Integral-type Lyapunov Function Research Articles

Adaptive Fuzzy Control for a Class of MIMO Nonlinear Systems with Unknown Dead-zones

A design scheme of adaptive fuzzy controller for a class of uncertain MIMO nonlinear systems with unknown dead-zones and a triangular control structure is proposed in this paper. The design is based on the principle of sliding mode control and the property of Nussbaum function. The approach does not require a priori knowledge of the signs of the control gains and the upper bounds and lower bounds of dead-zone parameters to be known a priori. By introducing the integral-type Lyapunov function and adopting the adaptive compensation term of the upper bound of the optimal approximation error and the dead-zone disturbance, the closed-loop control system is proved to be semi-globally stable in the sense that all signals involved are bounded, with tracking errors converging to zero.

Adaptive control of uncertain continuously stirred tank reactors with unknown actuator nonlinearities

Adaptive nonlinear control is investigated for continuously stirred tank reactor (CSTR) systems using neural networks. The CSTR plant under study belongs to a class of nonaffine nonlinear systems, and contains an unknown parameter that enters the model nonlinearly. Using adaptive backstepping and neural network (NN) approximation techniques, an alternative adaptive NN controller is developed that achieves asymptotic output tracking control. A novel integral-type Lyapunov function, which includes both system states and control input as its arguments, is constructed to solve the difficulty associated with the nonaffine control problem. Numerical simulation is performed to show the feasibility of the proposed approach for chemical process control.

Robust adaptive fuzzy control for a class of perturbed pure-feedback nonlinear systems

A new design scheme of direct adaptive fuzzy controller for a class of perturbed pure-feedback nonlinear systems is proposed. The design is based on backstepping and the approximation capability of the first type fuzzy systems. A continuous robust term is adopted to minify the influence of modeling errors or disturbances. By introducing the modified integral-type Lyapunov function, the approach is able to avoid the requirement of the upper bound of the first time derivation of the high frequency control gain. Through theoretical analysis, the closed-loop control system is proven to be semi-globally uniformly ultimately bounded, with tracking error converging to a residual set.

Stable adaptive control for nonlinear multivariable systems with a triangular control structure

A stable adaptive controller is developed for a class of nonlinear multivariable systems using nonlinearly parametrized function approximators. By utilizing the system triangular property, integral-type Lyapunov functions are introduced for deriving the control structure and adaptive laws without the need of estimating the "decoupling matrix" of the multivariable nonlinear system. It is shown that stability of the adaptive closed-loop system is guaranteed, and transient performance is analytically quantized by mean square and L/sub /spl infin// tracking error bound criteria.

Adaptive control of first-order systems with nonlinear parameterization

In this paper, an adaptive control method is presented for a class of first-order systems with nonlinear parameterization. The main features of the scheme are that a novel integral-type Lyapunov function is developed for constructing an asymptotically stable adaptive controller, and output tracking error bounds are provided to evaluate the control performance of the adaptive system. The design procedure and the effectiveness of the proposed controller are illustrated through an example study.