受正弦扰动时滞非线性系统的近似最优减振控制

研究时滞非线性系统在正弦扰动作用下的最优减振控制问题,给出一种无时滞近似最优减振控制律的迭代方法．通过假设Lagrange算子,将由原系统最优控制问题得到的既含时滞项又含有超前项的非线性两点边值问题转换为新的有利于求解的形式,再通过构造序列将其转化为不舍时滞项和超前项的线性非齐次两点边值问题序列．证明了该序列的收敛性．通过交替迭代序列得到了系统最优减振控制律．仿真结果表明,该方法在不同时滞下对扰动都具有很好的鲁棒性．     

State waypoint approach to continuous‐time nonlinear optimal control problems

In this paper, we propose an optimal control technique for a class of continuous‐time nonlinear systems. The key idea of the proposed approach is to parametrize continuous state trajectories by sequences of a finite number of intermediate target states; namely, waypoint sequences. It is shown that the optimal control problem for transferring the state from one waypoint to the next is given an explicit‐form suboptimal solution, by means of linear approximation. Thus the original continuous‐time nonlinear control problem reduces to a finite‐dimensional optimization problem of waypoint sequences. Any efficient numerical optimization method, such as the interior‐reflection Newton method, can be applied to solve this optimization problem. Finally, we solve the optimal control problem for a simple nonlinear system example to illustrate the effectiveness of this approach. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Cheap computation of optimal reduced-order models for systems with time delay

A simple method of optimally reducing the order of systems with time delays is proposed. The performance indices used for optimization are the integrals of the time-weighted squared error between the responses of the reduced-order and original models. The performance indices are first expressed in terms of the reduced order system unknown parameters and a minimization of these indices gives the reduced model optimal parameters. Cheap and accurate computation of optimal reduced order models with time delay has so far proved abortive as closed-form expressions for these indices have proved difficult to obtain. Simple feedback controllers parametrized by the internal model control method using the reduced models result in excellent performance when implemented on the original model.     

一类不确定时滞系统的最优控制

对控制能量存在约束条件下一类不确定时滞系统的最优控制问题进行了研究．首先基于一类随机模型误差的描述．定义了一个平均意义上的包含跟踪误差和控制能量在内的性能指标;然后通过谱分解极小化该性能指标,为一类不确定时滞系统导出了一种最优的控制器设计方法,可以兼顾模型不确定性和控制能量约束。仿真研究进一步说明了所提出方法的有效性．     

Sub-optimal PID controller settings for FOPDT systems with long dead time

We propose a method for setting up PI and PID controllers based on stable FOPDT process model, where dead-time dynamics is manipulated without approximation. The main idea used is a partial compensation of the system dynamics, which makes possible obtaining simple tuning rules. Remaining unknown controller parameters are determined on the basis of the modulus optimum and the minimum ISE criterions. Besides the performance indices, quality of the settings is also evaluated by the stability margin. Although optimal values of the parameters are valid for the reference tracking problem, a compensation of the disturbance lag that preserves the stability margin is proposed for the disturbance rejection problem.     

非线性系统近似最优PD动态补偿控制

本文研究了一类基于动态补偿的非线性系统的近似最优PD控制的问题.用微分方程的逐次逼近理论将非线性系统的最优控制问题转化为求解线性非齐次两点边值序列问题,并提供了从时域最优状态反馈到频域最优PD控制器参数的优化方法,从而获取系统最优的动态补偿网络,设计出最优PD整定参数,给出其实现算法.最后仿真示例将所提出的方法与传统的线性二次型调节器（LQR）逐次逼近方法相比较,表明该方法具有良好的动态性能和鲁棒性.     

Suboptimal local feedback control for a class of constrained discrete time nonlinear control problems

In this paper, we consider a class of constrained discrete time optimal control problems involving general nonlinear dynamics with fixed terminal time. A method to solve the feedback control problem for a class of unconstrained continuous time nonlinear systems has been proposed previously. In that work, the solution is based on synthesizing an approximate suboptimal feedback controller locally in the neighbourhood of a certain nominal optimal trajectory. This paper expands on the same theme by considering problems involving discrete time systems. Taking advantage of the nature of discrete time systems, a further reduction on the computational effort of synthesising the feedback controller is made possible. Also, this paper extends the applicability of the method to constrained systems. For illustration, a numerical example is solved using the proposed method.     

