非线性离散系统最优控制--逐次逼近方法

研究了非线性离散系统最优控制问题,提出一种逐次逼近方法;首先将系统的最优控制问题转化为非线性两点边值问题族,然后通过构造线性两点边值问题族,将非线性两点边值问题转化为非奇次线性两点边值问题族;得到的最优控制律由精确控制项和非线性补偿项两部分组成,精确控制项可以通过求解R iccati方程求出其精确解,非线性补偿项由逐次逼近法求解一族线性伴随向量方程的解序列求得;仿真结果证明了逐次逼近方法的有效性。     

具有小时滞的线性系统次优控制的无滞后转换法

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。     

不确定离散非线性系统的最优滑模控制

研究无限时域的不确定离散非线性系统的最优滑模控制问题.利用非线性系统的逐次逼近算法,通过求非线性两点边值的迭代解的方法构造最优滑模面.通过构造伴随向量的非线性补偿项,得到了由状态反馈项、输入前馈项和伴随向量形式的非线性补偿项组成的系统最优滑模控制律.讨论了控制器的物理实现.仿真结果表明所提出的控制方法是有效的.     

受扰线性离散时滞系统的最优控制设计

研究含外部确定扰动的线性离散时滞系统的最优控制问题.采用逐次逼近算法给出了系统前馈反馈最优控制律的设计方法,利用扰动观测器解决了最优控制律的物理可实现问题.仿真算例表明,该算法有效并容易实现,且对外部确定扰动的鲁棒性优于反馈最优控制.     

线性离散时滞系统次优控制的灵敏度法

研究离散时滞系统的次优控制问题.通过在系统中引入一个灵敏度参数并将系统变量关于灵敏度参数展开Maclaurin级数,使求解最优控制的两点边值问题化为一族线性两点边值问题.利用截取最优控制级数的有限项构成系统的次优控制律.实例证明该方法计算量较少.     

汽车主动悬架系统的前馈反馈最优控制及其仿真

研究汽车主动悬架系统的线性二次型前馈反馈最优控制问题.基于两自由度1/4汽车悬架主动控制模型,通过引入外部扰动补偿向量,给出了系统的有限时域前馈反馈最优控制器的设计方法.该控制器由状态反馈项和前馈补偿项构成,其中前馈项用于补偿路面扰动对系统的影响.控制器的反馈和前馈增益可通过求解矩阵微分方程得到.仿真算例说明了该方法的有效性.     

一类非线性系统次优控制的灵敏度法

本文研究一类非线性定常系统的次优控制问题。通过在系统中引入1个灵敏度参数并将系统变量关于灵敏度参数展开Maclaurin级数，使求解最优控制的非线性两点边值问题化为一族线性两点边值问题。利用截双最优控制级数的有限项求得系统的次优控制律。仿真实例表明，该方法对非线性系统次优控制律的设计是有效的。     

控制时滞与测量时滞采样系统的最优扰动抑制

研究在持续外部扰动作用下,具有控制时滞和测量时滞的采样线性系统前馈-反馈最优扰动抑制控制器设计问题.首先将采样系统离散化为时滞离散系统,再利用模型转换将时滞离散系统转换为无时滞系统;对转换后的系统设计前馈-反馈最优控制器,证明其存在唯一性;通过求解Riccati矩阵方程和Stein方程,设计含控制记忆项的最优控制律,利用控制记忆项补偿时滞对系统产生的影响;然后通过构造降维状态观测器解决前馈控制物理不可实现以及状态不完全可测的问题.最后通过仿真示例,证实运用模型转换方法所设计的最优扰动抑制控制器,能够有效地补偿时滞给系统带来的影响,并实现扰动抑制.     

