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Teng Niu Jingang Zhai Hongchao Yin Enmin Feng 《Journal of The Franklin Institute》2018,355(14):6169-6190
The bio-dissimilation of glycerol to 1,3-propanediol (1,3-PD) is a complex bioprocess due to the multiple inhibitions of substrate and products onto the cell growth. In consideration of both the inhibition mechanisms of 3-hydroxypropionaldehyde (3-HPA) and the transport modes of glycerol and 1,3-PD across the cell membrane, we establish a novel switched system which is represented by a ten-dimensional nonlinear dynamical equation containing both extracellular and intracellular environments. The uncoupled microbial fed-batch fermentation process are modeled using the switched system which the glycerol and alkali are respectively poured into. Taking the feeding rates of glycerol and alkali, the switching times and the mode sequence as the control variables, an optimal control model is proposed with the concentration of the terminal time 1,3-PD as performance index. In order to maximize the yield of 1,3-PD, the control parameterization technique and the exact penalty function method are used to solve the considered problem. Numerical results show that under the obtained optimal feeding rates of glycerol and alkali, switching times and mode sequence, the productivity of 1,3-PD at the terminal time is increased significantly compared with previous results. 相似文献
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A Markovian system approach to distributed H∞ filtering for sensor networks with stochastic sampling
This paper is concerned with the distributed H∞ filtering problem for a class of sensor networks with stochastic sampling. System measurements are collected through a sensor network stochastically and the phenomena such as random measurement missing and quantization are also considered. Firstly, the stochastic sampling process of the sensor network is modeled as a discrete-time Markovian system. Then, the logarithmic quantization effect is transformed into the parameter uncertainty of the filtering system, and a set of binary variables is introduced to model the random measurement missing phenomenon. Finally, the resulting augmented system is modeled as an uncertain Markovian system with multiple random variables. Based on the Lyapunov stability theory and the stochastic system analysis method, a sufficient condition is obtained such that the augmented system is stochastically stable and achieves an average H∞ performance level γ; the design procedure of the optimal distributed filter is also provided. A numerical example is given to demonstrate the effectiveness of the proposed results. 相似文献
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《Journal of The Franklin Institute》2002,339(4-5):479-498
In this paper, a numerical method to solve nonlinear optimal control problems with terminal state constraints, control inequality constraints and simple bounds on the state variables, is presented. The method converts the optimal control problem into a sequence of quadratic programming problems. To this end, the quasilinearization method is used to replace the nonlinear optimal control problem with a sequence of constrained linear-quadratic optimal control problems, then each of the state variables is approximated by a finite length Chebyshev series with unknown parameters. The method gives the information of the quadratic programming problem explicitly (The Hessian, the gradient of the cost function and the Jacobian of the constraints). To show the effectiveness of the proposed method, the simulation results of two constrained nonlinear optimal control problems are presented. 相似文献
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In this paper, a composite Chebyshev finite difference method for solving linear quadratic optimal control problems with inequality constraints on state and control variables is introduced. This method is an extension of Chebyshev finite difference scheme and is based on a hybrid of block-pulse functions and Chebyshev polynomials using the well known Chebyshev–Gauss–Lobatto nodes. The excellent properties of hybrid functions are used to convert optimal control problem into a mathematical programming problem whose solution is much more easier than the original one. Various types of optimal control problems are investigated to demonstrate the effectiveness of the proposed approximation scheme. The method is simple, easy to implement and provides very accurate results. 相似文献
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《Information processing & management》2023,60(2):103226
Nowadays assuring that search and recommendation systems are fair and do not apply discrimination among any kind of population has become of paramount importance. This is also highlighted by some of the sustainable development goals proposed by the United Nations. Those systems typically rely on machine learning algorithms that solve the classification task. Although the problem of fairness has been widely addressed in binary classification, unfortunately, the fairness of multi-class classification problem needs to be further investigated lacking well-established solutions. For the aforementioned reasons, in this paper, we present the Debiaser for Multiple Variables (DEMV), an approach able to mitigate unbalanced groups bias (i.e., bias caused by an unequal distribution of instances in the population) in both binary and multi-class classification problems with multiple sensitive variables. The proposed method is compared, under several conditions, with a set of well-established baselines using different categories of classifiers. At first we conduct a specific study to understand which is the best generation strategies and their impact on DEMV’s ability to improve fairness. Then, we evaluate our method on a heterogeneous set of datasets and we show how it overcomes the established algorithms of the literature in the multi-class classification setting and in the binary classification setting when more than two sensitive variables are involved. Finally, based on the conducted experiments, we discuss strengths and weaknesses of our method and of the other baselines. 相似文献
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《Journal of The Franklin Institute》2006,343(4-5):372-388