一类非线性多时滞系统的干扰解耦控制

考虑了一类MIMO非线性多时滞系统的干扰解耦控制问题.在一定条件下,通过构造非线性状态反馈控制规律,确保闭环系统的输出不受干扰影响而且是时滞无关的.基于微分几何理论,给出该状态反馈控制规律存在的充分必要条件.仿真验证了所得结果的有效性.     

一类非线性系统的无超调控制

针对一类严格反馈非线性系统,利用后推法设计一种无超调跟踪控制律.对于阶数小于4的对象,给出了控制律参数应满足的充要条件;对于阶数更高的对象,给出了求解一个充分条件的方法.该控制律适用于零与非零初始条件,且参考输出不限制为阶跃信号.通过两个数值仿真例子验证了所提出控制律的有效性.     

Adaptive neural control for a class of uncertain nonlinear systems with unknown time delay

A neural network (NN)‐based robust adaptive control design scheme is developed for a class of nonlinear systems represented by input–output models with an unknown nonlinear function and unknown time delay. By approximating on‐line the unknown nonlinear functions with a three‐layer feedforward NN, the proposed approach does not require the unknown parameters to satisfy the linear dependence condition. The control law is delay independent and possible controller singularity problem is avoided. It is proved that with the proposed neural control law, all the signals in the closed‐loop system are semiglobally bounded in the presence of unknown time delay and unknown nonlinearity. A simulation example is presented to demonstrate the method. Copyright © 2008 John Wiley & Sons, Ltd.     

Networked iterative learning control approach for nonlinear systems with random communication delay

This paper constructs a proportional-type networked iterative learning control (NILC) scheme for a class of discrete-time nonlinear systems with the stochastic data communication delay within one operation duration and being subject to Bernoulli-type distribution. In the scheme, the communication delayed data is replaced by successfully captured one at the concurrent sampling moment of the latest iteration. The tracking performance of the addressed NILC algorithm is analysed by statistic technique in virtue of mathematical expectation. The analysis shows that, under certain conditions, the expectation of the tracking error measured in the form of 1-norm is asymptotically convergent to zero. Numerical experiments are carried out to illustrate the validity and effectiveness.     

Multiple model adaptive control for a class of nonlinear systems with unknown control directions

This study introduces an improved multiple model adaptive control (MMAC) algorithm for a class of nonlinear discrete-time systems. The controller consists of a linear direct adaptive controller, a neural network-based nonlinear direct adaptive controller and a switching mechanism. The assumption of the nonlinear term is relaxed by incorporating a parameter estimator with an augmented error. The control direction of the system is not required to be known by employing a linear direct adaptive controller with the discrete Nussbaum gain and future output predictions. The stability of the closed-loop systems applying the proposed MMAC method is proved and the improved transient performance of the system is illustrated by the simulation results.     

Observer-based control of a class of time-delay nonlinear systems having triangular structure

Time-delay systems constitute a special class of dynamical systems that are frequently present in many fields of engineering. It has been shown in the literature that the existence of a stabilizing observer-based controller is related to delay-dependent conditions that are generally satisfied for a small time delay. Motivating works towards reducing the conservatism of the results are among the on-going research topics especially when partial-state measurements are imposed. This paper investigates the problem of observer-based stabilization of a class of time-delay nonlinear systems written in triangular form. First, we show that a delay nonlinear observer is globally convergent under the global Lipschitz condition of the system nonlinearity. Then, it is shown that a parameterized linear feedback that uses the observer states can stabilize the system whatever the size of the delay. An illustrative example is provided to approve the theoretical results.     

