关于Hybrid线性二次最优控制问题

本文证明了文[3]所讨论的具有Hybrid指标的线性二次最优控制问题实际上可被归入经典的线性二次最优控制问题,并且利用本文的方法还可把更一般的Hybrid线性二次最优控制问题也归人经典的线性二次最优控制问题,从而可借助关于后者的现成的理论推出针对前者的结论.     

一类奇异时滞系统的奇异二次指标最优控制问题

利用基本的代数等价变换，将一类奇异滞后系统的奇异二次指标最优控制问题转化为正常状态滞后系统的非奇异二次指标最优控制问题，并讨论了二的等价性，在一些常规条件下，给出了问题的解，并把最优控制综合为最优状态反馈。     

奇异系统的不定号二次型指标最优控制问题

讨论奇异系统的不定号LQ问题 (二次型指标中的权矩阵含有负特征值的最优控制问题). 首先指出问题的可解性, 并给出了问题等价转化为奇异系统的奇异LQ问题的充要条件. 然后基于等价的奇异系统奇异LQ问题, 给出问题存在唯一最优控制—轨线对的充分条件. 最后用一个算例说明结论的正确性.     

二级倒立摆的二次型最优控制研究

倒立摆系统以其自身的不稳定性而难以控制,也因此成为自动控制实验中验证控制策略优劣的极好的实验装置。针对二级倒立摆系统的平衡控制问题,对其进行数学建模,应用二次型最优控制理论设计了控制器。仿真结果表明,二次型最优控制对于典型非线性自不稳定系统有着很好的控制能力。     

自由时间最优控制问题的一种控制向量参数化方法

针对自由时间最优控制问题,提出一种控制向量参数化（CVP）方法.通过引入时间尺度因子,将自由时间最优控制问题转化为固定时间问题,并将终端时刻作为优化参数.基于CVP方法,最优控制问题被转化为一个非线性规划（NLP）问题.建立目标和约束函数的Hamiltonian函数,通过求解伴随方程获得目标和约束函数的梯度,采用序列二次规划（SQP）方法获得问题的数值解.对于控制有切换结构的优化问题,给出了一种网格精细化策略,以提高控制质量.补料分批反应器最优控制问题的仿真实验验证了所提出方法的有效性.     

线性–非二次最优控制问题的一种解法

讨论了求解状态终端无约束线性–非二次最优控制问题的拟Riccati方程方法, 并据此提出了计算无约束线性–非二次问题之数值解的方法; 然后将这个方法与一种能近似地化有约束问题为无约束问题的惩罚方法结合起来, 给出了一种算法, 可以计算状态终端有约束的线性–非二次最优控制问题之近似解.     

模糊神经网络补偿的伺服系统二次型最优控制

针对伺服系统二次型最优控制存在的问题,提出了基于模糊神经网络补偿的二次型最优控制方法,该控制方法利用模糊神经网络的实时学习能力,能够及时补偿被控对象建模不准确、参数摄动和外界干扰等非线性因素对控制系统性能的影响,增强控制系统的自适应能力,有效提高控制系统的跟踪性能和抗干扰鲁棒性能.仿真试验结果验证了该控制方法的有效性.     

控制能量有界的时不变系统线性二次型最优控制*

本文通过新的途径讨论控制能量有界的时不变系统一二次型最优控制问题，文中通过“不亏损的Ｓ－过程”方法将该问题转化成无约束的时不变性二次理优控制问题，从而利用后者的基本结果给出本文问题的最优控制的最优结构造，结果表明此时最优控制仍由一线性状态反馈控制器确定，但其增益矩阵的选择是与初始状态有关的，并且对某些安始状态还可能出现奇异情况。     

一类受限线性系统的最优控制

研究了一类受限线性系统的最优控制问题.对于输入和状态联合受限线性系统的最优控制,引入多参数二次规划方法进行求解;首先将控制问题转化为标准的多参数二次规划问题,然后应用多参数二次规划方法求得系统的可行状态空间及其子空间,并对每个子空间的求出其时变最优控制率,最后归纳上述过程得到一般性结论.方法不仅能使系统约束的处理更加系统化和透明化,还可以获得系统的显式分段仿射控制率.仿真结果表明了该方法的有效性.     

基于二次型系统最优的同步控制研究

针对塑料制件不同螺距和不同塑料材料性能的变化,研制一种用伺服电机驱动的新型模具脱螺纹同步机构;对这种螺纹型芯由步进驱动、同步升降由伺服电机跟随的螺纹脱模机构,由于生产工艺要求螺纹顶出与模具推板升起的距离严格同步,因此,采用控制器组成两轴电机的运动控制系统,进行调速与位置同步的控制,用基于二次型性能指标最佳的控制系统研究步进伺服驱动实现位置同步;系统能自动适应制件不同螺距和不同塑料材料性能的变化,解决目前由于脱螺纹时不同步所造成的各种质量问题。     

Probabilistic robust design with linear quadratic regulators

In this paper, we study robust design of uncertain systems in a probabilistic setting by means of linear quadratic regulators (LQR). We consider systems affected by random bounded nonlinear uncertainty so that classical optimization methods based on linear matrix inequalities cannot be used without conservatism. The approach followed here is a blend of randomization techniques for the uncertainty together with convex optimization for the controller parameters. In particular, we propose an iterative algorithm for designing a controller which is based upon subgradient iterations. At each step of the sequence, we first generate a random sample and then we perform a subgradient step for a convex constraint defined by the LQR problem. The main result of the paper is to prove that this iterative algorithm provides a controller which quadratically stabilizes the uncertain system with probability one in a finite number of steps. In addition, at a fixed step, we compute a lower bound of the probability that a quadratically stabilizing controller is found.     