This paper describes a simulation-based parameter design (PD) approach for optimizing machine operating strategy under stochastic running conditions. The approach presents a Taguchi-based definition to the PD problem in which control factors include machine operating hours, operating pattern, scheduled shutdowns, maintenance level, and product changeovers. Random factors include machine random variables (RVs) of cycle time (CT), time-between-failure (TBF), time-to-repair (TTR), and defects rate (DR). Machine performance, as a complicated function of control and random factors, is defined in terms of net productivity (NP) based on three key performance indicators: gross throughput (GT), reliability rate (RR), and quality rate (QR). It is noticed that the resulting problem definition presents both modeling and optimization difficulties. Modeling complications result from the sensitivity of machine RVs to different settings of machine operating parameters and the difficulty to estimate machine performance in terms of NP under stochastic running conditions. Optimization complications result from the limited capability of mathematical modeling and experimental design in tackling the resulting large-in-space combinatorial optimization problem. To tackle such difficulties, therefore, the proposed approach presents a combined empirical modeling and Monte Carlo simulation (MCS) method to model the sensitive factors interdependencies and to estimate NP under stochastic running conditions. For combinatorial optimization, the approach utilizes a simulated-annealing (SA) heuristic to solve the defined PD problem and to provide optimal or near optimal settings to machine operating parameters. Approach procedure and potential benefits are illustrated through a case study example. 相似文献
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《Journal of The Franklin Institute》2022,359(8):3575-3596
This paper considers a class of optimal control problems governed by Markov jump systems. Our focus is to develop a computational method, based on the control parametrization approach, for solving this class of optimal control problems. Due to the existence of the continuous-time Markov chain, the optimal control problem under consideration is a stochastic optimal control problem, and hence the control parametrization technique cannot be applied directly. For this, a derandomization approach is introduced to obtain a representative deterministic optimal control problem. Then, the control parametrization method is applied to obtain an approximate finite dimensional optimization problem which can be computed numerically using the gradient-based optimization method. For this, the gradient formulas of the cost function and the constraint functions with respect to control variables are derived. Finally, a practical application involving a RLC circuit model is solved using the method proposed. 相似文献
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This paper introduces an efficient direct approach for solving delay fractional optimal control problems. The concepts of the fractional integral and the fractional derivative are considered in the Riemann–Liouville sense and the Caputo sense, respectively. The suggested framework is based on a hybrid of block-pulse functions and orthonormal Taylor polynomials. The convergence of the proposed hybrid functions with respect to the L2-norm is demonstrated. The operational matrix of fractional integration associated with the hybrid functions is constructed by using the Laplace transform method. The problem under consideration is transformed into a mathematical programming one. The method of Lagrange multipliers is then implemented for solving the resulting optimization problem. The performance and computational efficiency of the developed numerical scheme are assessed through various types of delay fractional optimal control problems. Our numerical findings are compared with either exact solutions or the existing results in the literature. 相似文献
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The H∞ control problem is investigated in this paper for a class of networked control systems (NCS) with time-varying delay and packet disordering. A new model is proposed to describe the packet disordering phenomenon and then converted into a parameter-uncertain system with multi-step delay. Based on the obtained system model, a sufficient condition for robust stability of the NCS is derived. Furthermore, an optimization problem with linear matrix inequalities (LMIs) constraints is formulated to design the state feedback H∞ controller such that the closed-loop NCS is robust stable and has an optimal H∞ disturbance attenuation level. Finally, two illustrative examples are given to demonstrate the effectiveness of the proposed method. 相似文献
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A new approach to the problem of optimal control of linear dynamic systems is proposed that makes use of a method of input and state parametrization to transform the original problem into a problem of the Calculus of Variations. In contrast to the standard approaches for this class of problems, two salient features of the new approach are that no Lagrange multiplier functions need to be invoked and that the class of inputs can be restricted to the - relatively small - class of continuous functions, even for problems with fixed end-states. The resulting necessary conditions of optimality, i.e., the Euler-Lagrange equation and the boundary conditions for the transformed problem, are proved to be equivalent to those resulting from the standard method of First Variations. In case of quadratic cost functionals, the new approach provides a simpler alternative to the well known, but equally difficult, Riccati differential equation approach and results in a simple dynamic state-feedback implementation of the optimal control. 相似文献
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The main control goal of the fed-batch process is to maximize the yield of target product as well as to minimize the operation costs simultaneously. Considering the existence of time delay and the switching nature in the fed-batch process, a time-delayed switched system is proposed to formulate the 1,3-propanediol (1,3-PD) production process. Some important properties of the system are also discussed. Taking the switching instants and the terminal time as the control variables, a free terminal time delayed optimal control problem is then presented. Using a time-scaling transformation and parameterizing the switching instants into new parameters, an equivalently optimal control problem is investigated. A numerical solution method is developed to seek the optimal control strategy by the smoothing approximation method and the gradient of the cost functional together with that of the constraints. Numerical results show that the mass of target product per unit time at the terminal time is increased considerably. 相似文献
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The present paper proposes a numerical approach to a linear optimal control problem with a quadratic performance index. In this technique, the time interval is divided into a number of time segments and all of the unknown functions which appear in the performance index are either interpolated linearly with respect to time or assumed to be constant in each time segment. The augmented performance index is discretized within each time element through the ordinary finite element technique.The main advantage of the present method is as follows: all of the necessary conditions for the performance index to be stationary can be expressed in the form of algebraic equations and the performance sequence of the state variables can be eliminated. As a result, the optimal control problem is reduced to the simple one of finding the sequence of control variables alone, which minimizes the quadratic performance index.A general formulation of the method is given and simple numerical examples are shown to demonstrate the effectiveness of the technique. 相似文献
