Distributed Consensus Algorithm for Nonholonomic Wheeled Mobile Robot

This paper focuses on consensus of the nonholonomic wheeled mobile robotic systems whose geometric center and centroid do not coincide. A consensus control algorithm for mobile robots based on the nonstandard chain systems is proposed. Firstly, coordinate transformation is used to transform the nonholonomic robotic systems into the nonstandard chain model. Then, a distributed cooperative control algorithm is designed, and the Lyapunov stability theorem and LaSalle invariance principle are used to prove that each state of the mobile robot is consensus. Finally, the effectiveness of the algorithm is proved through numerical simulation.

Robust Stabilization and Observer-Based Stabilization for a Class of Singularly Perturbed Bilinear Systems

An infinite-bound stabilization of a system modeled as singularly perturbed bilinear systems is examined. First, we present a Lyapunov equation approach for the stabilization of singularly perturbed bilinear systems for all ε∈(0, ∞). The method is based on the Lyapunov stability theorem. The state feedback constant gain can be determined from the admissible region of the convex polygon. Secondly, we extend this technique to study the observer and observer-based controller of singularly perturbed bilinear systems for all ε∈(0, ∞). Concerning this problem, there are two different methods to design the observer and observer-based controller: one is that the estimator gain can be calculated with known bounded input, the other is that the input gain can be calculated with known observer gain. The main advantage of this approach is that we can preserve the characteristic of the composite controller, i.e., the whole dimensional process can be separated into two subsystems. Moreover, the presented stabilization design ensures the stability for all ε∈(0, ∞). A numeral example is given to compare the new ε-bound with that of previous literature.

Robust Controller Decorated by Nonlinear S Function and Its Application to Water Tank

In this manuscript, a concept of modifying the results of the existing robust controller decorated by a nonlinear S function is presented to improve the system performance. A case-based study of level control of water tanks illustrates the effectiveness of nonlinear decoration in improving robustness and controlling energy-saving performance with an S-function-decorated robust controller. The performance of the controlled system was analyzed through Lyapunov stability theorem and robust control theory, and was evaluated with a performance index. By demonstrating three comparing simulations of different scenes, it testifies to the fact that the nonlinear decorated robust controller meets the requirement of improving the system performance index. Compared with the nonlinear feedback and the fuzzy control, the performance index of the system using a nonlinear decorated controller is reduced by more than 10% with satisfactory robustness. This nonlinear decorated robust controller is proven to be energy efficient, simple and clear and easy to use, valuable for extensive application.

Multistability Analysis of State-Dependent Switched Hopfield Neural Networks With The Gaussian-Wavelet-Type Activation Function*

This paper studies the multistability of state-dependent switched Hopfield neural networks (SSHNNs) with the Gaussian-wavelet-type activation function. The coexistence and stability of multiple equilibria of SSHNNs are proved. By using Brouwer's fixed point theorem, it is obtained that the SSHNNs can have at least 7n or 6n equilibria under a specified set of conditions. By using the strictly diagonally dominance matrix (SDDM) theorem and Lyapunov stability theorem, 4n or 5n locally stable (LS) equilibria are obtained, respectively. Compared with the conventional Hopfield neural networks (HNNs) without state-dependent switching or SSHNNs with other kinds of activation functions, SSHNNs with this type of activation functions can have more LS equilibria, which implies that SSHNNs with Gaussian-wavelet-type activation functions can have even larger storage capacity and would be more dominant in associative memory application. Last, some simulation results are given to verify the correctness of the theoretical results.

Synchronization of a Class of Chaotic Systems with Different Dimensions

In this paper, two scaling matrices are used to research the synchronization of different dimensional chaotic systems with unknown parameters. Firstly, the definition of synchronization of chaotic systems with different dimensions is introduced. Secondly, based on Lyapunov stability theorem and adaptive control method, an adaptive feedback hybrid controller and parameter adaptive laws are designed to realize synchronization of uncertain chaotic systems with different dimensions. Finally, three numerical experiments are carried out to verify the effectiveness of the proposed method.

Robust stability analysis of impulsive quaternion-valued neural networks with distributed delays and parameter uncertainties

In this paper, an impulsive quaternion-valued neural networks (QVNNs) model with leakage, discrete, and distributed delays is considered. Based on the homeomorphic mapping method, Lyapunov stability theorem, and linear matrix inequality (LMI) approach, sufficient conditions for the existence, uniqueness, and global robust stability of the equilibrium point of the impulsive QVNNs are provided. A numerical example is provided to confirm the obtained results. A conclusion is presented in the end.

Trajectory Control of Robotic Manipulators: A Comparison Study

In this paper, two different types of model-based trajectory control schemes are designed and compared for the control of robotic manipulators. First, two PD-based control schemes and one sliding-mode control scheme are designed, where Lyapunov stability theorem is used as a mathematical design tool. Then, the performances of the PD-based control schemes are compared to those of the sliding-mode control schemes with realistic computer simulations. The global asymptotic stability and the boundedness of all internal signals of the designed control schemes are shown with Lyapunov stability theorem.

A Parallel Estimation System of Stator Resistance and Rotor Speed for Active Disturbance Rejection Control of Six-Phase Induction Motor

In this paper, a parallel estimation system of the stator resistance and the rotor speed is proposed in speed sensorless six-phase induction motor (6PIM) drive. First, a full-order observer is presented to provide the stator current and the rotor flux. Then, an adaptive control law is designed using the Lyapunov stability theorem to estimate the rotor speed. In parallel, a stator resistance identification scheme is proposed using more degrees of freedom of the 6PIM, which is also based on the Lyapunov stability theorem. The main advantage of the proposed method is that the stator resistance adaptation is completely decoupled from the rotor speed estimation algorithm. To increase the robustness of the drive system against external disturbances, noises, and parameter uncertainties, an active disturbance rejection controller (ADRC) is introduced in direct torque control (DTC) of the 6PIM. The experimental results clarify the effectiveness of the proposed approaches.

A New Type of Combination Synchronization among Multiple Chaotic Systems

Based on former combination synchronization studies, a new type of combination synchronization approach is developed in this research, with the consideration of parallel combination of drive systems. This new synchronization approach is referred to as combination synchronization-II. As a representative case, the combination synchronization-II between three drive systems and one response system is studied. Applying Lyapunov stability theorem and active backstepping design, sufficient conditions for the proposed combination synchronization approach are derived. Numerical simulations are performed to show the feasibility and effectiveness of the proposed approach. Based on the investigation in this research, the proposed approach provides an applicable method for designing universal combination synchronization among multiple chaotic systems.

Stabilization Conditions for a Class of Fractional-Order Nonlinear Systems

The stabilization problem of fractional-order nonlinear systems for 0<α<1 is studied in this paper. Based on Mittag-Leffler function and the Lyapunov stability theorem, two practical stability conditions that ensure the stabilization of a class of fractional-order nonlinear systems are proposed. These stability conditions are given in terms of linear matrix inequalities and are easy to implement. Moreover, based on these conditions, the method for the design of state feedback controllers is given, and the conditions that enable the fractional-order nonlinear closed-loop systems to assure stability are provided. Finally, a representative case is employed to confirm the validity of the designed scheme.