Optimal control of an elliptic system with conjugation conditions and Neumann boundary conditions

New optimal control problems for distributed systems whose state is described by Neumann boundary-value problems with conjugation conditions and non-unique solutions are constructed and analyzed. Highly accurate computation schemes for discretization of optimization problems are proposed for the case where the control set coincides with a complete Hilbert space.Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 93– 111, November–December 2004.The study was supported by the State Fund for Fundamental Research.This revised version was published online in April 2005 with a corrected cover date.     

Optimal control of the order of asymptotics for elliptic equations with fast oscillating coefficients. I. Formal constructions

Formal algorithms for complete asymptotic decompositions of solutions to optimal globally bounded control problems for elliptic equations with fast oscillating coefficients are constructed. If the kernel of a differential operator of the initial problem is nonzero, asymptotics of different orders may exist in the control system.Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 84–95, September–October 2004.     

Computational Finite-Element Schemes for Optimal Control of an Elliptic System with Conjugation Conditions

New optimal control problems are considered for distributed systems described by elliptic equations with conjugate conditions and a quadratic minimized function. Highly accurate computational discretization schemes are constructed for the case where a feasible control set coincides with the full Hilbert space of controls.     

Optimal Control of an Elliptic-Parabolic System with Conjugation Conditions

New optimal control problems for distributed systems described by initial boundary-value problems are considered in the paper for an elliptic-parabolic equation with conjugation conditions and quadratic cost functions. Theorems of existence of a unique optimal control are proved for all the considered cases.     

Optimal control for linear systems with state equality constraints

This paper deals with the optimal control problem for linear systems with linear state equality constraints. For deterministic linear systems, first we find various existence conditions for constraining state feedback control and determine all constraining feedback gains, from which the optimal feedback gain is derived by reducing the dimension of the control input space. For systems with stochastic noises, it is shown that the same gain used for constraining the deterministic system also optimally constrains the expectation of states inside the constraint subspace and minimizes the expectation of the squared constraint error. We compare and discuss performance differences between unconstrained (using penalty method), projected, and constrained controllers for both deterministic and stochastic systems. Finally, numerical examples are used to demonstrate the performance difference of the three controllers.     

在逐点状态约束下一个四阶线性系统的时间最优控制

在逐点状态约束下,最优控制问题的求解是很困难的,已有的最大值原理和形态规划理论很难用来求解在逐点状态约束下最优控制问题.本文讨论逐点状态约束下一个四阶线性系统的时间最优控制问题.我们采用转换的方法给出了最优时间与最优控制的具体表达式.     

状态和输入受限的切换奇异布尔控制网络的最优控制

本文研究了状态和输入均受限的切换奇异布尔控制网络的最优控制问题.利用矩阵半张量积方法获得受限切换奇异布尔控制网络的等价代数形式.然后通过类似针变化得到了存在最优控制的必要条件,并且提出了一个算法设计切换序列和控制策略使收益函数最大化.最后给出例子验证所得结果的有效性.     

Optimal Control of a Conventionally Correct System with Conjugation Conditions

New optimal control problems are constructed and considered for distributed systems whose states are described by Neumann boundary-value problems with conjugation conditions and non-unique solutions. The paper proposes accurate higher-order computation schemes for discretization of optimization problems for the case where a control set coincides with a full Hilbert space.     

对迟滞三明治系统基于Duhem算子的自适应控制

对具有迟滞非线性的三明治系统,设计了基于Duhem算子的神经网络自适应控制器.首先对前端动态子系统进行近似补偿;然后用Duhem算子描述所提出的迟滞状态,用神经网络逼近迟滞状态与迟滞输出的关系,实现对迟滞非线性的建模.基于该迟滞模型并采用伪控制技术设计神经网络自适应控制器,通过Lyapunov方法证明了系统的稳定性,并推导出神经网络的权值自适应调整律和控制律.最后通过仿真验证了该方案的有效性.     

Optimal control of the dynamic state of a thin compound plate

This paper addresses new optimal control problems for dynamic deflections of a thin compound plate with quadratic cost functionals. Theorems on the existence of optimal controls are proved for all the cases considered. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 151–175, July–August 2006.     

Optimal Control of a System Described by Hyperbolic Equation with Conjugation Conditions

New problems of optimal control of distributed systems described by a hyperbolic equation with conjugation conditions and a quadratic cost function are considered in the paper. Unique optimal control existence theorems are proved for all the analyzed cases.     

