微生物连续发酵酶催化动力系统的鲁棒性与并行计算

依据甘油连续发酵生产1,3-丙二醇的非线性酶催化动力系统.针对1,3-丙二醇可能存在的跨膜运输方式建立相应的动力学模型,提出了酶催化动力系统的定量鲁棒性定义,并建立了以鲁棒性为性能指标、非线性动力系统为主要约束的参数辨识模型.由于求解该辨识问题的数值计算量大,在普通的PC机上难以完成,因此本文构建了相应的并行算法.根据数值结果推断出1,3-丙二醇最有可能的跨膜运输方式,这对于进一步研究甘油连续发酵的机理具有重要的参考价值.     

一类具年龄结构的线性周期种群动力系统的最优控制

研究一类具有年龄结构的线性周期种群线性动力系统的最优控制问题,即讨论了具有周期的生死率和周期变化的控制项的模型．利用Mazur's定理,证明了最优控制问题最优解的存在性,同时由法锥概念的特征刻画,我们还得到了最优控制问题最优解存在的必要条件．     

微生物连续发酵模型及正解的存在性与稳定性分析

本文引入一个新的非线性动力系统,描述Klebsiella pneumoniae以甘油为底物发酵生成1,3-丙二醇的过程.此模型考虑了细胞内物质的浓度,研究甘油主动运输及1,3-丙二醇被动扩散的跨膜方式.证明模型解的存在唯一性,通过引入微分包含和上哈密尔顿函数证明正解的存在性.此外,以稀释速率0.1为例计算平衡点,并对系统的稳定性做出分析.     

微生物批式流加发酵生产1,3-丙二醇过程的优化

本文考虑了微生物批式流加发酵生产1,3-丙二醇的过程优化问题.用非线性切换系统描述拙式流加发酵过程.考虑终端时刻1,3-丙二醇的浓度最大化,给出了以甘油流加速度和流加时刻为控制变量的带有连续状态变量不等式约束的最优控制问题.应用时间转换方法处理变动切换时刻,应用惩罚函数和障碍函数方法处理连续状态变量不等式约束,然后基于梯度最优化算法和粒子群优化算法给出计算方法.     

描述神经元相互作用的非线性动力学方程的解析解

神经系统是由大量神经元构成的非线性动力系统,动力学行为十分复杂ＦＨＮ模型提供了在该系统中观察时间周期振荡这种非线性现象的实验证据．本文利用扰动法从理论上求出了ＦＨＮ模型所给出的非线性动力学方程的解析解,为进一步深入研究神经系统的动力学行为提供了理论依据     

非线性再生散度随机效应模型的极大似然估计及随机逼近算法

非线性再生散度随机效应模型包括了非线性随机效应模型和指数族非线性随机效应模型等．通过视模型中的随机效应为假想的缺失数据和应用Metropolis-Hastings(简称MH) 算法,提出了模型参数极大似然估计的随机逼近算法．模拟研究和实例分析表明了该算法的可行性．     

具有质体的非均匀恒化器模型正解的长时行为

本文讨论了一类具有质体非均匀恒化器模型解的持续性,首先利用上下解方法与极值原理得到恒化器模型的先验估计;然后利用非线性系统的持续性理论讨论恒化器模型正解的长时行为,并且得到了当模型中的参数满足特定条件时,该模型对应的半动力系统是强一致连续持续的.     

非线性再生散度随机效应模型的极大似然估计及EM算法

非线性再生散度随机效应模型是指数族非线性随机效应模型和非线性再生散度模型的推广和发展．通过视模型中的随机效应为假想的缺失数据和应用Metropolis-Hastings（MH）算法,提出了模型参数极大似然估计的Monte-Carlo EM（MCEM）算法,并用模拟研究和实例分析说明了该算法的可行性．     

旋转向量场中的阶二周期解

建立了一类具有状态脉冲控制的害虫控制模型以及一类特殊模型,根据半连续动力系统几何理论,研究了旋转向量场中阶二周期解的存在性和稳定性及变化规律.为现实的生物资源管理提供了可靠的策略依据,也丰富了半连续动力系统理论.     

一类具有阶段结构和脉冲效应的捕食者-食饵模型的动力学分析

研究了一个捕食者具有阶段结构,食饵具有脉冲效应和时滞的捕食者-食饵模型.利用离散动力系统的频闪映射,我们获得了捕食者-灭绝的周期解同时给出了该周期解全局吸引的充分条件.利用时滞脉冲微分方程的理论,得到了系统持续生存的充分条件.     

