In this paper, first, we employ classic Lie symmetry groups approach to obtain the Lie symmetry groupsof the well-known (2+1)-dimensional Generalized Sasa-Satsuma (GSS) equation. Second, based on a modified directmeth...In this paper, first, we employ classic Lie symmetry groups approach to obtain the Lie symmetry groupsof the well-known (2+1)-dimensional Generalized Sasa-Satsuma (GSS) equation. Second, based on a modified directmethod proposed by Lou [J. Phys. A: Math. Gen. 38 (2005) L129], more general symmetry groups are obtained andthe relationship between the new solution and known solution is set up. At the same time, the Lie symmetry groupsobtained are only special cases of the more general symmetry groups. At last, some exact solutions of GSS equationsare constructed by the relationship obtained in the paper between the new solution and known solution.展开更多
This paper presents a design of optimal controllers with respect to a meaningful cost function to force an underactuated omni-directional intelligent navigator （ODIN） under unknown constant environmental loads to tr...This paper presents a design of optimal controllers with respect to a meaningful cost function to force an underactuated omni-directional intelligent navigator （ODIN） under unknown constant environmental loads to track a reference trajectory in two-dimensional space. Motivated by the vehicle＇s steering practice, the yaw angle regarded as a virtual control plus the surge thrust force are used to force the position of the vehicle to globally track its reference trajectory. The control design is based on several recent results developed for inverse optimal control and stability analysis of nonlinear systems, a new design of bounded disturbance observers, and backstepping and Lyapunov＇s direct methods. Both state- and output-feedback control designs are addressed. Simulations are included to illustrate the effectiveness of the proposed results.展开更多
In this paper, with parametric uncertainties such as the mass of vehicle, the inertia of vehicle about vertical axis, and the tire cornering stiffness, we deal with the vehicle lateral control problem in intelligent v...In this paper, with parametric uncertainties such as the mass of vehicle, the inertia of vehicle about vertical axis, and the tire cornering stiffness, we deal with the vehicle lateral control problem in intelligent vehicle systems. Based on the dynamical model of vehicle, by applying Lyapunov function method, the control problem for lane keeping in the presence of parametric uncertainty is studied, the direct adaptive algorithm to compensate for parametric variations is proposed and the terminal sliding mode variable structure control laws are designed with look-ahead references systems. The stability of the system is investigated from the zero dynamics analysis. Simulation results show that convergence rates of the lateral displacement error, yaw angle error and slid angle are fast.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No. 10735030Shanghai Leading Academic Discipline Project under Grant No. B412+2 种基金National Natural Science Foundation of China under Grant No. 90718041Program for Changjiang Scholars and Innovative Research Team in University under Grant No. IRT0734K.C. Wong Magna Fund in Ningbo University
文摘In this paper, first, we employ classic Lie symmetry groups approach to obtain the Lie symmetry groupsof the well-known (2+1)-dimensional Generalized Sasa-Satsuma (GSS) equation. Second, based on a modified directmethod proposed by Lou [J. Phys. A: Math. Gen. 38 (2005) L129], more general symmetry groups are obtained andthe relationship between the new solution and known solution is set up. At the same time, the Lie symmetry groupsobtained are only special cases of the more general symmetry groups. At last, some exact solutions of GSS equationsare constructed by the relationship obtained in the paper between the new solution and known solution.
基金Supported in Part by the Australian Research Council under Grant DP0988424
文摘This paper presents a design of optimal controllers with respect to a meaningful cost function to force an underactuated omni-directional intelligent navigator （ODIN） under unknown constant environmental loads to track a reference trajectory in two-dimensional space. Motivated by the vehicle＇s steering practice, the yaw angle regarded as a virtual control plus the surge thrust force are used to force the position of the vehicle to globally track its reference trajectory. The control design is based on several recent results developed for inverse optimal control and stability analysis of nonlinear systems, a new design of bounded disturbance observers, and backstepping and Lyapunov＇s direct methods. Both state- and output-feedback control designs are addressed. Simulations are included to illustrate the effectiveness of the proposed results.
基金Sponsored by the National Natural Science Foundation of China(Grant No.10772152)
文摘In this paper, with parametric uncertainties such as the mass of vehicle, the inertia of vehicle about vertical axis, and the tire cornering stiffness, we deal with the vehicle lateral control problem in intelligent vehicle systems. Based on the dynamical model of vehicle, by applying Lyapunov function method, the control problem for lane keeping in the presence of parametric uncertainty is studied, the direct adaptive algorithm to compensate for parametric variations is proposed and the terminal sliding mode variable structure control laws are designed with look-ahead references systems. The stability of the system is investigated from the zero dynamics analysis. Simulation results show that convergence rates of the lateral displacement error, yaw angle error and slid angle are fast.
