Control Vector Parameterization Method Research Articles

An improved slope-based adaptive control vector parameterization method for dynamic programming

Control vector parameterization method is the most commonly used numerical computation method in solving dynamic programming problems. However, to balance the expected trajectory and the computational cost, this method faces difficulties in dividing the optimal discretization time grid. In this paper, we propose an effective control approach for non-uniform adaptive grid division. By analyzing the slope change trend of the control parameter, time nodes are adaptively refined by merging time grids with gentle slopes to remove unnecessary time nodes and adding time nodes to time grids with steep slopes to improve function approximation accuracy. Eventually, we obtain an adaptive time grid division method under which the trajectory of discretization control parameter is more approximate to the optimal control trajectory. Under the condition of intuitive slope information, the proposed method can achieve better performance with fewer optimization parameters and shorter computation time. Finally, the proposed method is applied to solve a classic optimal control problem and the obtained results are compared with the traditional control vector parameterization method. By comparison through the example, our proposed method can overcome the contradiction between approximation accuracy and computational cost in control vector parameterization method and improve the optimization efficiency.

Gaussian Distribution–Based Control Vector Parameterization Method for Constrained Hypersonic Vehicle Reentry Trajectory Optimization

Gaussian Distribution–Based Control Vector Parameterization Method for Constrained Hypersonic Vehicle Reentry Trajectory Optimization

Modeling and High-performance Trajectory Optimization of the Industrial Robot

Rapidity, accuracy and energy cost are the key performance indexes for of the work of industrial robot. In this paper, the shortest time and the minimum energy consumption are taken as the goal for the comprehensive optimization. The control vector parameterization method is used to reasonably refine the time grid of the optimization problem. Then, an efficient control strategy for non-uniform adaptive mesh refinement is proposed. According to different changing trends, time nodes are merged or inserted into the time grid. While reducing the number of discrete grids, it also ensures the accuracy of the solution. Taking the Manutec R3 industrial robot as the object, the trajectory optimization simulation calculation is carried out. According to the verification of the simulation computing, the proposed method can significantly improve the time grid refinement. Compared with the traditional CVP method, not only the calculation time is shortened, but also more accurate results can be obtained.

Hybrid Intelligence Assisted Sample Average Approximation Method for Chance Constrained Dynamic Optimization

Realistic industrial process is usually a dynamic process with uncertainty. Chance constraints are applicable to industrial process modeling under uncertain conditions, where constraints cannot be strictly met, or need not be fully met. Therefore, chance constrained dynamic optimization (CCDO) formulation is available to address realistic industrial process issues. Because of the dynamic and uncertainty, chance constrained dynamic optimization problems (CCDOPs) arising from practical industries are hard to cope with. In this article, a novel CCDO method is proposed to resolve this issue, where an adaptive sample average approximation method, a control vector parameterization method, and a state constraint handling strategy are integrated. Specially, a hybrid intelligent optimization algorithm is introduced to realize a global and efficient optimization performance. The proposed method is applied to CCDOPs modified by dynamic optimization standard test functions and industrial experiments to demonstrate its effectiveness. The experimental results show that the proposed method has good performance in solving CCDOPs.

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.

An improved smoothing technique-based control vector parameterization method for optimal control problems with inequality path constraints

Summary An improved control vector parameterization (CVP) method is proposed to solve optimal control problems with inequality path constraints by introducing the l1 exact penalty function and a novel smoothing technique. Both the state and control variables are allowed to appear explicitly in the inequality path constraints simultaneously. By applying the penalty function and smoothing technique, all the inequality path constraints are firstly reformulated as non-differentiable penalty terms and incorporated into the objective function. Then, the penalty terms are smoothed by using a novel smooth function, leading to a smooth optimal control problem with no inequality path constraints. With discretizing the control space, a corresponding nonlinear programming (NLP) problem is derived, and error between the NLP problem and the original problem is discussed. Results reveal that if the smoothing parameter is sufficiently small, the solution of the NLP problem is approximately equal to the original problem, which shows the convergence of the proposed method. After clarifying some theories of the proposed approach, a concomitant numerical algorithm is put forward with furnishing the updating rules of both the penalty parameter and smoothing parameter. Simulation examples verify the advantages of the proposed method for tackling nonlinear optimal control problems with different inequality path constraints. Copyright © 2016 John Wiley & Sons, Ltd.

