具非线性控制变量的非自治松驰系统时间最优追踪控制问题中的若干结果

本文讨论了一类广义非自治离散松驰系统的时间最优控制问题，将R^n中点曲线的目标约束推广为凸集值函数的超曲线约束．在证明了松驰系统与原系统可达集相等的基础上，得到了最优控制的存在性．由凸集分离定理及终端时间闺值函数方程，我们获得了最大值原理及最优控制时间的确定方法．较之Hamilton方法，本文的条件更一般．离散松驰系统的相关结论可以用于分散控制．     

非线性约束优化的光滑化平方根罚函数

介绍一种非线性约束优化的不可微平方根罚函数,为这种非光滑罚函数提出了一个新的光滑化函数和对应的罚优化问题,获得了原问题与光滑化罚优化问题目标之间的误差估计. 基于这种罚函数,提出了一个算法和收敛性证明,数值例子表明算法对解决非线性约束优化具有有效性.     

直接配置法求解连续铸钢过程中的最优控制问题

利用描述连续铸钢过程二冷区喷水控制下钢的热传导的半离散化模型 ,我们构造一包含温度梯度约束的最优控制问题 .针对此最优控制问题 ,采用直接配置法进行数值求解 ,得出相应的近似最优控制 .     

轮式移动舞台机器人双模模型预测控制北大核心CSCD

针对轮式移动舞台机器人的快速镇定和移动区域约束控制问题,提出一种快速双模模型预测控制(MPC)算法.考虑轮式移动舞台机器人的位姿约束和速度约束,采用控制Lyapunov函数概念和极坐标系模型设计模型预测控制算法.利用移动舞台机器人与目标的距离、瞄准角和方位角构造一个控制Lyapunov函数,建立移动舞台机器人的一个解析双模结构MPC控制器,再引入自由变量,参数化预测控制变量,降低双模MPC在线优化计算量.在约束条件下,建立了轮式移动舞台机器人闭环系统稳定性和MPC递推可行性理论结果.最后,通过与常规MPC比较,仿真验证所提算法的有效性和优越性.     

轮式移动舞台机器人双模模型预测控制

针对轮式移动舞台机器人的快速镇定和移动区域约束控制问题,提出一种快速双模模型预测控制(MPC)算法.考虑轮式移动舞台机器人的位姿约束和速度约束,采用控制Lyapunov函数概念和极坐标系模型设计模型预测控制算法.利用移动舞台机器人与目标的距离、瞄准角和方位角构造一个控制Lyapunov函数,建立移动舞台机器人的一个解析双模结构MPC控制器,再引入自由变量,参数化预测控制变量,降低双模MPC在线优化计算量.在约束条件下,建立了轮式移动舞台机器人闭环系统稳定性和MPC递推可行性理论结果.最后,通过与常规MPC比较,仿真验证所提算法的有效性和优越性.     

基于高斯伪谱的最优控制求解及其应用

研究一种基于高斯伪谱法的具有约束受限的最优控制数值计算问题.方法将状态演化和控制规律用多项式参数化近似,微分方程用正交多项式近似.将最优控制问题求解问题转化为一组有约束的非线性规划求解.详细论述了该种近似方法的有效性.作为该种方法的应用,讨论了一个障碍物环境下的机器人最优路径生成问题.将机器人路径规划问题转化为具有约束条件最优控制问题,然后用基于高斯伪谱的方法求解,并给出了仿真结果.     

基于二次函数光滑化逼近的修正低阶罚函数

针对不等式约束优化问题, 给出了通过二次函数对低阶精确罚函数进行光滑化逼近的两种函数形式, 得到修正的光滑罚函数. 证明了在一定条件下, 当罚参数充分大, 修正的光滑罚问题的全局最优解是原优化问题的全局最优解. 给出的两个数值例子说明了所提出的光滑化方法的有效性.     

