Near time optimal control with perturbation estimation for flexible spacecraft slewing maneuvers

A feedforward approach for generating near time optimal controller for flexible spacecraft rest-to-rest maneuvers is presented with the objective insensitivity to modeling errors, parameter uncertainty and minimizing the residual energy of the flexible modes. The perturbation estimation of flexible appendages to the rigid-hub is accomplished simply via compare the output of real plant with the reference model, and the approach is based on combine this estimation with the bang-bang control for the rigid-hub modes through analysis the basic constraint and the additional constraint, i.e. zero coupling torque and zero coupling torque derivative for general two orders system and three orders system with considerate attitude acceleration mode near time optimal controls. These time optimal controls with control constraints and state constraints leads to forming a boundary-value problem, and resolved the problem using an iterative numerical algorithm. The near time optimal control with perturbation estimation shows a good robust to parameter uncertainty and can suppress the vibration and minimizing the residual energy. The capability of this approach is demonstrated through a numerical example in detail.

Robustness Analysis of Discrete-time Indirect Model Reference Adaptive Control with Normalized Adaptive Laws

For a class of discrete-time systems with unmodeled dynamics and bounded disturbance, the design and analysis of robust indirect model reference adaptive control （MRAC） with normalized adaptive law are investigated. The main work includes three parts. Firstly, it is shown that the constructed parameter estimation algorithm not only possesses the same properties as those of traditional estimation algorithms, but also avoids the possibility of division by zero. Secondly, by establishing a relationship between the plant parameter estimate and the controller parameter estimate, some similar properties of the latter are also established. Thirdly, by using the relationship between the normalizing signal and all the signals of the closed-loop system, and some important mathematical tools on discrete-time systems, as in the continuous-time case, a systematic stability and robustness analysis approach to the discrete indirect robust MRAC scheme is developed rigorously.

Convergence and Superconvergence of Fully Discrete Finite Element for Time Fractional Optimal Control Problems

In this paper, we consider a fully discrete finite element approximation for time fractional optimal control problems. The state and adjoint state are approximated by triangular linear fi nite elements in space and L1 scheme in time. The control is obtained by the variational discretization technique. The main purpose of this work is to derive the convergence and superconvergence. A numerical example is presented to validate our theoretical results.

Feedforward and feedback optimal control for linear time-varying systems with persistent disturbances

The optimal control problem for linear time-varying systems affected by external persistent disturbances with known dynamic characteristics but unknown initial conditions is consider and a design procedure of a feedforward and feedbaek optimal controller is presented. The condition of existence and uniqueness of the control law is given. The disturbanee observer is proposed to make the feedforward control law realizable physically. Simulation results demonstrate that the feedforward and feedbaek optimal control law is more effective and robust than the elassical state feedbaek control law with respect to external disturbanees.

A new approach of optimal control for a class of continuous-time chaotic systems by an online ADP algorithm

We develop an online adaptive dynamic programming （ADP） based optimal control scheme for continuous-time chaotic systems. The idea is to use the ADP algorithm to obtain the optimal control input that makes the performance index function reach an optimum. The expression of the performance index function for the chaotic system is first presented. The online ADP algorithm is presented to achieve optimal control. In the ADP structure, neural networks are used to construct a critic network and an action network, which can obtain an approximate performance index function and the control input, respectively. It is proven that the critic parameter error dynamics and the closed-loop chaotic systems are uniformly ultimately bounded exponentially. Our simulation results illustrate the performance of the established optimal control method.

Commutant Lifting for Optimal Control of Time-varying Systems

This paper uses the commutant lifting theorem for representations of the nest algebra to deal with the optimal control of infinite dimensional linear time- varying systems. We solve the model matching problem and a certain optimal feedback control problem, each of which corresponds with one type of four-block problem. We also obtain a new formula for the optimal performance and prove the existence of an optimal controller.

