A new method for controlling the shape of the conditional output probability density function （PDF） for general nonlinear dynamic stochastic systems is proposed based on B-spline neural network （NN） model and T-S fuzzy model. Applying NN approximation to the measured PDFs, we transform the concerned problem into the tracking of given weights. Meanwhile, the complex multi-delay T-S fuzzy model with exogenous disturbances, parametric uncertainties and state constraints is used to represent the nonlinear weight dynamics. Moreover, instead of the non-convex design algorithms and PI control, the improved convex linear matrix inequality （LMI） algorithms and the generalized PID controller are proposed such that the multiple control objectives including stability, robustness, tracking performance and state constraint can be guaranteed simultaneously. Simulations are performed to demonstrate the efficiency of the proposed approach.
The problem of decentralized adaptive fuzzy control for a class of time-delayed interconnected nonlinear systems with unknown backlash-like hystersis is discussed. On the basis of the principle of variable structure control （VSC） and by using the fuzzy systems with linear adjustable parameters that are used to approximate plant unknown functions, a novel decentralized adaptive fuzzy control strategy with a supervisory controller is developed. A general method, which is modeled the backlash-like hysteresis, is proposed and removes the assumption that the boundedness of disturbance, and the slope of the backlash-like hystersis are known constants. Furthermore, the interconnection term is supposed to be pth-order polynomial in time-delayed states. In addition, the plant dynamic uncertainty and modeling errors are adaptively compensated by adjusting the parameters and gains on-line for each subsystems. By theoretical analysis, it is shown that the closed-loop fuzzy control systems are globally stable, with tracking error converging to zero. Simulation results demonstrate the effectiveness of the approach.
This paper deals with the problem of tracking control for a class of high order nonlinear systems with input delay. The unknown continuous functions of the system are estimated by fuzzy logic systems （FLS）. A state conversion method is introduced to eliminate the delayed input item. By means of the backstepping algorithm, the property of semi-globally uniformly ultimately bounded （SGUUB） of the closed-loop system is achieved. The stability of the closed-loop system is proved according to Lyapunov second theorem on stability. The tracking error is proved to be bounded which ultimately converges to an adequately small compact set. Finally, a computer simulation example of high order nonlinear systems is presented, which illustrates the effectiveness of the control scheme.