时滞重随机线性二次最优控制问题

研究一类含有时滞的重随机线性二次最优控制问题,讨论系统的状态变量和控制变量同时含有时滞变量且时滞变量各不相同情况下系统对应的最优控制问题,利用其伴随方程的解,给出此时系统对应的最优控制的显示表达式,并利用经典的平行四边形法则证得最优控制的唯一性.同时定义该系统对应的矩阵Riccati方程,并利用Riccati方程的解刻画最优反馈控制的形式及此时系统对应的值函数.     

一阶线性双曲型复方程的Riemann—Hilbert问题

讨论在单连通区域上的一阶线性双曲型复方程的Ｒｉｅｍａｎｎ－Ｈｉｌｂｅｒｔ边值问题,首先给出边值问题解的表示式,然后用逐次逼近法证明该边值问题解的存在性和唯一性．     

Approximate design of optimal tracking controller for time-delay systems

Time-delay is quite common in practical control systems. The analysis and synthesis of continuous time-delay systems are one of the most difficult mathematical problems with infinite dimensions. The research on the OTC problem for time-delay systems has m…     

Approximately optimal tracking control for discrete time-delay systems with disturbances

Optimal tracking control （OTC） for discrete time-delay systems affected by persistent disturbances with quadratic performance index is considered. By introducing a sensitivity parameter, the original OTC problem is transformed into a series of two-point boundary value （TPBV） problems without time-advance or time-delay terms. The obtained OTC law consists of analytic feedforward and feedback terms and a compensation term which is the sum of an infinite series of adjoint vectors. The analytic feedforward and feedback terms can be found by solving a Riccati matrix equation and two Stein matrix equations. The compensation term can be obtained by using an iteration formula of the adjoint vectors. Observers are constructed to make the approximate OTC law physically realizable. A simulation example shows that the approximate approach is effective in tracking the reference input and robust with respect to exogenous persistent disturbances.     

Approximately optimal tracking control for discrete time-delay systems with disturbances

Optimal tracking control (OTC) for discrete time-delay systems affected by persistent disturbances with quadratic performance index is considered. By introducing a sensitivity parameter, the original OTC problem is transformed into a series of two-point boundary value (TPBV) problems without time-advance or time-delay terms. The obtained OTC law consists of analytic feedforward and feedback terms and a compensation term which is the sum of a infinite series of adjoint vectors. The analytic feedforward and feedback terms can be found by solving a Riccati matrix equation and two Stein matrix equations. The compensation term can be obtained by using an iteration formula of the adjoint vectors. Observers are constructed to make the approximate OTC law physically realizable. A simulation example shows that the approximate approach is effective in tracking the reference input and robust with respect to exogenous persistent disturbances.     

Series-based approximate approach of optimal tracking control for nonlinear systems with time-delay

The optimal output tracking control （OTC） problem for nonlinear systems with time-delay is considered. Using a series-based approximate approach, the original OTC problem is transformed into iteration solving linear two-point boundary value problems without timedelay. The OTC law obtained consists of analytical linear feedback and feedforward terms and a nonlinear compensation term with an infinite series of the adjoint vectors. By truncating a finite sum of the adjoint vector series, an approximate optimal tracking control law is obtained. A reduced-order reference input observer is constructed to make the feedforward term physically realizable. Simulation examples are used to test the validity of the series-based approximate approach.     

Optimal disturbances rejection control for singularly perturbed systems with time-delay

The optimal control design for singularly perturbed time-delay systems affected by external disturbances is considered. Based on the decomposition theory of singular perturbation, the system is decomposed into a fast subsystem without time-delay and a slow time-delay subsystem with disturbances. The optimal disturbances rejection control law of the slow subsystem is obtained by using the successive approximation approach (SAA) and feedforward compensation method. Further, the feedforward and feedback composite control (FFCC) law for the original problem is developed. The FFCC law consists of linear analytic terms and a time-delay compensation term which is the limit of the solution sequence of the adjoint vector equations. A disturbance observer is introduced to make the FFCC law physically realizable. Numerical examples show that the proposed algorithm is effective.