Enhancing the stability and performance of practical control systems in the presence of nonlinearity,time delay,and uncertainty remains a significant challenge.Particularly,a class of strict-feedback nonlinear uncerta...Enhancing the stability and performance of practical control systems in the presence of nonlinearity,time delay,and uncertainty remains a significant challenge.Particularly,a class of strict-feedback nonlinear uncertain systems characterized by unknown control directions and time-varying input delay lacks comprehensive solutions.In this paper,we propose an observerbased adaptive tracking controller to address this gap.Neural networks are utilized to handle uncertainty,and a unique coordinate transformation is employed to untangle the coupling between input delay and unknown control directions.Subsequently,a new auxiliary signal counters the impact of time-varying input delay,while a Nussbaum function is introduced to solve the problem of unknown control directions.The leverage of an advanced dynamic surface control technique avoids the“complexity explosion”and reduces boundary layer errors.Synthesizing these techniques ensures that all the closed-loop signals are semi-globally uniformly ultimately bounded(SGUUB),and the tracking error converges to a small region around the origin by selecting suitable parameters.Simulation examples are provided to demonstrate the feasibility of the proposed approach.展开更多
A backstepping method is used for nonlinear spacecraft attitude stabilization in the presence of external disturbances and time delay induced by the actuator. The kinematic model is established based on modified Rodri...A backstepping method is used for nonlinear spacecraft attitude stabilization in the presence of external disturbances and time delay induced by the actuator. The kinematic model is established based on modified Rodrigues parameters (MRPs). Firstly, we get the desired angular velocity virtually drives the attitude parameters to origin, and then backstep it to the desired control torque required for stabilization. Considering the time delay induced by the actuator, the control torque functions only after the delayed time, therefore time compensation is needed in the controller. Stability analysis of the close-loop system is given afterwards. The infinite dimensional actuator state is modeled with a first-order hyperbolic partial differential equation (PDE), the L-2 norm of the system state is constructed and is proved to be exponentially stable. An inverse optimality theorem is also employed during controller design. Simulation results illustrate the efficiency of the proposed control law and it is robust to bounded external disturbances and time delay mismatch.展开更多
The robust guaranteed cost sampled-data control was studied for a class of uncertain nonlinear systems with time-varying delay. The parameter uncertainties are time-varying norm-bounded and appear in both the state an...The robust guaranteed cost sampled-data control was studied for a class of uncertain nonlinear systems with time-varying delay. The parameter uncertainties are time-varying norm-bounded and appear in both the state and the input control matrices. By applying an input delay approach, the system was transformed into a continuous time-delay system. Attention was focused on the design of a robust guaranteed cost sampled-data control law which guarantees that the closed-loop system is asymptotically stable and the quadratic performance index is less than a certain bound for all admissible uncertainties. By applying Lyapunov stability theory, the theorems were derived to provide sufficient conditions for the existence of robust guaranteed cost sampled-data control law in the form of linear matrix inequalities (LMIs), especially an optimal state-feedback guaranteed cost sampled-data control law which ensures the minimization of the guaranteed cost was given. The effectiveness of the proposed method was illustrated by a simulation example with the asymptotically stable curves of system state under the initial condition of x(0)=[0.679 6 0].展开更多
基金National Natural Science Foundation of China(62373102)Jiangsu Natural Science Foundation(BK20221455)Anhui Provincial Key Research and Development Project(2022i01020013)。
文摘Enhancing the stability and performance of practical control systems in the presence of nonlinearity,time delay,and uncertainty remains a significant challenge.Particularly,a class of strict-feedback nonlinear uncertain systems characterized by unknown control directions and time-varying input delay lacks comprehensive solutions.In this paper,we propose an observerbased adaptive tracking controller to address this gap.Neural networks are utilized to handle uncertainty,and a unique coordinate transformation is employed to untangle the coupling between input delay and unknown control directions.Subsequently,a new auxiliary signal counters the impact of time-varying input delay,while a Nussbaum function is introduced to solve the problem of unknown control directions.The leverage of an advanced dynamic surface control technique avoids the“complexity explosion”and reduces boundary layer errors.Synthesizing these techniques ensures that all the closed-loop signals are semi-globally uniformly ultimately bounded(SGUUB),and the tracking error converges to a small region around the origin by selecting suitable parameters.Simulation examples are provided to demonstrate the feasibility of the proposed approach.
文摘A backstepping method is used for nonlinear spacecraft attitude stabilization in the presence of external disturbances and time delay induced by the actuator. The kinematic model is established based on modified Rodrigues parameters (MRPs). Firstly, we get the desired angular velocity virtually drives the attitude parameters to origin, and then backstep it to the desired control torque required for stabilization. Considering the time delay induced by the actuator, the control torque functions only after the delayed time, therefore time compensation is needed in the controller. Stability analysis of the close-loop system is given afterwards. The infinite dimensional actuator state is modeled with a first-order hyperbolic partial differential equation (PDE), the L-2 norm of the system state is constructed and is proved to be exponentially stable. An inverse optimality theorem is also employed during controller design. Simulation results illustrate the efficiency of the proposed control law and it is robust to bounded external disturbances and time delay mismatch.
基金Project(12511109) supported by the Science and Technology Studies Foundation of Heilongjiang Educational Committee of 2011, China
文摘The robust guaranteed cost sampled-data control was studied for a class of uncertain nonlinear systems with time-varying delay. The parameter uncertainties are time-varying norm-bounded and appear in both the state and the input control matrices. By applying an input delay approach, the system was transformed into a continuous time-delay system. Attention was focused on the design of a robust guaranteed cost sampled-data control law which guarantees that the closed-loop system is asymptotically stable and the quadratic performance index is less than a certain bound for all admissible uncertainties. By applying Lyapunov stability theory, the theorems were derived to provide sufficient conditions for the existence of robust guaranteed cost sampled-data control law in the form of linear matrix inequalities (LMIs), especially an optimal state-feedback guaranteed cost sampled-data control law which ensures the minimization of the guaranteed cost was given. The effectiveness of the proposed method was illustrated by a simulation example with the asymptotically stable curves of system state under the initial condition of x(0)=[0.679 6 0].