具有终端不等式约束的线性二次控制问题

本文研究具有终端不等式约束的线性二次控制问题,得到了最优控制的反馈形式.所得到的反馈形式与相应的无约束问题的Riccati微分方程和一个函数矩阵的线性方程的解有关.     

基于参数李雅普诺夫函数的鲁棒预测控制器

针对多包描述的不确定系统,提出一种新的鲁棒约束预测控制器.离线设计时引入参数Lyapunov函数以减少单一Lyapunov函数设计时的保守性,得到多包系统Worst-case情况下性能最优的不变集,在线求解多包系统无穷时域性能指标的min-max优化问题.设计采用了时变的终端约束集,扩大了初始可行域,而且能够获得较优的控制性能.仿真结果验证了该方法的有效性.     

考虑Vasicek利率和相依风险的最优投资与再保险

本文研究了利率由Vasicek过程描述,两类保险业务具有相依风险的最优投资和再保险模型.盈余过程由扩散近似模型刻画,保险人的目标是在给定期望终端财富的情况下,寻找使得终端财富的方差最小的投资和再保险策略.通过使用随机线性二次最优控制理论,建立Hamilton-Jacobi-Bellman(HJB)方程,我们获得了值函数的精确表达式以及最优投资和再保险策略.另外,我们给出了有效策略和有效前沿.最后,通过数值例子说明了模型参数对最优投资和再保险策略的影响.     

An efficient computational method for the optimal control problem for the Burgers equation

Pointwise control of the viscous Burgers equation in one spatial dimension is studied with the objective of minimizing the distance between the final state function and target profile along with the energy of the control. An efficient computational method is proposed for solving such problems, which is based on special orthonormal functions that satisfy the associated boundary conditions. Employing these orthonormal functions as a basis of a modal expansion method, the solution space is limited to the smallest lower subspace that is sufficient to describe the original problem. Consequently, the Burgers equation is reduced to a set of a minimal number of ordinary nonlinear differential equations. Thus, by the modal expansion method, the optimal control of a distributed parameter system described by the Burgers equation is converted to the optimal control of lumped parameter dynamical systems in finite dimension. The time-variant control is approximated by a finite term of the Fourier series whose unknown coefficients and frequencies giving an optimal solution are sought, thereby converting the optimal control problem into a mathematical programming problem. The solution space obtained is based on control parameterization by using the Runge–Kutta method. The efficiency of the proposed method is examined using a numerical example for various target functions.     

A computational method for free terminal time optimal control problem governed by nonlinear time delayed systems

This paper considers a free terminal time optimal control problem governed by nonlinear time delayed system, where both the terminal time and the control are required to be determined such that a cost function is minimized subject to continuous inequality state constraints. To solve this free terminal time optimal control problem, the control parameterization technique is applied to approximate the control function as a piecewise constant control function, where both the heights and the switching times are regarded as decision variables. In this way, the free terminal time optimal control problem is approximated as a sequence of optimal parameter selection problems governed by nonlinear time delayed systems, each of which can be viewed as a nonlinear optimization problem. Then, a fully informed particle swarm optimization method is adopted to solve the approximate problem. Finally, two free terminal time optimal control problems, including an optimal fishery control problem, are solved by using the proposed method so as to demonstrate its applicability.     

A filled function method for optimal discrete-valued control problems

In this paper, we present a new approach to solve a class of optimal discrete-valued control problems. This type of problem is first transformed into an equivalent two-level optimization problem involving a combination of a discrete optimization problem and a standard optimal control problem. The standard optimal control problem can be solved by existing optimal control software packages such as MISER 3.2. For the discrete optimization problem, a discrete filled function method is developed to solve it. A numerical example is solved to illustrate the efficiency of our method.     

