A method for solving a boundary problem for a nonlinear controlled system

An algorithm is proposed for constructing a control function that transfers a wide class of nonlinear systems of ordinary differential equations from an initial state to an arbitrarily small neighborhood of a given terminal state. The algorithm is convenient for numerical implementation. Taking into account the restrictions on the control and phase coordinates, a constructive criterion is obtained for choosing terminal states for which this transfer is possible. The problem of an interorbital flight is considered and modeled numerically.     

Method for solving a boundary problem for a nonlinear control system with incomplete information

An easy-to-implement numerical method is proposed for synthesizing a feedback control function that transfers a wide class of nonlinear stationary systems from an initial state to a given terminal state with allowance for measured data. A constructive criterion is obtained for choosing terminal states for which this transfer is guaranteed. The problem of an interorbital flight is considered and numerically simulated.     

Solving a Local Boundary Value Problem for a Nonlinear Nonstationary System in the Class of Feedback Controls

An algorithm convenient for numerical implementation is proposed for constructing differentiable control functions that transfer a wide class of nonlinear nonstationary systems of ordinary differential equations from an initial state to a given point of the phase space. Constructive sufficient conditions imposed on the right-hand side of the controlled system are obtained under which this transfer is possible. The control of a robotic manipulator is considered, and its numerical simulation is performed.     

A method of solving boundary-value problems for a non-linear control system allowing for delay in the control action

An algorithm is developed for constructing a control function that guarantees that a wide class of non-linear control systems, described by ordinary differential equations, is transferred from an initial state into a specified final state, allowing for constraints on the system and a delay in the control signal. A constructive criterion is found for the choice of the final states and the value of the delay in the control signal for which the above transfer is possible. An interorbital flight problem is studied as an example and is modelled numerically.     

An algorithm for the calculation of transfer functions of two variable systems or networks

An algorithm is described to derive the transfer function of two variable networks or systems from the state equations. The algorithm is suitable for computer-aided procedures and gives recurrence relations from which the coefficients of the transfer function can be calculated. An alternative to this algorithm is to solve the state equations directly which requires a matrix inversion step at each frequency. By using the algorithm the coefficients of the transfer function are calculated only once and this offers substantial saving in computer time.     

Synthesis of Control Systems with a Specified Characteristic Polynomial

A synthesis method is proposed for single-loop modal control systems for discrete and continuous plants, including plants with delay. The controllers are designed in the operator space given the closed-loop transfer function. The proposed method can be used to synthesize both free and forced motion in a closed-loop system.     

一类时滞非线性系统的采样迭代学习控制

本文针对一类时滞非线性系统提出一种采样迭代学习控制算法,严格证明了该算法的指数收敛性.当系统满足所给出的条件时,跟踪误差以指数速率收敛至一个与采样周期有关的误差范围内.     

Transfer pricing in a dynamic marketing-operations interface

A transfer price mechanism is proposed to coordinate the strategies of the marketing and operations functional areas operating in a dynamic interface environment in a decentralized firm. Marketing and operations are strategic decision-makers in a differential game, in which marketing has price and advertising and operations has production as control variables, and advertising goodwill and production backlog are state variables. A constant transfer price is entered into the objective functionals for marketing and operations, and subgame perfect feedback strategies are derived for price, advertising, and production as functions of the state variables. The feedback strategies allow a solution for the dynamic system involving goodwill and backlog, and the total payoff to the firm, the sum of the payoffs to marketing and operations, is determined as a function of the transfer price. Finally, for certain parameter conditions an interior maximum of the payoff function is achieved, and the optimal transfer price is identified.     

一类不确定混沌系统的自适应跟踪控制

对一类不确定混沌系统 ,讨论了系统的自适应跟踪控制问题 .基于 Lyapunov函数方法 ,构造出了一类新的自适应控制器 .该控制器的构造简单 ,并能控制着混沌系统的状态全局渐近跟踪预先给定的任何有界轨线 .仿真实例验证了所得控制器的有效性 .     

A semi-analytical direct optimal control solution for strongly excited and dissipative Hamiltonian systems

A semi-analytical direct optimal control solution for strongly excited and dissipative Hamiltonian systems is proposed based on the extended Hamiltonian principle, the Hamilton-Jacobi-Bellman (HJB) equation and its variational integral equation, and the finite time element approximation. The differential extended Hamiltonian equations for structural vibration systems are replaced by the variational integral equation, which can preserve intrinsic system structure. The optimal control law dependent on the value function is determined by the HJB equation so as to satisfy the overall optimality principle. The partial differential equation for the value function is converted into the integral equation with variational weighting. Then the successive solution of optimal control with system state is designed. The two variational integral equations are applied to sequential time elements and transformed into the algebraic equations by using the finite time element approximation. The direct optimal control on each time element is obtained respectively by solving the algebraic equations, which is unconstrained by the system state observed. The proposed control algorithm is applicable to linear and nonlinear systems with the quadratic performance index, and takes into account the effects of external excitations measured on control. Numerical examples are given to illustrate the optimal control effectiveness.     