Formation control of multiple elliptic agents with limited sensing ranges

This paper presents a design of cooperative controllers that force a group of N mobile agents with an elliptic shape and limited sensing ranges to perform a desired formation and that guarantee no collisions between any agents in the group. The desired formation can be stabilized at feasible reference trajectories with bounded time derivatives. The formation control design is based on explicit algebraic separation conditions between ellipses, root conditions of cubic polynomials, the Lyapunov direct method, and smooth or p‐times differentiable step functions. These functions are incorporated into novel potential functions to solve the collision avoidance problem without the need for switchings despite the agents' limited sensing ranges. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Optimal preview control for a linear continuous-time stochastic control system in finite-time horizon

This paper discusses the design of the optimal preview controller for a linear continuous-time stochastic control system in finite-time horizon, using the method of augmented error system. First, an assistant system is introduced for state shifting. Then, in order to overcome the difficulty of the state equation of the stochastic control system being unable to be differentiated because of Brownian motion, the integrator is introduced. Thus, the augmented error system which contains the integrator vector, control input, reference signal, error vector and state of the system is reconstructed. This leads to the tracking problem of the optimal preview control of the linear stochastic control system being transformed into the optimal output tracking problem of the augmented error system. With the method of dynamic programming in the theory of stochastic control, the optimal controller with previewable signals of the augmented error system being equal to the controller of the original system is obtained. Finally, numerical simulations show the effectiveness of the controller.     

Optimal control of a stochastic system with an exponential-of-integral performance criterion

An approach based on the theory of positive semigroups is introduced for the analysis of the infinite-horizon, exponential-of-integral optimal control problem for a stochastic system of the Ito form. Existence conditions for state-feedback admissible controllers are formulated and optimality conditions are derived. Connections between the exponential-of-integral optimal control problem and stochastic differential games are discussed.     

Some Problems of Soil Media Ecology and Optimal Control Processes in Them

New multicomponent soil media ecology problems and respective optimal control problems are considered in the paper. Existence theorems for the unique optimal control are proved for all the cases considered. Computation algorithms of high-accuracy discretization are constructed for some new classes of problems with discontinuous solutions.     

A priori error estimates of a meshless method for optimal control problems of stochastic elliptic PDEs

In this paper, we study the optimal control problems of stochastic elliptic equations with random field in its coefficients. The main contributions of this work are two aspects. Firstly, a meshless method coupled with the stochastic Galerkin method is investigated to approximate the control problems, which is competitive for high-dimensional random inputs. Secondly, a priori error estimates are derived for the solutions to the control problems. Some numerical tests are carried out to confirm the theoretical results and to demonstrate the efficiency of the proposed method.     

基于误差系统的信息融合最优预见跟踪控制

针对期望轨迹和干扰可预见的最优跟踪问题, 提出了一种基于误差系统的信息融合最优控制方法. 将线性伺服系统转化为误差系统; 利用信息融合估计方法, 通过融合期望轨迹、干扰输入、误差系统状态等信息, 获得误差系统协状态以及控制增量的最优估计. 构建了由积分项、状态反馈控制项和预见前馈补偿项组成的最优预见控制系统. 线性直流电机系统的控制仿真结果表明, 信息融合最优预见控制下的位置跟踪精度比传统最优预见控制下的要高.     

资源约束系统的控制与调度协同优化方法

对于一类通信约束的网络控制系统, 应用通信序列的概念和混合逻辑动态的构架, 将其建模成一类集成控制和调度的资源约束系统模型. 采用线性矩阵不等式来描述离散周期系统的周期通信序列和H_∞ 控制的协同优化问题, 并用一种递增优化序列算法来求解优化的调度策略及其相应的渐近稳定及r指数稳定的H_∞控制器. 该算法结合线性矩阵不等式凸优化问题解决了调度与控制的协同设计问题, 同时也节省了搜索优化解的计算时间.     

Optimal control of a single-link flexible manipulator

This paper deals with an exact state space dynamic model for manipulators with flexible links. We use the Bernoulli-Euler beam equations to derive a frequency domain matrix transfer function. This transfer function is then used to compute the Laplace transform of the state vector as a function of the lateral position along a single link manipulator. The problem of optimal end point control of the beam is then addressed. A sixth-order state space model is derived for the manipulator and the controller is based on this model. Several control laws are studied for this model. Next, the manipulator is modeled as eighth order but the control law based on the sixth-order model is retained. We then estimate the six states from the output of the eighth-order model and feed these states back to the controller to derive the control torque used to drive the manipulator. A filter is introduced to compensate for spillover. The results are very satisfactory, and are illustrated by simulated case studies.     

Optimal control of a linear system subject to partially specified input noise

One of the most basic problems in control theory is that of controlling a discrete‐time linear system subject to uncertain noise with the objective of minimizing the expectation of a quadratic cost. If one assumes the noise to be white, then solving this problem is relatively straightforward. However, white noise is arguably unrealistic: noise is not necessarily independent, and one does not always precisely know its expectation. We first recall the optimal control policy without assuming independence and show that, in this case, computing the optimal control inputs becomes infeasible. In the next step, we assume only the knowledge of lower and upper bounds on the conditional expectation of the noise and prove that this approach leads to tight lower and upper bounds on the optimal control inputs. The analytical expressions that determine these bounds are strikingly similar to the usual expressions for the case of white noise.