The direct adaptive dynamic regulation of unknown nonlinear multi variable systems is investigated in this chapter in order to address the problem of controlling non-Brunovsky and non-square systems with control inputs less than the number of states. The proposed neuro-fuzzy model acts as a universal approximator. While with the careful selection of a Lyapunov-like function, the authors prove t...

*Correspondence: [email protected] 2Department of Applied Mathematics, Huainan Normal University, Huainan, 232038, China Full list of author information is available at the end of the article Abstract By constructing two scaling matrices, i.e., a function matrix (t) and a constant matrix W which is not equal to the identity matrix, a kind ofW – (t) synchronization between fractional-order an...

A direct adaptive neural network tracking control scheme is presented for a class of SISO affine nonlinear uncertain systems. Uncertainties meet the match conditions. Parameters in neural networks are updated using a gradient descent method which designed in order to minimize a quadratic cost function of the error between the unknown ideal implicit controller and the used neural networks contro...

We present a novel method to compute Lyapunov functions for continuous-time systems with multiple local attractors. In the proposed method one first computes an outer approximation of the local attractors using a graphtheoretic approach. Then a candidate Lyapunov function is computed using a Massera-like construction adapted to multiple local attractors. In the final step this candidate Lyapuno...

The discrete-time periodic Lyapunov equation has several important applications in the analysis and design of linear periodic control systems. Specific applications considered in the paper are the solution of stateand output-feedback optimal periodic control problems, the stabilization by periodic state feedback and the square-root balancing of discrete-time periodic systems. Efficient numerica...

We study the basic age-structured population model describing the HIV infection process, which is defined by PDEs. The model allows the production rate of viral particles and the death rate of productively infected cells to vary and depend on the infection age. By using the direct Lyapunov method and constructing suitable Lyapunov functions, dynamical properties of the agestructured model witho...

In this paper, we describe a method of stability analysis for a GA-Based reference adaptive fuzzy sliding model controller for the handling of these problems for a nonlinear system. Firstly, an uncertain and nonlinear plant for the tracking of a reference trajectory is well approximated and described via a fuzzy model involving fuzzy logic control rules. Then, the initial values of the conseque...

This paper describes the design of an adaptive direct control scheme for a class of nonlinear systems. The architecture is based on a fuzzy inference system (FIS) of Takagi Sugeno (TS) type to approximate a feedback linearization control law. The parameters of the consequent part of the fuzzy system are adapted and changed according to a law derived using Lyapunov stability theory. The asymptot...

A novel approach to neural network based tracking-control of robot manipulator including actuator dynamics is proposed by using of backstepping method. A simple two-step backstepping is considered for an nlink robotic system, and a feedforward neural controller is designed at second step where structured and unstructured uncertainties in robot dynamics and actuator model are approximated by thi...

LOW-RANK ITERATIVE METHODS FOR PROJECTED GENERALIZED LYAPUNOV EQUATIONS TATJANA STYKEL Abstract. We generalize an alternating direction implicit method and the Smith method for large-scale projected generalized Lyapunov equations. Such equations arise in model reduction of descriptor systems. Low-rank versions of these methods are also presented, which can be used to compute low-rank approximat...