Empirical mode decomposition-based time grid refinement optimization approach for optimal control problems

This paper presents a novel and efficient grid refinement approach for choosing discretization level of control vector parameterization (CVP) method. Different from the uniform time grid CVP method, the proposed method adaptively refines the time grid knots by applying the empirical mode decomposition at each iteration. An attractive property of the proposed method is that fewer parameters are needed to achieve better optimization results, which means that a high-quality solution can be obtained with lower computation cost. The related derivation shows the advantage of simplicity for implementation. Compared with the existing approaches, for which all the control variables are parameterized on the same time grid, the proposed method is more flexible. A standard optimal control problem is tested as an illustration to demonstrate the validity of the proposed method, results indicate better performance index and lower computation cost of the proposed method.

Optimal timing of technology adoption under the changeable abatement coefficient through R&D

Advanced abatement technology adoption has been attached a great importance upon the economic profit especially in the traditional energy intensive industries. In making the adoption decision, a firm has to evaluate the economic profit between the adoption of the advanced technologies and the traditional ones. Moreover, due to the learning-by-searching (LBS) effect, it is preferable to invest upon the installed abatement technology to further increasing the economic profit. Thus, to describe a comprehensive decision strategy, we proposed a hybrid model including output, R&D investment as well as the adoption time to be optimized at the same time. Regarding these as the decision variables, our formulation gives rise to an optimal switching problem for a hybrid system, however, which can hardly be solved analytically. To implement the numerical simulation, we make a transformation in the parameter filed in order to use the control vector parameterization method to solve the original problem. Thus, the proposed optimal control problem can be converted into a non-linear programming problem (NLP), which can be solved conveniently and effectively using the current technique. Based on these facts, we shows that some key economic parameters that inherently define the revenue relationships outside the firm can significantly influence the time of adoption. Furthermore, considering the problem in the multi-technology adoption case, the process can perform in such an unusual way that the firm can leap over some transition technologies to adopt a higher advanced one directly, from which corresponding results are discussed as well.

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.

Dynamic optimization of chemical engineering problems using a control vector parameterization method with an iterative genetic algorithm

An approach that combines genetic algorithm (GA) and control vector parameterization (CVP) is proposed to solve the dynamic optimization problems of chemical processes using numerical methods. In the new CVP method, control variables are approximated with polynomials based on state variables and time in the entire time interval. The iterative method, which reduces redundant expense and improves computing efficiency, is used with GA to reduce the width of the search region. Constrained dynamic optimization problems are even more difficult. A new method that embeds the information of infeasible chromosomes into the evaluation function is introduced in this study to solve dynamic optimization problems with or without constraint. The results demonstrated the feasibility and robustness of the proposed methods. The proposed algorithm can be regarded as a useful optimization tool, especially when gradient information is not available.

Novel Control Vector Parameterization Method with Differential Evolution Algorithm and Its Application in Dynamic Optimization of Chemical Processes

Two general approaches are adopted in solving dynamic optimization problems in chemical processes, namely, the analytical and numerical methods. The numerical method, which is based on heuristic algorithms, has been widely used. An approach that combines differential evolution (DE) algorithm and control vector parameterization (CVP) is proposed in this paper. In the proposed CVP, control variables are approximated with polynomials based on state variables and time in the entire time interval. Region reduction strategy is used in DE to reduce the width of the search region, which improves the computing efficiency. The results of the case studies demonstrate the feasibility and efficiency of the proposed methods.