Switching neuronal state: optimal stimuli revealed using a stochastically-seeded gradient algorithm

Inducing a switch in neuronal state using energy optimal stimuli is relevant to a variety of problems in neuroscience. Analytical techniques from optimal control theory can identify such stimuli; however, solutions to the optimization problem using indirect variational approaches can be elusive in models that describe neuronal behavior. Here we develop and apply a direct gradient-based optimization algorithm to find stimulus waveforms that elicit a change in neuronal state while minimizing energy usage. We analyze standard models of neuronal behavior, the Hodgkin-Huxley and FitzHugh-Nagumo models, to show that the gradient-based algorithm: 1) enables automated exploration of a wide solution space, using stochastically generated initial waveforms that converge to multiple locally optimal solutions; and 2) finds optimal stimulus waveforms that achieve a physiological outcome condition, without a priori knowledge of the optimal terminal condition of all state variables. Analysis of biological systems using stochastically-seeded gradient methods can reveal salient dynamical mechanisms underlying the optimal control of system behavior. The gradient algorithm may also have practical applications in future work, for example, finding energy optimal waveforms for therapeutic neural stimulation that minimizes power usage and diminishes off-target effects and damage to neighboring tissue.     

Estimation of optimal feeding strategies for fed-batch bioprocesses

A generic methodology for feeding strategy optimization is presented. This approach uses a genetic algorithm to search for optimal feeding profiles represented by means of artificial neural networks (ANN). Exemplified on a fed-batch hybridoma cell cultivation, the approach has proven to be able to cope with complex optimization tasks handling intricate constraints and objective functions. Furthermore, the performance of the method is compared with other previously reported standard techniques like: (1) optimal control theory, (2) first order conjugate gradient, (3) dynamical programming, (4) extended evolutionary strategies. The methodology presents no restrictions concerning the number or complexity of the state variables and therefore constitutes a remarkable alternative for process development and optimization. This revised version was published online in June 2005 with corrections to the Appendix.     

A parameter optimization approach for the optimal control of large-scale musculoskeletal systems.

This paper describes a computational method for solving optimal control problems involving large-scale, nonlinear, dynamical systems. Central to the approach is the idea that any optimal control problem can be converted into a standard nonlinear programming problem by parameterizing each control history using a set of nodal points, which then become the variables in the resulting parameter optimization problem. A key feature of the method is that it dispenses with the need to solve the two-point, boundary-value problem derived from the necessary conditions of optimal control theory. Gradient-based methods for solving such problems do not always converge due to computational errors introduced by the highly nonlinear characteristics of the costate variables. Instead, by converting the optimal control problem into a parameter optimization problem, any number of well-developed and proven nonlinear programming algorithms can be used to compute the near-optimal control trajectories. The utility of the parameter optimization approach for solving general optimal control problems for human movement is demonstrated by applying it to a detailed optimal control model for maximum-height human jumping. The validity of the near-optimal control solution is established by comparing it to a solution of the two-point, boundary-value problem derived on the basis of a bang-bang optimal control algorithm. Quantitative comparisons between model and experiment further show that the parameter optimization solution reproduces the major features of a maximum-height, countermovement jump (i.e., trajectories of body-segmental displacements, vertical and fore-aft ground reaction forces, displacement, velocity, and acceleration of the whole-body center of mass, pattern of lower-extremity muscular activity, jump height, and total ground contact time).     

Automated Design of Complex Dynamic Systems

Several fields of study are concerned with uniting the concept of computation with that of the design of physical systems. For example, a recent trend in robotics is to design robots in such a way that they require a minimal control effort. Another example is found in the domain of photonics, where recent efforts try to benefit directly from the complex nonlinear dynamics to achieve more efficient signal processing. The underlying goal of these and similar research efforts is to internalize a large part of the necessary computations within the physical system itself by exploiting its inherent non-linear dynamics. This, however, often requires the optimization of large numbers of system parameters, related to both the system''s structure as well as its material properties. In addition, many of these parameters are subject to fabrication variability or to variations through time. In this paper we apply a machine learning algorithm to optimize physical dynamic systems. We show that such algorithms, which are normally applied on abstract computational entities, can be extended to the field of differential equations and used to optimize an associated set of parameters which determine their behavior. We show that machine learning training methodologies are highly useful in designing robust systems, and we provide a set of both simple and complex examples using models of physical dynamical systems. Interestingly, the derived optimization method is intimately related to direct collocation a method known in the field of optimal control. Our work suggests that the application domains of both machine learning and optimal control have a largely unexplored overlapping area which envelopes a novel design methodology of smart and highly complex physical systems.     