模糊输入时滞系统的输出反馈控制及稳定性分析

针对一类状态不可测的模糊输入时滞系统,应用平行分布补偿算法(PDC),设计了模糊观测器,提出了基于模糊观测器的输出反馈控制方法,给出了保证模糊时滞系统渐近稳定的新的充分条件.应用广义Lyapunov函数和线性矩阵不等式方法,证明了模糊输入时滞系统的渐近稳定性,同时给出了控制和观测增益矩阵的分离设计算法.仿真结果进一步验证了所提出的方法和条件的有效性.     

一类时滞非线性系统的自适应模糊控制

对于一类SISO输入时滞已知,状态时滞不确定但有上界的能采用后推设计方法的非线性系统提出一种基于后推设计、自适应模糊控制和滑模控制的控制方案.通过状态变换,把输入时滞系统转化为无输入时滞的系统.用模糊系统来估计系统的未知连续函数,对转化后的新系统设计自适应滑模控制器,使得新系统的状态有界,通过递推证得原系统的状态半全局一致有界.     

Resource-optimal control of linear systems

A numerical method for minimizing the resource consumption for linear dynamical systems is proposed. It is based on forming a finite-time control that steers the linear system from an arbitrary initial state to the desired terminal state in a given fixed time; this control gives an approximate solution of the problem. It is shown that the structure of the finite-time control makes it possible to determine the structure of the resource-optimal control. A method for determining an initial approximation is described, and an iterative algorithm for calculating the optimal control is proposed. A system of linear algebraic equations relating the deviations of the initial conditions in the adjoint system to the deviations of the phase coordinates from the prescribed terminal state at the terminal point in time is obtained. A computational algorithm is described. The radius of local convergence is found and the quadratic rate of convergence is established. It is proved that the computational procedure and the sequence of controls converge to the resource-optimal control.     

Performance analysis of a distributed fixed-step power control algorithm via window concept in cellular mobile systems

In cellular mobile systems, the received carrier-to-interference ratio (CIR) can be maintained within the desirable range provided that the path gain remains approximately constant over a number of consecutive power control steps. However, when channels suffer short-term fading, it is not clear whether existing power control algorithms remain convergent. This paper proposes a distributed fixed-step power control algorithm with binary feedback via window concept for cellular mobile systems. The essence of the proposed algorithm is that the power control step size can be regulated by window size. The performance of the proposed scheme is analyzed in short-term fading channels. A sufficient condition for system stability is derived using a simple received CIR model and a power control window. It is shown herein that the bound of the received CIR of each user varies as a function of the target CIR, the size of the power control step and the link gain. The analysis and simulation results show that if the step size is properly set according to the window size, the proposed algorithm can achieve a small convergence region and a fast convergence rate.     

Global finite-time stabilization of a class of nonlinear system based on a dynamic gain approach

In this paper, finite-time control problem of a class of nonlinear systems is considered. By using a dynamic gain-based backstepping approach, a state feedback controller involving the dynamic gains is constructed with the help of appropriate Lyapunov function, which guarantees the closed-loop system to be globally finite-time stabilization. A simulation example is provided to illustrate the effectiveness of the proposed control scheme.     

Synthesis of discrete stabilization for a nonlinear stationary control system under incomplete information

The paper presents an algorithm for synthesizing discrete control functions in the case of incomplete information and discrete measurer. Under these control functions, solutions of a wide class of nonlinear stationary systems are transferred from the given initial state into an arbitrary neighborhood of the origin with due account taken of the constraints imposed on the control. Constructive criteria for the selection of the initial states and discretization step are derived, which ensure implementation of the suggested algorithm. The efficiency of the method is illustrated with numerical simulation of the problem of interorbital transfer.     

Adaptive projective synchronization for a class of switched chaotic systems

This paper addresses the problem of projective synchronization of chaotic systems and switched chaotic systems by adaptive control methods. First, a necessary and sufficient condition is proposed to show how many state variables can realize projective synchronization under a linear feedback controller for the chaotic systems. Then, accordingly, a new algorithm is given to select all state variables that can realize projective synchronization. Furthermore, according to the results of the projective synchronization of chaotic systems, the problem of projective synchronization of the switched chaotic systems comprised by the unified chaotic systems is investigated, and an adaptive global linear feedback controller with only one input channel is designed, which can realize the projective synchronization under the arbitrary switching law. It is worth mentioning that the proposed method can also realize complete synchronization of the switched chaotic systems. Finally, the numerical simulation results verify the correctness and effectiveness of the proposed method.     

Real-time calculation of current optimal feedbacks for a delay system

A linear optimal control problem for a nonstationary system with a single delay state variable is examined. A fast implementation of the dual method is proposed in which a key role is played by a quasi-reduction of the fundamental matrices of solutions to the homogeneous part of the delay models under analysis. As a result, an iteration step of the dual method involves only the integration of auxiliary systems of ordinary differential equations over short time intervals. A real-time algorithm is described for calculating optimal feedback controls. The results are illustrated by the optimal control problem for a second-order stationary system with a fixed delay.     

Synthesis of linear systems with desired equivalent form

A method for feedback synthesis of linear control systems with desired linearly equivalent form of the closed loop system matrix is proposed. The method is based on the serial canonical form of linear multivariable systems which is an alternative to the Luenberger canonical form. A stable computational algorithm for finding the serial canonical form using orthogonal similarity transformations is described. The algorithm for synthesis involves a simple recurrent procedure and gives the possibility to achieve any attainable equivalent form of the closed loop system. The results obtained are extended to the synthesis of reduced order state observers.