微生物批式流加发酵过程中的时滞最优控制

考虑到1,3-丙二醇(1,3-PD)批式流加发酵过程中的时滞现象,提出一个非线性时滞微分方程来描述该过程.以终端时刻1,3-PD的单位时间产量作为性能指标,同时,以甘油和碱的流加速度、发酵过程的终端时刻作为控制向量,建立一个含控制和状态约束的时滞最优控制模型.为了求解该最优控制问题,首先通过时间尺度变换,将该最优控制问题转化为具有固定终端时刻的等价最优控制问题;然后,应用控制参数化方法,将等价的最优控制问题用一系列有限维优化问题来近似;最后,构造一种改进的粒子群优化方法来求解相应的近似优化问题.数值结果表明,终端时刻的1,3-PD的单位时间产量比已有结果提高了约58%.     

改进的单纯形法优化微生物间歇发酵的操作条件

建立了以微生物间歇发酵甘油生产1,3-丙二醇（1,3-PD）的两阶段非线性动力系统和终端要求为约束,以初始浓度和发酵时间为优化参数,以终端时刻1,3-PD的生产强度最大为性能指标的参数优化模型。证明了该模型中最优参数的存在性。最后构造了改进的单纯形法求解该问题,数值结果给出了微生物间歇发酵在厌氧条件下的最优的发酵时间、初始生物量和甘油浓度,从而为1,3-PD的产业化生产提供理论指导。     

Robust receding horizon control of constrained nonlinear systems

We present a method for the construction of a robust dual-mode, receding horizon controller which can be employed for a wide class of nonlinear systems with state and control constraints and model error. The controller is dual-mode. In a neighborhood of the origin, the control action is generated by a linear feedback controller designed for the linearized system. Outside this neighborhood, receding horizon control is employed. Existing receding horizon controllers for nonlinear, continuous time systems, which are guaranteed to stabilize the nonlinear system to which they are applied, require the exact solution, at every instant, of an optimal control problem with terminal equality constraints. These requirements are considerably relaxed in the dual-mode receding horizon controller presented in this paper. Stability is achieved by imposing a terminal inequality, rather than an equality, constraint. Only approximate minimization is required. A variable time horizon is permitted. Robustness is achieved by employing conservative state and stability constraint sets, thereby permitting a margin of error. The resultant dual-mode controller requires considerably less online computation than existing receding horizon controllers for nonlinear, constrained systems     

Metabolic system identification and optimization in continuous culture

To date, there still exist some uncertain factors in the continuous fermentation of glycerol to 1,3-Propanediol (1,3-PD) by Klebsiella pneumoniae because of the limitation in bio-techniques. In this paper, among these uncertain factors, we aim to infer the transport mechanisms of the substrate and the product across the cell membrane of the biomass. On the basis of different inferences of transport mechanisms, we reconstruct various metabolic systems and develop their dynamical systems. To determine the most reasonable metabolic system from all possible ones, we give a quantitative definition of biological robustness and propose an identification model on this basis. An improved Particle Swarm Optimization algorithm is developed to solve the identification model. Numerical results show that the identified system can describe the fermentation process well. Furthermore, to maximize the concentration of 1,3-PD, an optimization model is proposed. Numerical results show that the concentration of 1,3-PD can be increased considerably by employing the obtained optimal strategy.     

基于PSO算法的微生物间歇发酵动力学参数辨识

主要根据微生物间歇培养过程的特征、动态行为及实验数据,建立了能够更好反映间歇发酵过程的简化的多阶段参数辨识模型,然后证明了该模型中最优参数的存在性;最后结合模型特点构造了一种改进的粒子群优化（PSO）算法求得最优参数,并利用所得的参数进行过程仿真。结果表明该模型和算法大大减少了实验数据和计算数值之间的误差,能够更好地模拟微生物间歇发酵过程。     

改进粒子群算法优化微生物连续发酵过程

针对微生物连续发酵生产1,3-丙二醇动力学模型,以稳态时刻1,3-丙二醇的浓度最大化为目标函数,建立以注入甘油浓度和稀释速率为优化变量的优化模型。证明了该模型最优解的存在性。进一步,构造了改进的粒子群优化算法求解此优化模型。数值结果表明稳态时刻1,3-丙二醇的浓度比已有结果有显著提高。     

约束非线性系统的一个准无限时域预测控制方案

提出了一个具有准无限预测时域的模型预测控制方案,该方案可用于输入和状态的非线性系统的控制,用优化柔性状态约束条件代替了硬性状态约束,以避免优化问题的不可解,开环优化问题含有附加的终端代价项和终的约束条件,这样预测时域延伸至准无限,而需在线优化获得的控制函数仅为有限时域,如果在最初时刻优化问题有解,则闭环系统具有保证稳定性。     

A computational method for solving time-delay optimal control problems with free terminal time

This paper considers a class of optimal control problems for general nonlinear time-delay systems with free terminal time. We first show that for this class of problems, the well-known time-scaling transformation for mapping the free time horizon into a fixed time interval yields a new time-delay system in which the time delays are variable. Then, we introduce a control parameterization scheme to approximate the control variables in the new system by piecewise-constant functions. This yields an approximate finite-dimensional optimization problem with three types of decision variables: the control heights, the control switching times, and the terminal time in the original system (which influences the variable time delays in the new system). We develop a gradient-based optimization approach for solving this approximate problem. Simulation results are also provided to demonstrate the effectiveness of the proposed approach.     

