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The application of Pontryagin's maximum principle to the optimization of linear systems with time delays results in a system of coupled twopoint boundaryvalue problems involving both delay and advance terms.




 In this paper the suboptimal control of linear systems with timedelay is studied. We introduce an increment of state terms as an additional disturbance, and use the asymptotic approximation method in differential equation theory to solve the problem. We transform the twopoint boundary value problem with timedelay terms and timeadvance terms to a group of problems without timedelay terms and timeadvance terms according to the concept of nondelay transformation approach. By taking the... In this paper the suboptimal control of linear systems with timedelay is studied. We introduce an increment of state terms as an additional disturbance, and use the asymptotic approximation method in differential equation theory to solve the problem. We transform the twopoint boundary value problem with timedelay terms and timeadvance terms to a group of problems without timedelay terms and timeadvance terms according to the concept of nondelay transformation approach. By taking the N th iterative value of the optimal solutions, we obtain a suboptimal control law. A simulation example is given to test the validity of the algorithm. When the system of the timedelay is small, the number of iterative times may be decreased greatly. Therefore the method is more suitable for the suboptimal control of small timedelay systems.  该文研究线性时滞定常系统的次优控制问题。根据无滞后转换法的思想 ,先引入状态向量的增量 ,将其视为附加扰动输入 ,再利用微分方程的逐次逼近法 ,将既含有时滞项又含有超前项的两点边值问题化为既不含时滞项又不含超前项的两点边值问题族。然后 ,把第 N次逼近得到的控制律近似为系统的最优控制律 ,得到次优控制律。并用实例仿真验证了该算法的有效性。该方法可使小时滞系统的迭代次数大大减少 ,因此尤其适合于小时滞系统的次优控制。  The suboptimal control for linear large_scale systems with small time_delay is studied. First, all the increments of state terms and interconnected terms among subsystems are considered as additional disturbances. Then by using the non_delay transformation approach and the successive approximation method of differential equations, we transform a higher order two_point boundary value problem with time_delay and time_advance terms into a group of decoupled lower order ones without time_delay and time_advance... The suboptimal control for linear large_scale systems with small time_delay is studied. First, all the increments of state terms and interconnected terms among subsystems are considered as additional disturbances. Then by using the non_delay transformation approach and the successive approximation method of differential equations, we transform a higher order two_point boundary value problem with time_delay and time_advance terms into a group of decoupled lower order ones without time_delay and time_advance terms. Finally, the definite iterative values of optimal solutions are taken as a suboptimal control law for the large_scale system. For the linear large_scale systems with small time_delay, iterative times computing suboptimal control law can be greatly reduced. Therefore, this approach is specially suited for the suboptimal controller design for the linear large_scale systems with small time_delay.  研究具有小时滞的线性大系统的次优控制问题 .首先将子系统状态向量增量和子系统耦合项视为大系统附加扰动输入 .再利用无滞后转换法的思想结合微分方程的逐次逼近法 ,将一个既含有时滞项又含有超前项的高阶两点边值问题分解为若干个解耦的、既不含时滞项又不含超前项的低阶两点边值问题族 .最后用最优控制的有限次逼近结果作为大系统的次优控制律 .对小时滞线性大系统而言 ,利用此方法可使计算次优控制律的迭代次数大大减少 ,因此该方法尤其适合于具有小时滞的线性大系统的次优控制器设计  The suboptimal control for nonlinear systems with timedelay in state variables is considered, and a successive approximation approach is proposed. For the nonlinear twopoint boundary value problem with both timedelay terms and timeadvanced terms driven by the optimal control theory, a sequence of nonhomogeneous linear twopoint boundary value problems are constructed, the solution sequence of which uniformly converges to the optimal solution of the original problem. Some finite iterative result... The suboptimal control for nonlinear systems with timedelay in state variables is considered, and a successive approximation approach is proposed. For the nonlinear twopoint boundary value problem with both timedelay terms and timeadvanced terms driven by the optimal control theory, a sequence of nonhomogeneous linear twopoint boundary value problems are constructed, the solution sequence of which uniformly converges to the optimal solution of the original problem. Some finite iterative result of the twopoint boundary value problem sequence is taken as a suboptimal control law of the system. The simulation results show the effectiveness of the presented algorithm.  对状态变量含有时滞的非线性系统的次优控制问题进行了研究,提出了一种次优控制的逐次逼近设计方法.针对由最优控制理论导出的既含有时滞项又含有超前项的非线性两点边值问题,构造了其解序列一致收敛于原问题最优解的非齐次线性两点边值问题序列.从而将两点边值问题解序列的有限次迭代结果作为系统的次优控制律.仿真结果表明了所提出方法的有效性.   << 更多相关文摘 
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