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《Journal of The Franklin Institute》2022,359(2):859-869
In this paper, we considered a time-optimal control problem for a new type of linear parameter varying (LPV) system which is obtained through data identification in the process of dealing with actual problems. The addition of non-linear terms is compensation for the method that does not require linear expansion at the equilibrium point. Since the objective function is the terminal time which is an implicit function concerning decision variables, it is a non-standard optimal control problem with uncertain terminal time. To find the global optimal solution to this problem, firstly, the control parameterization method is used to transform it into a nonlinear optimization problem of parameter selection, and then the modifed particle swarm optimization (PSO) algorithm is combined to solve the equivalent nonlinear programming problem. Numerical examples are used to illustrate the effectiveness of the proposed algorithm. 相似文献
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BackgroundDepletion of petroleum resources has enforced the search for alternative sources of renewable energy. Introduction of biofuels into the market was expected to become a solution to this disadvantageous situation. Attempts to cover fuel demand have, however, caused another severe problem—the waste glycerol generated during biodiesel production at a concentration of approximately 10% w/w. This, in turn, prompted a global search for effective methods of valorization of the waste fraction of glycerol.ResultsUtilization of the waste fraction at 48 h with an initial glycerol concentration of 30 g·L-1 and proceeding with 62% efficiency enabled the production of 9 g·L-1 dihydroxyacetone at 50% substrate consumption. The re-use of the immobilized biocatalyst resulted in a similar concentration of dihydroxyacetone (8.7 g·L-1) in two-fold shorter time, with an efficiency of 85% and lower substrate consumption (35%).ConclusionsThe method proposed in this work is based on the conversion of waste glycerol to dihydroxyacetone in a reaction catalyzed by immobilized Gluconobacter oxydans cell extract with glycerol dehydrogenase activity, and it could be an effective way to convert waste glycerol into a valuable product. 相似文献
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《Journal of The Franklin Institute》2023,360(14):10433-10456
An effective approach is proposed for optimal control problems in aerospace engineering. First, several interval lengths are treated as optimization variables directly to localize the switching points accurately. Second, the variable intervals are usually refined into more subintervals homogeneously to obtain the trajectories with high accuracy. To reduce the number of optimization variables and improve the efficiency, the control and the state vectors are parameterized using different meshes in this paper such that the control can be approximated asynchronously by fewer parameters where the trajectories change slowly. Then, the variables are departed as independent variables and dependent variables, the gradient formulae, based on the partial derivatives of dependent parameters with respect to independent parameters, are computed to solve nonlinear programming problems. Finally, the proposed approach is applied to the classic moon lander and hang glider problems. For the moon lander problem, the proposed approach is compared with CVP, Fast-CVP and GPM methods, respectively. For the hang glider problem, the proposed approach is compared with trapezoidal discretization and stopping criteria methods, respectively. The numerical results validate the effectiveness of the proposed approach. 相似文献
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This paper deals with the problem of model reference control for linear parameter varying (LPV) systems. The LPV systems under consideration depend on a set of parameters that are bounded and available online. The main contribution of this paper is to design an LPV model reference control scheme for LPV systems whose state-space matrices depend affinely on a set of time-varying parameters that are bounded and available online. The design problem is divided into two subproblems: the design of the coefficient matrices of the controller and the design of the gain of the state feedback controller for LPV systems. The singular value decomposition is used to obtain the coefficient matrices, while the linear matrix inequality methodology is used to obtain the parameter-dependent state feedback gain of the control scheme. A simple numerical example is used to illustrate the proposed design and a coupled-tank process example is used to demonstrate the usefulness and practicality of the proposed design. Simulation and experimental results indicate that the proposed scheme works well. 相似文献
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In this paper, a convex optimization algorithm is proposed to solve the online trajectory optimization problem of boost back of vertical take-off/vertical landing reusable launch vehicles. To achieve high-precision landing of launch vehicles, trajectory optimization of the boost-back flight phase considering the accuracy of entry is carried out, especially in emergencies. The trajectory optimization problem is formulated as an optimal control problem with minimum fuel consumption, and then it is transformed into a series of convex optimization subproblems, which can be solved by primal-dual interior-point method accurately and rapidly. During the transformation, flip-Radau pseudospectral discretization method, lossless convexification and successive convexification technology are applied. To drive the vehicle to predetermined entry points at the expected velocity, terminal constraints are expressed as orbital constraints of the endpoint in the boost-back flight phase. Considering the influence of Earth's rotation, the right ascension of the ascending node of the target orbit is updated according to the time and true anomaly at the end of the boost-back flight phase. Furthermore, the homotopy method is applied to the situation where there is no good initial guess when emergency happens. The algorithm presented in this paper performs well upon the simulation experiments of mission change and thrust decline. With good accuracy, high computational efficiency, and excellent robustness, the convex approach proposed has a great potential for onboard application in reusable launch vehicles and other space vehicles. 相似文献