Observer design for matrix second order linear systems with uncertain disturbance input-a parametric approach

A simple parametric approach to design a full-order observer for matrix second-order linear systems with uncertain disturbance input in the matrixsecond-order framework is proposed. The basic idea is to minimize the H2 norm of the transfer function from disturbance to estimation error using the design degrees of freedom provided by a parametric approach in the observer design. Besides the design parameters, the eigenvalues of the closed-loop system are also optimized within desired regions on the left-half of the complex plane. Using the proposed approach, additional specifications can be easily achieved. A spring-mass system is using to show the effect of the proposed approaches.

Guaranteed Cost Attitude Tracking Control for Uncertain Quadrotor Unmanned Aerial Vehicle Under Safety Constraints

In this paper,guaranteed cost attitude tracking con-trol for uncertain quadrotor unmanned aerial vehicle(QUAV)under safety constraints is studied.First,an augmented system is constructed by the tracking error system and reference system.This transformation aims to convert the tracking control prob-lem into a stabilization control problem.Then,control barrier function and disturbance attenuation function are designed to characterize the violations of safety constraints and tolerance of uncertain disturbances,and they are incorporated into the reward function as penalty items.Based on the modified reward function,the problem is simplified as the optimal regulation problem of the nominal augmented system,and a new Hamilton-Jacobi-Bellman equation is developed.Finally,critic-only rein-forcement learning algorithm with a concurrent learning tech-nique is employed to solve the Hamilton-Jacobi-Bellman equa-tion and obtain the optimal controller.The proposed algorithm can not only ensure the reward function within an upper bound in the presence of uncertain disturbances,but also enforce safety constraints.The performance of the algorithm is evaluated by the numerical simulation.

Robust Consensus of Multi-Agent Systems with Uncertain Exogenous Disturbances

The objective of this paper is to investigate the consensus of the multi-agent systems w/th nonlinear coupling function and external disturbances. The disturbance includes two parts, one part is supposed to be generated by an exogenous system, which is not required to be neutrally stable as in the output regulation theory, the other part is the modeling uncertainty in the exogenous disturbance system. A novel composite disturbance observer based control （DOBC） and H∞ control scheme is presented so that the disturbance with the exogenous system can be estimated and compensated and the consensus of the multi-agent systems with fixed and switching graph can be reached by using Hoo control law. Simulations demonstrate the advantages of the proposed DOBC and H∞ control scheme.

Robust Optimization Operation of Power System Considering the Non-probabilistic Uncertainty of Parameter

Probabilistic method requires a lot of sample information to describe the probability distributions of uncertain variables and has difficulty in dealing with the optimization problem with uncertain parameters which contains unsufficient information.To solve this problem,a robust optimization operation method based on information gap decision theory(IGDT) is presented considering the non-probabilistic uncertainties of parameters.By the proposed method the maximum resistance to the disturbance of uncertain parameters is achieved and the optimization strategies with uncertain parameters are presented.Finally,numerical simulation is performed on the modified IEEE-14 bus system.Numerical results show the effectiveness of the proposed approach.

Science Letters:A minimax optimal control strategy for uncertain quasi-Hamiltonian systems

A minimax optimal control strategy for quasi-Hamiltonian systems with bounded parametric and/or external disturbances is proposed based on the stochastic averaging method and stochastic differential game. To conduct the system energy control, the partially averaged Ito stochastic differential equations for the energy processes are first derived by using the stochastic averaging method for quasi-Hamiltonian systems. Combining the above equations with an appropriate performance index, the proposed strategy is searching for an optimal worst-case controller by solving a stochastic differential game problem. The worst-case disturbances and the optimal controls are obtained by solving a Hamilton-Jacobi-Isaacs （HJI） equation. Numerical results for a controlled and stochastically excited DulTlng oscillator with uncertain disturbances exhibit the efficacy of the proposed control strategy.

Chaos Control in Electromechanical Seismograph System with Noise Disturbances

In order to eliminate chaotic oscillation of electromechanical characteristics of seismograph system, the complex dynamic the four-dimensional nonlinear equations of seismograph system were analyzed. Sliding mode method was applied to stabilize the chaotic orbits of the eleetromechanieal seismograph system to arbitrary chosen fixed points and periodic orbits precisely, and MATLAB simulations were presented to confirm the validity of the controller. The results show that using sliding mode method can make the system track target orbit strictly and smoothly with short transition time, and its insensitivity to noise disturbances is shown. It also provides reference for relevant chaos control in relevant system.