Reinforcement learning-based event-triggered optimal control for unknown nonlinear systems with input delay

The optimal control issue of discrete-time nonlinear unknown systems with time-delay control input is the focus of this work. In order to reduce communication costs, a reinforcement learning-based event-triggered controller is proposed. By applying the proposed control method, closed-loop system's asymptotic stability is demonstrated, and a maximum upper bound for the infinite-horizon performance index can be calculated beforehand. The event-triggered condition requires the next time state information. In an effort to forecast the next state and achieve optimal control, three neural networks (NNs) are introduced and used to approximate system state, value function, and optimal control. Additionally, a M NN is utilized to cope with the time-delay term of control input. Moreover, taking the estimation errors of NNs into account, the uniformly ultimately boundedness of state and NNs weight estimation errors can be guaranteed. Ultimately, the validity of proposed approach is illustrated by simulations.     

Linear adaptive control of a class of SISO nonaffine nonlinear systems

This paper addresses the problem of linear adaptive control for a class of uncertain continuous-time single-input single-output (SISO) nonaffine nonlinear dynamic systems. Using the implicit function theory, the existence of an ideal controller which can achieve control objectives is firstly demonstrated. However, this ideal controller cannot be known and computed even if the system model is well known. The aim of our work is to construct this unknown ideal controller using a simple linear controller with the free parameters updated online by a stable adaptation mechanism designed to minimise the error between the unknown ideal controller and the used linear controller. Since the mathematical model of the system is assumed unknown in this work, the proposed control scheme can be regarded as a simple model free controller for the studied class of nonaffine systems. We prove that the closed-loop system is stable and all the signals are bounded. An application of the proposed linear adaptive controller for a nonaffine system is illustrated through the simulation results to demonstrate the effectiveness of the proposed control scheme.     

Robust adaptive control of nonlinear systems with unknown time delays

In this paper, robust adaptive control is presented for a class of parametric-strict-feedback nonlinear systems with unknown time delays. Using appropriate Lyapunov-Krasovskii functionals, the uncertainties of unknown time delays are compensated for. Controller singularity problems are solved by employing practical robust control and regrouping unknown parameters. By using differentiable approximation, backstepping design can be carried out for a class of nonlinear systems in strict-feedback form. It is proved that the proposed systematic backstepping design method is able to guarantee global uniform ultimate boundedness of all the signals in the closed-loop system and the tracking error is proven to converge to a small neighborhood of the origin. Simulation results are provided to show the effectiveness of the proposed approach.     

Finite‐time optimal control for interconnected nonlinear systems

This work addresses the finite‐time optimal control problem for a class of interconnected nonlinear systems with powers of positive odd rational numbers. A series of homogeneous controllers, which are capable of guaranteeing the local finite‐time stability of the closed‐loop systems, are first developed using the adding one power integrator method and backstepping technique. Then, the nested saturation controllers are further proposed to achieve global finite‐time stability. Furthermore, the corresponding design parameters are optimized, and thus, an optimal controller is obtained. A numerical simulation example is finally given to illustrate the effectiveness of the proposed control strategy.     

非线性时变系统的自耦PID控制方法

针对一类非线性时变系统的控制问题,使用了一种基于自耦PID的控制理论方法.该方法首先将时变不确定、模型不确定定义为一个扩张状态,并将非线性时变系统映射为未知线性系统;然后使用自耦PID控制方法构造了一个闭环系统;最后在复频域分析了闭环系统的鲁棒稳定性和抗扰动鲁棒性.理论分析与仿真结果都表明了本文控制方法具有良好的动态品质和稳态性能,在未知复杂系统控制领域具有广泛的应用前景.     

Suboptimal control for nonlinear systems: a successive approximation approach

This paper presents a successive approximation approach (SAA) designing optimal controllers for a class of nonlinear systems with a quadratic performance index. By using the SAA, the nonlinear optimal control problem is transformed into a sequence of nonhomogeneous linear two-point boundary value (TPBV) problems. The optimal control law obtained consists of an accurate linear feedback term and a nonlinear compensation term which is the limit of an adjoint vector sequence. By using the finite-step iteration of the nonlinear compensation sequence, we can obtain a suboptimal control law. Simulation examples are employed to test the validity of the SAA.