Effects of Input Redundancy on Time Optimal Control

由于有输入冗余性的系统的流行，这份报纸与输入冗余性集中于这些问题，在我们关于增加新输入冗余性进可控制的系统的效果担心的地方。预定最佳的控制问题被讨论，在如此的效果到最佳的时间被评估的地方。基于存在的假设和最佳的控制的唯一，如果，纸证明增加输入冗余性的数字将从一样的起始的状态导致最佳的时间的严格的减小在那里存在在冗余的输入隧道之中的非闲散的隧道。而且如果这个问题是正常的，那么所有冗余的输入隧道被用来弄短最佳的时间。在另一方面没有规度的假设，最佳的时间将也作为如果至少一条这些冗余的输入隧道是完全可控制的，比作原来的系统为冗余的系统是更小的。最后，二个数字例子被部署表明这份报纸的主要结果。

Comparison of time optimal control for two level quantum systems

The time optimal problem for a two level quantum sys-tem is studied. We compare two different control strategies of bang-bang control and the geometric control, respectively, es-pecial y in the case of minimizing the time of steering the state from North Pole to South Pole on the Bloch sphere with bounded control. The time performances are compared for different param-eters by the individual numerical simulation experiments, and the experimental results are analyzed. The results show that the ge-ometric control spends less time than the bang-bang control does.

TIME AND NORM OPTIMAL CONTROLS:A SURVEY OF RECENT RESULTS AND OPEN PROBLEMS

We present in this paper a survey of recent results on the relation between time and norm optimality for linear systems and the infinite dimensional version of Pontryagin＇s maximum principle. In particular, we discuss optimality （or nonoptimality） of singular controls satisfying the maximum principle and smoothness of the costate in function of smoothness of the target.

Time Optimal Control in Time Series Movement

The paper analyses time series that exhibit equilibrium states. It analyses the formation of equilibrium and how the system can return to the aforementioned equilibrium. The tool that is used in the aforementioned analysis is time optimal control in the phase plane. It is proved that equilibrium state is sustainable if initial state is not too far from the equilibrium as well as control vector is large enough. On the other hand, if initial state is one standard deviation away from equilibrium state, it is proved that equilibrium cannot be reached. It is the same case with control vector. If it is unbounded, time optimal control cannot be applied. The approach that is introduced represents unconventional method of analysing equilibrium in time series.

Performance and robustness analysis of a fuzzy-immune flow controller in ATM networks with time-varying multiple time-delays

For the Asynchronous Transfer Mode （ATM） networks with time-varying multiple time-delays, a more realistic model for the available bit rate （ABR） traffic class with explicit rate feedback is introduced. A fuzzy-immune controller is designed, which can adjust the rates of ABR on-line, overcome the bad effect caused by the saturation nonlinearity and satisfy the weighted fairness. Also, the sufficient condition that guarantees the stability of the closed-loop system with a fuzzy-immune controller is presented in theory for the first time. The algorithm exhibits good performance, and most importantly, has a solid theoretical foundation and can be implemented in practice easily. Simulation results show that the control system is rapid, adaptive, robust, and meanwhile, the quality of service （QoS） is guaranteed.

Indefinite Linear Quadratic Optimal Control Problem for Singular Linear Discrete-time System: Krein Space Method

有限时间地平线不定线性二次(LQ ) 为单个线性分离变化时间的系统的最佳的控制问题被讨论。为单个系统的不定的 LQ 最佳的控制问题能在一个合理假设下面为标准州空间的系统被转变到那。不定的 LQ 最佳的控制问题对为向后的随机的系统的设计的双，这被显示出。因此，最佳的 LQ 控制器能被计算 Kalman 过滤器的获得矩阵获得。为不定的 LQ 问题保证一个唯一的答案的必要、足够的条件被给。这个问题的一个明确的解决方案以 Riccati 差别方程的答案被获得。

Time-Optimal Control Problem for <i>n</i>×<i>n</i>Co-Operative Parabolic Systems with Control in Initial Conditions

In this paper, time-optimal control problem for a liner n× n co-operative parabolic system involving Laplace operator is considered. This problem is, steering an initial state y(0)=u?, with control u?so that an observation y(t) hitting a given target set in minimum time. First, the existence and uniqueness of solutions of such system under conditions on the coefficients are proved. Afterwards necessary and sufficient conditions of optimality are obtained. Finally a scaler case is given.