Finite-Time Synchronization for Heterogeneous Complex Networks with Time-Varying Delays

This paper studies the problem of finite-time synchronization for a class of heterogeneous complex networks which not only have node time-varying delays and coupled time-varying delays but also contain uncertain disturbance. An appropriate controller is designed such that this type of network can be synchronized within a finite time. By constructing a proper Lyapunov function and using the finite-time stability theory, the sufficient conditions for the network to achieve finite-time synchronization are given and the finite time is estimated. Finally, the conclusions obtained are extended to the case of homogeneous complex networks with time-varying delays and uncertain disturbance.

Direct Torque Control of Chaos in Permanent Magnet Synchronous Motor

Permanent magnet synchronous motor（PMSM） displays chaotic osdllation with certain parameter values, which threatens the secure operation of the power system. To control these unwanted chaotic oscillations, a new control scheme which depended on external torque was designed. Based on Lyapunov stability theorem and the matrix theory, several sufficient conditions were derived, which ensured the global asymptotic stability and exponential stability for the chaotic PMSM with uncertain pulse disturbance. The designed controller based on external torque was able to eliminate the chaotic oscillations. A numerical example was given to demonstrate the effectiveness of the proposed results.

High Speed Aircraft Robust Fuzzy Controller Design Based on H_∞Performance

The dynamics of the high-speed vehicle（HSV） is partially or completely unknown because of various reasons, such as modeling errors, in-flight failure, and external disturbances. In this paper, a global stability robust fuzzy controller is designed to control the flight F-16 with uncertain perturbation. For the desired H_∞ output-feedback controllers, a necessary and sufficient condition of quadratic stability is derived with the well-established results of the Lyapunov stability theory and nonnegative matrix. The controllers not only guarantee the global asymptotically stability of the resultant closed-loop system with external disturbance and parameter perturbation, but also have a desired H∞ performance in a large flight envelop（LFE）.

H_∞ controller design for a 4-meter direct-drive azimuth axis

To pursue a higher imaging resolution for exploring more details in the information conveyed by the Universe, the next generation of optical telescopes based on a direct drive widely employ the extremely large aperture structure, which also introduces more disturbances and uncertain factors to the control system. Facing this new challenge, the PID control method in main-axis control systems of traditional astronomical telescopes cannot suffice for the requirement of the tracking precision and disturbance sensitivity in angular velocity. To overcome this shortcoming, we establish a dynamic model and propose an H∞ controller for a 4-meter azimuth direct drive control system that consists of a revolving platform（azimuth axis）, a three-phase torque motor, a motor drive, an encoder, a data acquisition card and a small computers. Simulations are carried out to analyze the model and guide the real experiments.Experimental results show that the proposed H∞ controller reduces the tracking error by a maximum of 80.69%（average 57.8%） and the disturbance sensitivity by a maximum of 82.3%（average 50.96%） compared with the traditional tuned PI controller;furthermore, the order of the model describing the proposed controller can be reduced to three, thus its feasibility in real systems is guaranteed.

Iterative learning control for nonlinear systems with uncertain state delay and arbitrary initial error

Most of the existing iterative learning control algorithms proposed for time-delay systems are based on the condition that the time-delay is precisely available, and the initial state is reset to the desired one or a fixed value at the start of each operation, which makes great limitation on the practical application of corresponding results. In this paper, a new iterative learning control algorithm is studied for a class of nonlinear system with uncertain state delay and arbitrary initial error. This algorithm needs to know only the boundary estimation of the state delay, and the initial state is updated, while the convergence of the system is guaranteed. Without state disturbance and output measurement noise, the system output will strictly track the desired trajectory after successive iteration. Furthermore, in the presence of state disturbance and measurement noise, the tracking error will be bounded uniformly. The convergence is strictly proved mathematically, and sufficient conditions are obtained. A numerical example is shown to demonstrate the effectiveness of the proposed approach.