Distributed optimal control of multiple systems

This article considers distributed optimal control of multiple linear systems. Distributed approximately optimal controllers are proposed for each system with the aid of communications between systems. The proposed controllers make the states of the closed-loop systems exponentially converge to the states of the closed-loop systems with the centralised optimal controllers if the communication digraph is strongly connected. If the communication digraph is switching and there are communication delays, the proposed controllers also make the states of the closed-loop systems exponentially converge to the states of the closed-loop systems with the centralised optimal controllers. Simulation results show effectiveness of the proposed controllers.     

Optimal discrete systems using time-weighted performance index withprespecified closed-loop eigenvalues

A design problem of optimal regulators for discrete-time linear multi-input systems is investigated for the prespecified closed-loop eigenvalues. Then the design freedom, which remains after the prespecified closed-loop eigenvalues are assigned, is used to minimize a time-weighted performance index. Necessary conditions for the optimality of the controller that satisfies the prespecified closed-loop eigenvalues are derived and an algorithm for computing the optimal constant feedback gain is presented     

二次型最优离散系统的两个必要条件

本文给出了线性定常二次型最优离散系统的两个必要条件,得到了单输入单输出系统开环特征多项式系数a_i和最优闭环特征多项式系数b_i与权阵Q之间的直接关系,所得结论有益于设计一个具有指定闭环极点的最优控制系统。     

考虑成员企业风险态度的制造商资金约束闭环供应链定价与回收决策

针对制造商资金约束的闭环供应链,考虑制造商、零售商和回收商面对市场需求不确定性表现出不同的风险态度,研究闭环供应链如何确定其最优定价与回收决策.首先,依据均值-方差法给出制造商、零售商、回收商和闭环供应链的效用函数;然后,基于博弈论的思想分别确定集中式决策下闭环供应链的最优策略和效用,以及分散式决策下制造商、零售商和回收商的最优策略和效用;最后,分析相关参数对最优策略和效用的影响.研究结果表明,制造商、零售商和回收商的风险态度在很大程度上能够影响其最优批发价格、最优零售价格及最优回收率,进而影响其效用.贷款利率能够影响制造商、零售商、回收商和闭环供应链的效用,且对资金约束的制造商的效用影响最为显著.     

线性定常系统的综合性最优控制问题

本文讨论了具有二次型性能指标的线性定常系统的降低性能指标灵敏度、降低轨迹灵敏 度和配置闭环极点的综合性最优控制问题,提出了新的综合性能指标,从而得到了易于计算 的结果;解决了多参数变化时降低轨迹灵敏度的综合性最优控制问题;推导了闭环特征值对 Q阵的梯度阵公式,提出了一种配置互异的全部闭环极点Q阵算法,并给出了算例.     

Anti-windup synthesis via sampled-data piecewise affine optimal control

Discrete-time receding horizon optimal control is employed in model-based anti-windup augmentation. The optimal control formulation enables designs that minimize the mismatch between the unconstrained closed-loop response with a given controller and the constrained closed-loop response with anti-windup augmentation. Recently developed techniques for off-line computation of the constrained linear regulator's solution, which is piecewise affine, facilitate implementation. The resulting sampled-data, anti-windup closed-loop system's properties are established and its performance is demonstrated on a simulation example.     

二阶离散系统最优闭环极点配置

本文采用逆方法分析二阶离散系统最优闭环极点配置问题,只要所指定的闭环特征方程的系数满足文中推导出的条件式,就可以通过状态反馈法构成具有希望闭环极点配置的最优闭环系统,无需进一步验证其它最优条件。     

A recursive algorithm for ARMAX model identification in closed loop

The joint problem of the recursive estimation of an optimal predictor for the closed-loop system and the unbiased parameter estimation of an ARMAX plant model in closed-loop operation is considered. A special reparameterized optimal predictor for the closed-loop is introduced. This allows a parameter estimation algorithm for the plant model to be derived which is globally asymptotically stable in a deterministic environment and gives asymptotically unbiased parameters estimates under richness conditions     

线性离散状态空间的最优l_∞控制器设计

基于开环零点 ,利用状态反馈性质 ,导出求取满足最优l∞ 误差序列的一个插值条件 .由最优误差序列得到闭环系统的马尔可夫参数 ,从而求取最优闭环极点 ,然后 ,应用一般的极点配置方法解出最优反馈矩阵 .仿真分析验证了本文的结果     

多变量数字鲁棒最优控制器的设计及应用

针对线性多变量离散控制系统,给出一种新的鲁棒最优控制器的设计方法．该方法提出了多变量系统的行特征函数的设计新思想,实现等价系统的动态解耦,使闭环控制系统的传递函数矩阵为正规矩阵,达到鲁棒H∞最优稳定;进一步,通过对等价解耦控制系统应用l∞最优控制方法,又能使原闭环控制系统获得最优时域指标．通过在某纸机3种定量和水分控制系统中的在线应用,验证了数字控制器的最优性与鲁棒性．     

Synthesis of sub-optimal feedback controls for a class of distributed parameter systems†

Technique are derived for the synthesis of sub-optimal feedback controls for parabolic and first-order hyperbolic systems. An explicit result for the time-invariant gain of a specified controller is obtained by a least square approximation of the closed-loop control to the optimal open-loop control. If a least square approximation of the state trajectories is used, a parameter search is shown to give the time-invariant gain. A time-varying gain can be obtained by a re-definition of the original optimal control problem, again with the controller functionality specified. The only require-mont in the closed-loop synthesis is that an optimal open-loop solution exists and is computable.     

