Research On Adaptive Optimal Iterative Learning Control Based on Least Squares

Traditional Optimal Iterative Learning Control (TOILC) can effectively improve the tracking performance of the servo system. However, there may be parameter perturbation in the running process of the servo system, and its parameters are constantly changing slowly. As a result, the convergence of TOILC becomes worse, and the tracking performance of the system deteriorates seriously. Therefore, in view of the time-varying characteristics of the system, a least squares optimal iterative learning control (LSAOILC) algorithm is proposed. In the process of iteration, the nominal model of the system is identified according to the input and output signals so as to update the optimal iterative learning controller, which does not need to obtain the exact system model information in advance, making up for the shortage of TOILC. The simulations and experiments prove the effectiveness of the proposed strategy for the servo system.

Analytical Solution and Quasi-Periodic Behavior of a Charged Dilaton Black Hole

With the vast breakthrough brought by the Event Horizon Telescope, the theoretical analysis of various black holes has become more critical than ever. In this paper, the second-order asymptotic analytical solution of the charged dilaton black hole flow in the spinodal region is constructed from the perspective of dynamics by using the two-timing scale method. Through a numerical comparison with the original charged dilaton black hole system, it is found that the constructed analytical solution is highly consistent with the numerical solution. In addition, several quasi-periodic motions of the charged dilaton black hole flow are numerically obtained under different groups of irrational frequency ratios, and the phase portraits of the black hole flow with sufficiently small thermal parameter perturbation display good stability. Finally, the final evolution state of black hole flow over time is studied according to the obtained analytical solution. The results show that the smaller the integral constant of the system, the greater the periodicity of the black hole flow.

On Comparing the Performance of Swarm-Based Algorithms with Human-Based Algorithm for Nonlinear Systems

This paper exploits various meta-heuristic optimization techniques to learn PID controller parameters for nonlinear systems. The nonlinear systems considered here are well known ball and beam, inverted pendulum, and robotic arm manipulator. The gain parameters of the controllers are optimized by using two categories of meta-heuristic optimization techniques—swarm-based grasshopper optimization algorithm and particle swarm optimization and human-based, i.e., teacher learning-based optimization. Mean square error has been used to measure the performance of various algorithms. Robustness of these algorithms is studied and compared using parameter perturbation and external disturbance. There are substantial improvements in the performance of these plants using the mentioned algorithms as shown in the simulation results. A detailed comparative analysis of these algorithms has also been done.

Formation Control of Unmanned Vessels with Saturation Constraint and Extended State Observation

This paper addressed the formation control problem of surface unmanned vessels with model uncertainty, parameter perturbation, and unknown environmental disturbances. A formation control method based on the control force saturation constraint and the extended state observer (ESO) was proposed. Compared with the control methods which only consider the disturbances from external environment, the method proposed in this paper took model uncertainties, parameter perturbation, and external environment disturbances as the compound disturbances, and the ESO was used to estimate and compensate for the disturbances, which improved the anti-disturbance performance of the controller. The formation controller was designed with the virtual leader strategy, and backstepping technique was designed with saturation constraint (SC) function to avoid the lack of force of the actuator. The stability of the closed-loop system was analyzed with the Lyapunov method, and it was proved that the whole system is uniformly and ultimately bounded. The tracking error can converge to arbitrarily small by choosing reasonable controller parameters. The comparison and analysis of simulation experiments showed that the controller designed in this paper had strong anti-disturbance and anti-saturation performance to the compound disturbances of vessels and can effectively complete the formation control.

Chaos of a Single-Walled Carbon Nanotube Resulting from Periodic Parameter Perturbation

Carbon nanotubes (CNTs) are used in various nano-electromechanical systems (NEMS), and the parameters (including the system parameters and the excitation parameters) may result in chaos in these systems. Thus, understanding the mechanism of the chaos arising from NEMS is vital for CNT’s applications. Motivated by this need, the chaotic properties of a single-walled carbon nanotube system resulting from parametric excitation and external excitation are investigated in this paper. The criteria for the existence of the chaotic behavior in the system with periodic and quasi-periodic perturbations are obtained by the homoclinic Melnikov and the second-order average methods. Furthermore, in order to show the connection between periodic motion and complex behavior, the subharmonic periodic solutions, inside and outside the homoclinic loop, are analyzed. The global structure and the saddle-node bifurcation of the unperturbed averaged system are also considered. Finally, the Poincaré section and the transversal intersection of the unstable and stable manifolds are presented to verify the occurrence of chaos or subharmonic solution. The simulation results confirm the correctness of the theoretical analysis.

Application of Multi-Parameter Perturbation Method to Functionally-Graded, Thin, Circular Piezoelectric Plates

In this study, a multi-parameter perturbation method is used for the solution of a functionally-graded, thin, circular piezoelectric plate. First, by assuming that elastic, piezoelectric, and dielectric coefficients of the functionally-graded materials vary in the form of the same exponential function, the basic equation expressed in terms of two stress functions and one electrical potential function are established in cylindrical coordinate system. Three piezoelectric coefficients are selected as perturbation parameters, and the established equations are solved by the multi-parameter perturbation method, thus obtaining up to first-order perturbation solutions. The validity of the perturbation solution obtained is verified by numerical simulations, based on layer-wise theory. The perturbation process indicates that adopting three piezoelectric coefficients as perturbation parameters follows the basic idea of perturbation theory—i.e., if the piezoelectricity may be regarded as a kind of introduced disturbance, the zero-order solution of the disturbance system corresponds exactly to the solution of functionally-graded plates without piezoelectricity. The result also indicates that the deformation magnitude of piezoelectric plates is smaller than that of plates without piezoelectricity, due to the well-known piezoelectric stiffening effect.