Optimal Control for Time-Delay Bilinear Systems with Sinusoidal Disturbances

This paper considers the optimal control problem for time-delay bilinear systems affected by sinusoidal disturbances with known frequency and measurable amplitude and phase. Firstly, using the differential homeomorphism, a time-delay bilinear system affected by sinusoidal disturbances is changed to a time-delay pseudo linear system through the coordinate transformation. Then the system with time-delay in control variable is transformed to a linear controllable system without delay using model transformation. At last based on the theory of linear quadratic optimal control, an optimal control law which is used to eliminate the influence of the disturbances is derived from a Riccati equation and Matrix equations. The simulation results show the effectiveness of the method.

ROBUSTNESS OF OPTIMALLY ROBUST CONTROLLERS——Dedicated to the Sixtieth Birthday of Prof. You Zhao-yong

The largest robust stability radius r(P0) of a system P0 is defined as the radius of the largest ball Bmax in the gap metric centered at P0 which can be stabilized by one single controller. Any controller which stabilizes Bmax is called an optimally robust controller of P0. Any controller, regarded as a system, should have its own largest robust stability radius also. In this paper it is shown that the largest robust stability radius of any optimally robust controller of P0 is larger than or equal to r(Po). Moreover, the variation of the closed-loop transfer matrix caused by the perturbation of the system is estimated.

A Direct Compensative Robust Optimal Control (DCROC) Law for Ship Straight-line Track-keeping

A linear quadratic optimal direct track-keeping control law was proposed based on first-order Nomoto nominal model. Furthermore, based on Lyapunov stabilized theory, considering parametric uncertainty from variations of ship speed and disturbances uncertain from wind, wave and sea current, a direct compensative robust optimal control (DCROC) law was developed. It can guarantee closed-loop system globally and uniformly converge to a remained set. High accuracy and robustness were achieved. By introducing some nonlinear blocks, closed-loop system achieves global and uniform asymptotical stableness. Numerical simulations on a Mariner Class ship are presented to validate the control law.

Observer-based Adaptive Optimal Control for Unknown Singularly Perturbed Nonlinear Systems With Input Constraints

This paper introduces an observer-based adaptive optimal control method for unknown singularly perturbed nonlinear systems with input constraints. First, a multi-Time scales dynamic neural network MTSDNN observer with a novel updating law derived from a properly designed Lyapunov function is proposed to estimate the system states. Then, an adaptive learning rule driven by the critic NN weight error is presented for the critic NN, which is used to approximate the optimal cost function. Finally, the optimal control action is calculated by online solving the Hamilton-Jacobi-Bellman HJB equation associated with the MTSDNN observer and critic NN. The stability of the overall closed-loop system consisting of the MTSDNN observer, the critic NN and the optimal control action is proved. The proposed observer-based optimal control approach has an essential advantage that the system dynamics are not needed for implementation, and only the measured input U+002F output data is needed. Moreover, the proposed optimal control design takes the input constraints into consideration and thus can overcome the restriction of actuator saturation. Simulation results are presented to confirm the validity of the investigated approach. © 2014 Chinese Association of Automation.

Active suspension with optimal control based on a full vehicle model

The 7-DOF model of a full vehicle with an active suspension is developed in this paper.The model is written into the state equation style.Actuator forces are treated as inputs in the state equations.Based on the basic optimal control theory,the optimal gains for the control system are figured out.So an optimal controller is developed and implemented using Matlab/Simulink,where the Riccati equation with coupling terms is deduced using the Hamilton equation.The all state feedback is chosen for the controller.The gains for all vehicle variables are traded off so that majority of indexes were up to optimal.The active suspension with optimal control is simulated in frequency domain and time domain separately,and compared with a passive suspension.Throughout all the simulation results,the optimal controller developed in this paper works well in the majority of instances.In all,the comfort and ride performance of the vehicle are improved under the active suspension with optimal control.

EQUIVALENCE OF THREE DIFFERENT KINDS OF OPTIMAL CONTROL PROBLEMS FOR STOKES EQUATIONS

This article presents an equivalence theorem for three different kinds of optimal control problems, which are optimal target control problems, optimal norm control problems, and optimal time control problems. Controlled systems in this study are internally controlled Stokes equations.