The primary difficulty in the identification of Hammerstein nonlinear systems (a static memoryless nonlinear system in series with a dynamic linear system) is that the output of the nonlinear system (input to the linear system) is unknown. By employing the theory of affine projection, we propose a gradient-based adaptive Hammerstein algorithm with variable step-size which estimates the Hammerst...

In this paper, implicit controls are investigated for different classes of nonlinear systems, nonaffine systems in pure-feedback form and affine systems in strict-feedback form. While control system design for general unknown nonaffine nonlinear systems needs further investigation, elegant control designs are presented for known systems and systems with unknown scalar parametrization. Though fo...

Trajectory tracking of nonlinear dynamical systems with affine open-loop controls is investigated. The control task is to enforce the system state to follow a prescribed desired trajectory as closely as possible. We introduce exactly realizable desired trajectories as these trajectories which can be tracked exactly by an appropriate control. Exactly realizable trajectories are characterized mat...

In statistical control, the cost function is viewed as a random variable and one optimizes the distribution of the cost function through the cost cumulants. We consider a statistical control problem for a control-affine nonlinear system with a nonquadratic cost function. Using the Dynkin formula, the Hamilton–Jacobi–Bellman equation for the nth cost moment case is derived as a necessary conditi...

A deterministic optimal control problem is solved for a control-affine nonlin-ear system with a nonquadratic cost function. We algebraically solve the Hamilton-Jacobi equation for the gradient of the value function. This eliminates the need to explicitly solve the solution of a Hamilton-Jacobi partial differential equation. We interpret the value function in terms of the control Lyapunov functi...

This paper proposes an adaptive backstepping control strategy for a class of uncertain non affine systems using self recurrent neural networks. To assure the stable tracking of nonlinear non affine system, it is first converted to an affine like form and subsequently a wavelet based adaptive backstepping controller is developed. Self recurrent wavelet neural network (SRWNN) is used to approxima...

This paper introduces a new decentralized adaptive neural network controller for a class of large-scale nonlinear systems with unknown non-affine subsystems and unknown interconnections represented by nonlinear functions. A multilayer feedforward neural network is used to represent the controller’s structure. The ultimate boundedness of the closed loop system is guaranteed through Lyapunov stab...

This paper mainly investigates fuzzy control with affine T-S delayed models, which can be applied to some nonlinear systems. Motivated from performing the linearization process associated with distinct operating points for nonlinear systems, an affine T-S fuzzy model with delayed state is addressed. The overall control then can be performed by the fuzzy inference mechanism, in which the consequ...