Approximation design of optimal controllers for nonlinear systems with sinusoidal disturbances

This paper considers an infinite-time optimal damping control problem for a class of nonlinear systems with sinusoidal disturbances. A successive approximation approach (SAA) is applied to design feedforward and feedback optimal controllers. By using the SAA, the original optimal control problem is transformed into a sequence of nonhomogeneous linear two-point boundary value (TPBV) problems. The existence and uniqueness of the optimal control law are proved. The optimal control law is derived from a Riccati equation, matrix equations and an adjoint vector sequence, which consists of accurate linear feedforward and feedback terms and a nonlinear compensation term. And the nonlinear compensation term is the limit of the adjoint vector sequence. By using a finite term of the adjoint vector sequence, we can get an approximate optimal control law. A numerical example shows that the algorithm is effective and robust with respect to sinusoidal disturbances.     

Optimal control of bioprocess systems using hybrid numerical optimization algorithms

In the paper, we consider the bioprocess system optimal control problem. Generally speaking, it is very difficult to solve this problem analytically. To obtain the numerical solution, the problem is transformed into a parameter optimization problem with some variable bounds, which can be efficiently solved using any conventional optimization algorithms, e.g. the improved Broyden–Fletcher–Goldfarb–Shanno algorithm. However, in spite of the improved Broyden–Fletcher–Goldfarb–Shanno algorithm is very efficient for local search, the solution obtained is usually a local extremum for non-convex optimal control problems. In order to escape from the local extremum, we develop a novel stochastic search method. By performing a large amount of numerical experiments, we find that the novel stochastic search method is excellent in exploration, while bad in exploitation. In order to improve the exploitation, we propose a hybrid numerical optimization algorithm to solve the problem based on the novel stochastic search method and the improved Broyden–Fletcher–Goldfarb–Shanno algorithm. Convergence results indicate that any global optimal solution of the approximate problem is also a global optimal solution of the original problem. Finally, two bioprocess system optimal control problems illustrate that the hybrid numerical optimization algorithm proposed by us is low time-consuming and obtains a better cost function value than the existing approaches.     

Control parameterization enhancing transform for optimal control of switched systems

In this paper, a class of optimal switching control problems with prespecified order of the sequence of subsystems is considered, where the switching instants are included in the cost functional. Both the switching instants and the control function are to be chosen such that the cost functional is minimized. Through the discretization of the control space, each control component is approximated by a piecewise constant function. The partition points and the heights of each of these piecewise constant functions are taken as decision varibles. Using the control parameterization enhancing transform, we map both types of switching instants into preassigned knot points via the introduction of an additional control, known as the enhancing control. In this way, we construct a sequence of approximate optimal parameter selection problems with fixed switching time points. We then show that these approximate optimal parameter selection problems are solvable as mathematical programming problems. The convergence analysis of this approximation is investigated. Two examples are solved using the proposed method so as to demonstrate the effectiveness of the method proposed.     

Coupled Galerkin and parameterization methods for optimal control of discretely connected parallel beams

Galerkin and wavelet methods for optimal boundary control of a couple of discretely connected parallel beams are proposed. First, the problem with boundary controls is converted into a problem with distributed controls. The problem is, then, reduced by a Galerkin-based approach into determining the optimal control of a linear time-invariant lumped parameter system, which will be solved by a wavelet-based method using Legendre wavelets. The integration-operational matrix and Kronecker product are utilized to significantly simplify the optimization problem into a system of linear equations. A numerical example is presented to demonstrate the applicability and the efficiency of the proposed method.     

Solving some optimal path planning problems using an approach based on measure theory

In this paper we solve a collection of optimal path planning problems using a method based on measure theory. First we consider the problem as an optimization problem and then we convert it to an optimal control problem by defining some artificial control functions. Then we perform a metamorphosis in the space of problem. In fact we define an injection between the set of admissible pairs, containing the control vector function and a collision-free path defined on free space and the space of positive Radon measures. By properties of this kind of measures we obtain a linear programming problem that its solution gives rise to constructing approximate optimal trajectory of the original problem. Some numerical examples are proposed.