The numerical method for the optimal supporting position and related optimal control for the catalytic reaction system

This paper considers the numerical approximation for the optimal supporting position and related optimal control of a catalytic reaction system with some control and state constraints, which is governed by a nonlinear partial differential equations with given initial and boundary conditions. By the Galerkin finite element method, the original problem is projected into a semi-discrete optimal control problem governed by a system of ordinary differential equations. Then the control parameterization method is applied to approximate the control and reduce the original system to an optimal parameter selection problem, in which both the position and related control are taken as decision variables to be optimized. This problem can be solved as a nonlinear optimization problem by a particle swarm optimization algorithm. The numerical simulations are given to illustrate the effectiveness of the proposed numerical approximation method.     

Cooperative optimal control: broadening the reach of bio-inspiration

Inspired by the process by which ants gradually optimize their foraging trails, this paper investigates the cooperative solution of a class of free final time, partially constrained final state optimal control problems by a group of dynamical systems. We propose an iterative, pursuit-based algorithm which generalizes previously proposed models and converges to an optimal solution by iteratively optimizing an initial feasible trajectory/control pair. The proposed algorithm requires only short-range, limited interactions between group members, avoids the need for a 'global map' of the environment in which the group evolves, and solves an optimal control problem in 'small' pieces, in a manner which will be made precise. The performance of the algorithm is illustrated in a series of simulations and laboratory experiments.     

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control

In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ₁-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.     

Local versus global optimal sports techniques in a group of athletes

Various optimization algorithms have been used to achieve optimal control of sports movements. Nevertheless, no local or global optimization algorithm could be the most effective for solving all optimal control problems. This study aims at comparing local and global optimal solutions in a multistart gradient-based optimization by considering actual repetitive performances of a group of athletes performing a transition move on the uneven bars. Twenty-four trials by eight national-level female gymnasts were recorded using a motion capture system, and then multistart sequential quadratic programming optimizations were performed to obtain global optimal, local optimal and suboptimal solutions. The multistart approach combined with a gradient-based algorithm did not often find the local solution to be the best and proposed several other solutions including global optimal and suboptimal techniques. The qualitative change between actual and optimal techniques provided three directions for training: to increase hip flexion–abduction, to transfer leg and arm angular momentum to the trunk and to straighten hand path to the bar.     

Optimal coordination and control of posture and locomotion.

This paper presents a theoretical model of stability and coordination of posture and locomotion, together with algorithms for continuous-time quadratic optimization of motion control. Explicit solutions to the Hamilton-Jacobi equation for optimal control of rigid-body motion are obtained by solving an algebraic matrix equation. The stability is investigated with Lyapunov function theory, and it is shown that global asymptotic stability holds. It is also shown how optimal control and adaptive control may act in concert in the case of unknown or uncertain system parameters. The solution describes motion strategies of minimum effort and variance. The proposed optimal control is formulated to be suitable as a posture and stance model for experimental validation and verification. The combination of adaptive and optimal control makes this algorithm a candidate for coordination and control of functional neuromuscular stimulation as well as of prostheses.     

Optimal coordination and control of posture and movements

This paper presents a theoretical model of stability and coordination of posture and locomotion, together with algorithms for continuous-time quadratic optimization of motion control. Explicit solutions to the Hamilton–Jacobi equation for optimal control of rigid-body motion are obtained by solving an algebraic matrix equation. The stability is investigated with Lyapunov function theory and it is shown that global asymptotic stability holds. It is also shown how optimal control and adaptive control may act in concert in the case of unknown or uncertain system parameters. The solution describes motion strategies of minimum effort and variance. The proposed optimal control is formulated to be suitable as a posture and movement model for experimental validation and verification. The combination of adaptive and optimal control makes this algorithm a candidate for coordination and control of functional neuromuscular stimulation as well as of prostheses. Validation examples with experimental data are provided.