ARX-NNPLS Model Based Optimization Strategy and Its Application in Polymer Grade Transition Process

Since it is often difficult to build differential algebraic equations (DAEs) for chemical processes, a new data-based modeling approach is proposed using ARX (AutoRegressive with eXogenous inputs) combined with neural network under partial least squares framework (ARX-NNPLS), in which less specific knowledge of the process is required but the input and output data. To represent the dynamic and nonlinear behavior of the process, the ARX combined with neural network is used in the partial least squares (PLS) inner model between input and output latent variables. In the proposed dynamic optimization strategy based on the ARX-NNPLS model, neither parameterization nor iterative solving process for DAEs is needed as the ARX-NNPLS model gives a proper representation for the dynamic behavior of the process, and the computing time is greatly reduced compared to conventional control vector parameterization method. To demonstrate the ARX-NNPLS model based optimization strategy, the polyethylene grade transition in gas phase fluidized-bed reactor is taken into account. The optimization results show that the final optimal trajectory of quality index determined by the new approach moves faster to the target values and the computing time is much less.

Dynamic Operation Optimization of a Trigeneration System

It is considered that the electric, thermal and cooling loads of a building complex are covered by a tri-generation system consisting of a gas engine with heat recovery, an absorption chiller driven by thermal energy, electrically driven compression chillers and two thermal storage tanks (one with hot and one with cold water). Supplementary electricity is supplied by the local network. The behavior of such a system during transients is characterized primarily by the transient performance of the storage tanks and the absorption chiller (start-up and shut-down). The objective of the work reported here is the operation optimization of the system under load-varying conditions taking into consideration the transient behavior of the three aforementioned components. The simulation of the dynamic behavior of the absorption chiller, in particular, is based on the Gompertz function (sigmoid curve). Minimization of the total cost for covering the energy needs of the building is selected as the objective function, while the operating point of each component is to be determined by optimization under specified constraints. The optimal values of the control variables are determined using a multi–stage control vector parameterization method and optimization software based on Sequential Quadratic Programming. The solution of the optimization problem is accompanied by a sensitivity analysis. Suggestions are written for continuation and improvement of the work.

Dynamic Real-time Optimization of Reservoir Production

Water flooding is a common technology of enhanced oil recovery and has been widely used to the world's oil fields. But it is difficult to maintain a uniform displacement of water, which causes the ineffective circulation of injected water. Therefore, the real-time dynamic control strategy is studied to work out development plans scientifically and make better economic profits in this paper. The net present value of crude oil exploitation during a certain period of time is choosen to performance index of the control problem. Hydrodynamic equations of oil, water and gas, which describe the displacement process, are used as governed equations. Meanwhile, the boundary constraints of wells and balance relationship of injection-production are taken into account. Based on the above equations, a control model of oil field development is established. The control vector parameterization method is illustrated in detail to deal with the unconstrained, control constrained and state constrained optimal control problem. Finally, a simulation example is employed to verify the validity of the proposed control algorithm.

Optimization of boiler start-up using a nonlinear boiler model and hard constraints

The basis for control optimization is a nonlinear modeling for a drum-type boiler consisting of furnace, economizer, evaporator, superheaters, attemperator, turbine bypass and thick-walled components such as boiler drum and superheater header. After the mathematical formulation of the boiler start-up optimization problem and of the cost function, including the related hard constraints for inputs and states, the optimal reference and input control are calculated using a multi-stage control vector parameterization method and SQP techniques. The results of this optimization process are optimal reference values and the corresponding input trajectories. The control structures applied minimize both the fuel consumption and start-up time of the boiler.

Optimal grade transition control for polymerization reactors

A nonlinear control system integrating an off-line optimizer and a nonlinear MPC controller is developed to perform optimal grade transition operations at the industrial polyolefin reactors. In this, paper, the details of the optimizer are given: The sequential nonlinear programming is performed in the optimizer by employing control vector parameterization method together with sensitivity analysis. The switching times (i.e. times of chaning in the input actions) can be also optimized by new formulation and a modification in trial functions. The simulation result illustrates the capability of the control system with the proposed optimizer.