method for robust adaptive backstepping control of nonlinear systems with parametric uncertainties and disturbances in the strict feedback form. The method is called dynamic surface control. Traditional backstepping algorithms require repeated differentiations of the modelled nonlinearities. The addition of n first order low pass filters allows the algorithm to be implemented without differentiating any model nonlinearities, thus ending the complexity arising due to the 'explosion of terms' that makes other methods difficult to implement in practice. The combined robust adaptive backstepping/first order filter system is proved to be semiglobally asymptotically stable for sufficiently fast filters by a singular perturbation approach. The simulation results demonstrate the feasibility and effectiveness of the controller designed by the method.
文摘This paper presents a sliding mode (SM) based identifier to deal with the parameter identification problem for a class of parameter uncertain nonlinear dynamic systems with input nonlinearity. A sliding mode controller (SMC) is used to ensure the global reaching condition of the sliding mode for the nonlinear system; an identifier is designed to identify the uncertain parameter of the nonlinear system. A numerical example is studied to show the feasibility of the SM controller and the asymptotical convergence of the identifier.
文摘The problem of robust H∞ control of a class of nonlinear systems with input dynamicaluncertainty is dealt with. By the recursive design approach, a robust controller is constructed suchthat the closed-loop system has an arbitrarily small L2 gain from disturbance to output and in theabsence of disturbance, the closed-loop system is globally asymptotically stable.
文摘This paper proposes a new non-intrusive trigonometric polynomial approximation interval method for the dynamic response analysis of nonlinear systems with uncertain-but-bounded parameters and/or initial conditions.This method provides tighter solution ranges compared to the existing approximation interval methods.We consider trigonometric approximation polynomials of three types:both cosine and sine functions,the sine function,and the cosine function.Thus,special interval arithmetic for trigonometric function without overestimation can be used to obtain interval results.The interval method using trigonometric approximation polynomials with a cosine functional form exhibits better performance than the existing Taylor interval method and Chebyshev interval method.Finally,two typical numerical examples with nonlinearity are applied to demonstrate the effectiveness of the proposed method.
基金supported by the Foundation for Young University Key Teacher by the Educational Department of Henan Province (Grant No. 2014GGJS-021)the National Natural Science Foundation of China (Grant Nos. 41375111, 41675104 & 41230420)
文摘In this paper, we apply the approach of conditional nonlinear optimal perturbation related to the parameter(CNOP-P)to study parameter uncertainties that lead to the stability(maintenance or degradation) of a grassland ecosystem. The maintenance of the grassland ecosystem refers to the unchanged or increased quantity of living biomass and wilted biomass in the ecosystem,and the degradation of the grassland ecosystem refers to the reduction in the quantity of living biomass and wilted biomass or its transformation into a desert ecosystem. Based on a theoretical five-variable grassland ecosystem model, 32 physical model parameters are selected for numerical experiments. Two types of parameter uncertainties could be obtained. The first type of parameter uncertainty is the linear combination of each parameter uncertainty that is computed using the CNOP-P method. The second type is the parameter uncertainty from multi-parameter optimization using the CNOP-P method. The results show that for the 32 model parameters, at a given optimization time and with greater parameter uncertainty, the patterns of the two types of parameter uncertainties are different. The different patterns represent physical processes of soil wetness. This implies that the variations in soil wetness(surface layer and root zone) are the primary reasons for uncertainty in the maintenance or degradation of grassland ecosystems, especially for the soil moisture of the surface layer. The above results show that the CNOP-P method is a useful tool for discussing the abovementioned problems.
文摘In this paper, a new evolutionary algorithm based on a membrane system is proposed to solve the dynamic or uncertain optimization problems. The proposed algorithm employs objects, a dynamical membrane structure and several reaction rules of the membrane systems. The object represents a candidate solution of the optimization problems. The dynamical structure consists of the nested membranes where a skin membrane contains several membranes, which is useful for the proposed algorithm that finds optimal solutions. The reaction rules are designed to locate and track the optimal solutions of the dynamic optimization problems （DOPs）, which are inspired by processing the chemical compounds in the region of cellular membranes. Experimental study is conducted based on the moving peaks benchmark to evaluate the performance of the proposed algorithm in comparison with three state-of-the-art dynamic optimization algorithms. The results indicate the proposed algorithm is effective to solve the DOPs.