基于神经动态优化的非线性系统近似最优跟踪控制

提出一种输入约束下一类连续时间非线性系统最优跟踪控制问题的近似求解方法.针对有限时间跟踪性能指标下一类单输入单输出非线性系统,利用所提出的最优跟踪控制方法实现目标系统所对应性能指标近似最优.首先将系统的性能指标沿时间泰勒展开,得到一个近似的性能指标;其次,在系统状态可观测条件下,将该问题进一步转化为以控制输入为决策变量的非线性规划问题;再次,利用神经动态优化方法,求解含不等式约束下的近似最优控制问题并给出相应的递归神经网络模块原理图;进而,针对整个闭环系统进行理论分析,证明在一定条件下闭环系统的稳定性;最后,通过两个实例仿真验证所提出方法的有效性.     

A multistage system of microbial fed-batch fermentation and its parameter identification

In fed-batch fermentation of glycerol bio-dissimilation to 1,3-propanediol (1,3-PD) by Klebsiella pneumoniae, glycerol and alkali are fed into the reactor to provide nutrient and maintain a suitable environment for cells growth. Taking the feeding process as a time-continuous process, we present a nonlinear multistage dynamical system to formulate the fed-batch fermentation. In view of the big errors between experimental data and computational values, a parameter identification model is established. Finally, an improved Nelder–Mead simplex search method is developed to seek the unknown parameters in the model. Numerical simulations show that the multistage dynamical system can describe the fed-batch process better, compared with the previous results.     

Optimal robust vehicle motion control under equality and inequality constraints

In this paper, a new robust controller is proposed to improve the motion control performance of an autonomous four-wheel steering vehicle. The vehicle is subject to time-varying uncertainties caused by parameter perturbation and unmodeled disturbance. First of all, the vehicle motion control problem is modeled as a constraint-following problem with the goal to drive the vehicle system to follow the given constraints. For safety reasons, inequality constraints are imposed on the lateral displacement of the vehicle. Next, the diffeomorphism mapping method is used to deal with the inequality constraints in the vehicle motion control, and the constrained lateral displacement space is mapped to an unbounded space. On this basis, a new multi-parameter robust constraint-following control is designed. Based on Lyapunov stability theory, the approximate constraint tracking performance of the path tracking system is proved. In order to make a trade-off between the system performance and control cost, a multi-parameter optimization problem is established, and the optimal robust controller is obtained. Last, the main theoretical results are verified by the Carsim-Simulink co-simulations.     

线性时滞系统基于观测器的最优输出跟踪控制器近似设计

研究线性时滞系统的最优输出跟踪控制器近似设计过程.首先根据原系统最优输出跟踪控制问题构造了两个分别具有已知初始条件和终端条件的微分方程迭代序列,并证明它们一致收敛于原问题的最优解.然后通过对该解序列的有限次迭代,得到最优输出跟踪控制问题的一个近似解,进一步给出一个计算近似最优输出跟踪控制律的算法.最后通过构造降维参考输入观测器解决了最优输出跟踪控制器中前馈项的物理可实现问题.仿真结果表明该方法是有效的,且易于实现.     

Nonlinear model predictive control for models in quasi‐linear parameter varying form

This article presents a nonlinear model predictive control (NMPC) approach based on quasi‐linear parameter varying (quasi‐LPV) representations of the model and constraints. Stability of the proposed algorithm is ensured by the offline solution of an optimization problem with linear matrix inequality constraints in conjunction with an online terminal state constraint. Furthermore, an iterative approach is presented with which the NMPC optimization problem can be handled by solving a series of Quadratic Programs at each time step, this being highly computationally efficient. A practical and simple way of obtaining quasi‐LPV representations of the system using velocity‐based linearization is presented in two examples.     

计算机数控系统光滑时间最优轨迹规划

基于控制向量参数化(CVP)方法, 研究了计算机数控(CNC)系统光滑时间最优轨迹规划方法. 通过在规划问题中引入加加速度约束, 实现轨迹的光滑给进. 引入时间归一化因子, 将加加速度约束的时间最优轨迹规划问题转化为固定时间的一般性最优控制问题. 以路径参数对时间的三阶导数(伪加加速度)和终端时刻为优化变量, 并采用分段常数近似伪加加速度, 将最优控制问题转化为一般的非线性规划(NLP)问题进行求解. 针对加加速度、加速度等过程不等式约束, 引入约束凝聚函数, 将过程约束转化为终端时刻约束, 从而显著减少约束计算. 构造目标和约束函数的Hamiltonian函数, 利用伴随方法获得求解NLP问题所需的梯度.