Designing parametric linear quadratic regulators for parametric LTI systems via LMIs

This paper addresses the problem of determining parametric linear quadratic regulators (LQRs) for continuous-time linear-time invariant systems affected by parameters through rational functions. Three situations are considered, where the sought controller has to minimise the best cost, average cost, and worst cost, respectively, over the set of admissible parameters. It is shown that candidates for such controllers can be obtained by solving convex optimisation problems with linear matrix inequality (LMI) constraints. These candidates are guaranteed to approximate arbitrarily well the sought controllers by sufficiently increasing the size of the LMIs. In particular, the candidate that minimises the average cost approximates arbitrarily well the true LQR over the set of admissible parameters. Moreover, conditions for establishing the optimality of the found candidates are provided. Some numerical examples illustrate the proposed methodology.     

基于动态规划的约束优化问题多参数规划求解方法及应用

结合动态规划和单步多参数二次规划, 提出一种新的约束优化控制问题多参数规划求解方法. 一方面能得到约束线性二次优化控制问题最优控制序列与状态之间的显式函数关系, 减少多参数规划问题求解的工作量; 另一方面能够同时求解得到状态反馈最优控制律. 应用本文提出的多参数二次规划求解方法, 建立无限时间约束优化问题状态反馈显式最优控制律. 针对电梯机械系统振动控制模型做了数值仿真计算.     

统计特性已知的复杂系统控制器设计方法

对于具有白噪声加性干扰的复杂系统的控制问题,建立了Takagi-Sugeno模糊控制模型,利用Kalman滤波对系统状态信息进行局部估计,用动态规划获得了控制增益,这样导出的控制器具有学习特点,使得闭环系统具有期望的性能指标。以倒立摆为仿真实例,仿真结果表明了所设计控制器的有效性。     

Data-driven policy iteration algorithm for continuous-time stochastic linear-quadratic optimal control problems

This paper studies a continuous-time stochastic linear-quadratic (SLQ) optimal control problem on infinite-horizon. Combining the Kronecker product theory with an existing policy iteration algorithm, a data-driven policy iteration algorithm is proposed to solve the problem. In contrast to most existing methods that need all information of system coefficients, the proposed algorithm eliminates the requirement of three system matrices by utilizing data of a stochastic system. More specifically, this algorithm uses the collected data to iteratively approximate the optimal control and a solution of the stochastic algebraic Riccati equation (SARE) corresponding to the SLQ optimal control problem. The convergence analysis of the obtained algorithm is given rigorously, and a simulation example is provided to illustrate the effectiveness and applicability of the algorithm.     

The explicit linear quadratic regulator for constrained systems

For discrete-time linear time invariant systems with constraints on inputs and states, we develop an algorithm to determine explicitly, the state feedback control law which minimizes a quadratic performance criterion. We show that the control law is piece-wise linear and continuous for both the finite horizon problem (model predictive control) and the usual infinite time measure (constrained linear quadratic regulation). Thus, the on-line control computation reduces to the simple evaluation of an explicitly defined piecewise linear function. By computing the inherent underlying controller structure, we also solve the equivalent of the Hamilton-Jacobi-Bellman equation for discrete-time linear constrained systems. Control based on on-line optimization has long been recognized as a superior alternative for constrained systems. The technique proposed in this paper is attractive for a wide range of practical problems where the computational complexity of on-line optimization is prohibitive. It also provides an insight into the structure underlying optimization-based controllers.     

An algorithm for multi-parametric quadratic programming and explicit MPC solutions

Explicit solutions to constrained linear model predictive control problems can be obtained by solving multi-parametric quadratic programs (mp-QP) where the parameters are the components of the state vector. We study the properties of the polyhedral partition of the state space induced by the multi-parametric piecewise affine solution and propose a new mp-QP solver. Compared to existing algorithms, our approach adopts a different exploration strategy for subdividing the parameter space, avoiding unnecessary partitioning and QP problem solving, with a significant improvement of efficiency.     

A Long-step barrier method for convex quadratic programming

In this paper we propose a long-step logarithmic barrier function method for convex quadratic programming with linear equality constraints. After a reduction of the barrier parameter, a series of long steps along projected Newton directions are taken until the iterate is in the vicinity of the center associated with the current value of the barrier parameter. We prove that the total number of iterations isO(nL) orO(nL), depending on how the barrier parameter is updated.On leave from Eötvös University, Budapest and partially supported by OTKA 2116.     

A new algorithm for numerical solution of dynamic elastic-plastic hardening and softening problems

The objective of this paper is to develop a new algorithm for numerical solution of dynamic elastic-plastic strain hardening/softening problems, particularly for the implementation of the gradient dependent model used in solving strain softening problems. The new algorithm for the solution of dynamic elastic-plastic problems is derived based on the parametric variational principle. The gradient dependent model is employed in the numerical model to overcome the mesh-sensitivity difficulty in dynamic strain softening or strain localization analysis. The precise integration method, which has been used for the solution of linear problems, is adopted and improved for the solution of dynamic non-linear equations. The new algorithm is proposed by taking the advantages of the parametric quadratic programming method and the precise integration method. Results of numerical examples demonstrate the validity and the advantages of the proposed algorithm.     

信赖域共轭梯度法求解二次规划逆问题

为了有效地求解二次规划逆问题,提出了一种求解其对偶问题的子问题的光滑化信赖域共轭梯度法。该方法采用增广拉格朗日法求解其对偶问题,引入光滑函数将对偶问题的子问题转换成连续的无约束优化问题,将信赖域法与共轭梯度法结合,设计出求解二次规划逆问题的算法流程。数值实验结果表明,该方法可行且有效,与牛顿法相比,更适合求解大规模问题。