Two-degree-of-freedom ?2-optimal tracking with preview

A simple SISO two-degree-of-freedom pole-placement design method is presented that provides ?₂-optimal tracking of a given reference signal. The closed-loop pole locations are first chosen by the system designer. The closed-loop zeros are then placed in an optimal fashion by a computationally inexpensive algorithm to achieve asymptotic tracking with an optimal transient response. The preview approach, which has become a common method for dealing with systems which have non-minimum phase behavior, can then optionally be used to further improve the transient behavior for both minimum phase and non-minimum phase systems. Unlike previous results based on the preview approach, the solution presented here takes into consideration the closed-loop pole dynamics, and is ?₂ optimal with respect to all other two-degree-of-freedom preview controllers with the same closed-loop poles. A simple solution to the H₂ model matching problem, where the design parameter Q is not rational, but polynomial, is the heart of the solution method.     

System equivalence in a class of nonlinear optimal control problems

In a family of nonlinear optimal control problems, equivalence classes of problems that yield identical optimal closed-loop systems are delineated. The equivalence relations are established as one-to-one correspondences between the solutions of the Hamilton-Jacobi equations associated with the problems. Two such equivalence relations are presented. These allow an arbitrary problem in the family to be reduced to an equivalent basic standard form of problem. Also, a new formal procedure for solving this basic problem is given that allows the determination of coefficients in the series expansion of the optimal closed-loop system. The set of algebraic equations to be solved is considerably simpler than that derived by other methods.     

Reduction of controller fragility by pole sensitivity minimization

Presents a method for the reduction of controller fragility. The method is based on the sensitivity of closed-loop poles to perturbations in the controller parameters. By means of a state space parameterization of the controller, the closed-loop pole sensitivity can be reduced. A controller fragility measure based on the closed-loop pole sensitivity is proposed. Conditions for the optimal state-space realization of the controller are presented, along with a numerical method for obtaining the solution     

On constrained infinite-time linear quadratic optimal control with stochastic disturbances

In this work, we study the infinite-time linear quadratic optimal control problem for systems with stochastic disturbances and constrained inputs. A number of stochastic problem formulations under the full state information (FSI) structure are considered with a particular focus on the subject of feedback structure and its impact on certainty equivalence. In particular, we clarify results concerning the open-loop hard constrained, closed-loop statistically constrained, and closed-loop hard constrained cases. Extension to the infinite-time framework provides a vehicle for interpreting these controllers and indicates that the last of the three is of most interest to regulation type applications. Additionally, the partial state information problem is considered, and conditions are given for which a separated configuration consisting of the optimal estimator cascaded with the FSI optimal controller remains optimal.     

Optimal realizations of fixed-point implemented digital controllers with the smallest dynamic range

A novel approach is proposed to design optimal finite word length (FWL) realizations of digital controllers implemented in fixed-point arithmetic. A minimax-based search procedure is first formulated to obtain an optimal controller realization that optimizes an FWL closed-loop stability measure. Since this FWL closed-loop stability measure is solely linked to the fractional part or precision of fixed-point format, the resulting realization may not have the smallest dynamic range. A measure is then derived to indicate the dynamic range of fixed-point implemented realization. By choosing an appropriate orthogonal transformation of this dynamic range measure of the optimal precision controller realization, a numerical optimization method is developed to make the controller realization having the smallest dynamic range without sacrificing FWL closed-loop stability robustness. The proposed approach is more efficient than a direct optimization of some combined FWL closed-loop stability and dynamic range measure via a numerical means. The proposed approach is established within a unified framework that includes both the shift and delta operator parameterizations, which makes it possible to compare the closed-loop stability characteristics of the optimal FWL controller realizations using shift and delta operators, respectively. Through analysing the simulation results of a design example, some useful insights and understandings are obtained regarding the FWL controller realizations based on shift and delta operators.     

Optimal SAM defense system: An application of optimal control concept to operations research

An operations research problem concerning the optimal surface-to-air-missile (SAM) firing pattern to defend a surface target is solved via applications of the concept of closed-loop (feedback) and open-loop optimal control. The SAM defense problem is formulated as a Markov decision process with the number of SAM's in each salvo as the decision variable. Interesting cases, including the presence of imperfect sensor observation and a bound on the number of SAM's available are considered. The principle of dynamic programming and the technique of nonlinear integer programming are applied to reach closed-loop and open-loop solutions. Numerical examples are given for illustration.     

Parallel Optimal Control for Weakly Coupled Nonlinear Systems Using Successive Galerkin Approximation

This technical note presents a new algorithm for the closed-loop parallel optimal control of weakly coupled nonlinear systems with respect to performance criteria using the successive Galerkin approximation (SGA). By using the weak coupling theory, the optimal control law can be obtained from two reduced-order optimal control problems in parallel, but the resulting problem is difficult to solve for nonlinear systems. In order to overcome the difficulties inherent in the nonlinear optimal control problem, the parallel optimal control laws are constructed in terms of the approximated solutions to two independent Hamilton-Jacobi-Bellman equations using the SGA method. One of the purposes of this note is to design the closed-loop parallel optimal control law for the weakly coupled nonlinear systems using the SGA method. The second is to reduce the computational complexity when the SGA method is applied to the high-order weakly coupled systems.      

Open-loop and closed-loop robust optimal control of batch processes using distributional and worst-case analysis

The recognition that optimal control trajectories for batch processes can be highly sensitive to model uncertainties has motivated the development of methods for explicitly addressing robustness during batch processes. This study explores the incorporation of robust performance analysis into open-loop and closed-loop optimal control design. Several types of robust performance objectives are investigated that incorporate worst-case or distributional robustness metrics for improving the robustness of batch control laws, where the distributional approach computes the distribution of the performance index caused by parameter uncertainty. The techniques are demonstrated on a batch crystallization process. A comprehensive comparison of the robust performance of the open-loop and closed-loop system is provided.