Dynamic optimization using adaptive direct multiple shooting

An α-Model Parametrization Algorithm for Optimization with Differential-Algebraic Equations

An optimization task with nonlinear differential-algebraic equations (DAEs) was approached. In special cases in heat and mass transfer engineering, a classical direct shooting approach cannot provide a solution of the DAE system, even in a relatively small range. Moreover, available computational procedures for numerical optimization, as well as differential- algebraic systems solvers are characterized by their limitations, such as the problem scale, for which the algorithms can work efficiently, and requirements for appropriate initial conditions. Therefore, an αDAE model optimization algorithm based on an α-model parametrization approach was designed and implemented. The main steps of the proposed methodology are: (1) task discretization by a multiple-shooting approach, (2) the design of an α-parametrized system of the differential-algebraic model, and (3) the numerical optimization of the α-parametrized system. The computations can be performed by a chosen iterative optimization algorithm, which can cooperate with an outer numerical procedure for solving DAE systems. The implemented algorithm was applied to solve a counter-flow exchanger design task, which was modeled by the highly nonlinear differential-algebraic equations. Finally, the new approach enabled the numerical simulations for the higher values of parameters denoting the rate of changes in the state variables of the system. The new approach can carry out accurate simulation tests for systems operating in a wide range of configurations and created from new materials.

Dynamic Optimization Using Local Collocation Methods and Improved Multiresolution Technique

Dynamic optimization has wide applications in scientific and industrial researches. Multiresolution techniques provide an efficient way to solve dynamic optimization problems but have some disadvantages. An improved multiresolution technique is developed in this paper to overcome these disadvantages. The proposed technique consists of local collocation methods and a multiresolution-based mesh refinement method. New, generalized dyadic meshes are proposed to overcome the dyadic limitation, and the mesh refinement method is improved so that it can start with the coarsest generalized dyadic mesh. Additionally, the proposed technique involves a mesh refinement algorithm to remove the redundant mesh points in the constant control regions by analyzing the control slopes. The technique is applied to three chemical process control optimization problems and compared with other methods to demonstrate its effectiveness. Numerical results show that the proposed technique can solve chemical process control optimization problems accurately and efficiently and has advantages over other methods.

A novel non-uniform control vector parameterization approach with time grid refinement for flight level tracking optimal control problems

High quality control method is essential for the implementation of aircraft autopilot system. An optimal control problem model considering the safe aerodynamic envelop is therefore established to improve the control quality of aircraft flight level tracking. A novel non-uniform control vector parameterization (CVP) method with time grid refinement is then proposed for solving the optimal control problem. By introducing the Hilbert-Huang transform (HHT) analysis, an efficient time grid refinement approach is presented and an adaptive time grid is automatically obtained. With this refinement, the proposed method needs fewer optimization parameters to achieve better control quality when compared with uniform refinement CVP method, whereas the computational cost is lower. Two well-known flight level altitude tracking problems and one minimum time cost problem are tested as illustrations and the uniform refinement control vector parameterization method is adopted as the comparative base. Numerical results show that the proposed method achieves better performances in terms of optimization accuracy and computation cost; meanwhile, the control quality is efficiently improved.

Production optimization for concentration and volume-limited fed-batch reactors in biochemical processes

Since a very slight violation of constraint could cause process safety and product quality problems in biochemical processes, an adaptive approach of fed-batch reactor production optimization that can strictly satisfy constraints over the entire operating time is presented. In this approach, an improved smooth function is proposed such that the inequality constraints can be transformed into smooth constraints. Based on this, only an auxiliary state is needed to monitor violations in the augmented performance index. Combined with control variable parameterization (CVP), the dynamic optimization is executed and constraint violations are examined by calculating the sensitivities of states to ensure that the inequality constraints are satisfied everywhere inside the time interval. Three biochemical production optimization problems, including the manufacturing of ethanol, penicillin and protein, are tested as illustrations. Meanwhile, comparisons with pure penalty CVP method, famous dynamic optimization toolbox DOTcvp and literature results are carried out. Research results show that the proposed method achieves better performances in terms of optimization accuracy and computation cost.

Temperature profile optimization: potential for multi-enzymatic biopolymer depolymerization processes

Optimal control of temperature was applied to a population balance model of enzymatically catalyzed depolymerization of a soluble polymer coupled with denaturation of enzyme. The reaction time required to reach a desired yield was predicted to be reduced by more than 10[Formula: see text] compared with isothermal operation. Also the yield within a given time could be increased by more than 5[Formula: see text] points. It was also possible to increase the yield and reduce the reaction time if a time-varying temperature profile was used. Furthermore, a simple-to-implement linear increasing temperature profile was shown to realize most of the saving potential. Rigorous optimization of the enzyme mixture and composition was predicted to have an even greater potential for improving the economic feasibility of the process. Optimization coupled with optimal control can be performed quickly in silico using the algorithm developed in this study if a validated and parameterized population balance model is available.

Fast engineering optimization: A novel highly effective control parameterization approach for industrial dynamic processes

Control vector parameterization (CVP) is an important approach of the engineering optimization for the industrial dynamic processes. However, its major defect, the low optimization efficiency caused by calculating the relevant differential equations in the generated nonlinear programming (NLP) problem repeatedly, limits its wide application in the engineering optimization for the industrial dynamic processes. A novel highly effective control parameterization approach, fast-CVP, is first proposed to improve the optimization efficiency for industrial dynamic processes, where the costate gradient formulae is employed and a fast approximate scheme is presented to solve the differential equations in dynamic process simulation. Three well-known engineering optimization benchmark problems of the industrial dynamic processes are demonstrated as illustration. The research results show that the proposed fast approach achieves a fine performance that at least 90% of the computation time can be saved in contrast to the traditional CVP method, which reveals the effectiveness of the proposed fast engineering optimization approach for the industrial dynamic processes.