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

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OPTIMAL control APPLICATIONS & METHODS 2017年第4期38卷 586-600页

作者： Liu, Ping Li, Xiangyu Liu, Xinggao Hu, Yunqing Zhejiang Univ Coll Control Sci & Engn State Key Lab Ind Control Technol Hangzhou 310027 Zhejiang Peoples R China CSR Zhuzhou Inst Co Ltd Zhuzhou 412001 Hunan Peoples R China

An improved control vector parameterization (CVP) method is proposed to solve optimal control problems with inequality path constraints by introducing the l(1) 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 (c) 2016 John Wiley & Sons, Ltd.

关键词： nonlinear optimal control inequality path constraints control vector parameterization penalty function smoothing technique

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Dynamic Optimization using control vector parameterization with State Transition Algorithm 36

Dynamic Optimization using Control Vector Parameterization w...

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第36届中国控制会议

作者： Miao Huang Xiaojun Zhou Chunhua Yang Weihua Gui School of Information Science and Engineering Cental South University

ISBN: (纸本)9781538629185

In real-world applications,a majority of optimization problems belong to dynamic optimization,which involves optimization over time and whose underlying space is *** this paper,a novel dynamic optimization technique based on state transition algorithm(STA) is investigated to solve dynamic optimization problems(DOPs).Firstly,an infinite dynamic optimization problem is converted into a finite nonlinear programming problem(NLP) based on the control vector parameterizations(CVP),in which,instead of discretizing both state and control variables,only the control profiles are approximated by piecewise constant ***,a stochastic global method is proposed to solve the resulting nonlinear programming problem based on state transition *** applying it in two well-known dynamic optimization instances,simulation results show that the proposed approach is able to obtain similar or even better performance indicators compared with other methods in terms of computational cost,solution accuracy and stability.

关键词： State transition algorithm dynamic optimization control vector parameterization

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Establishment of UAV Formation Flight Using control vector parameterization and Sequential Convex Programming 35

Establishment of UAV Formation Flight Using Control Vector P...

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第35届中国控制会议

作者： GUO Juan CHU Jing YAN Jie Northwestern Polytechnical University

ISBN: (纸本)9781509009107

Formation flight of multiple Unmanned Aerial Vehicles(UAVs) could provide an effective, efficient yet low cost alternative to existing technologies. This paper addresses the energy-optimal establishment of UAV formation flight that shall satisfy final configuration constraints. First, the problem of formation establishment is formulated as an energy-optimal control problem which is constrained by the nonlinear dynamics. Then, the optimal control problem is solved using a direct *** this direct method the original problem is transcribed into a sequence of convex optimization problems via the control vector parameterization approach. After that, the sequential convex programming(SCP) technology is employed to derive the optimal solution. Essentially, each instance of SCP is a quadratic programming problem subject to linear constraints that can be solved very efficiently. In the end, the proposed method is applied to the establishment of V formation for three UAVs, where the free open source solver CVX is exploited. By comparison with the global optimization technique provided in MATLAB, the solution converges very fast to the global minimum.

关键词： UAV formation flight Optimal control control vector parameterization Sequential Convex Programming

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An iterative multi-objective particle swarm optimization-based control vector parameterization for state constrained chemical and biochemical engineering problems

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BIOCHEMICAL ENGINEERING JOURNAL 2015年 103卷 138-151页

作者： Zhang, Panpan Chen, Hongmei Liu, Xinggao Zhang, Zeyin Zhejiang Univ Dept Control Sci & Engn Inst Ind Proc Control State Key Lab Ind Control Technol Hangzhou 310027 Zhejiang Peoples R China Weifang Univ Inst Electromech & Vehicle Engn Weifang 262061 Peoples R China Zhejiang Univ Dept Math Hangzhou 310027 Zhejiang Peoples R China

Dynamic optimization of the state constrained chemical and biochemical engineering problems has always been the research hotspot due to the difficulties of handling constraints. In this paper, a novel approach, CVP-IMOPSO, is presented to tackle this kind of problems, where the original optimization problem is firstly converted into a multi-objective dynamic optimization problem based on a method of handling state constraint;and control vector parameterization (CVP) is then applied to transform the resulting infinite dimensional problem into a nonlinear programming (NLP) problem;finally, an efficient iterative multi-objective particle swarm optimization (IMOPSO), embedded with an region reduction strategy, is proposed to tackle this MOO problem. This strategy reduces the search space gradually during the iteration process so as to further promote the convergence rate and diversity of MOPSO. Three well-known classic optimization problems for chemical and biochemical engineering processes have been tested as illustration, and the detailed comparisons among IMOPSO, MOPSO and NSGA-II are carried out for seven benchmark problems. The research results not only show that the proposed IMOPSO is an efficient algorithm for MOO problems, but also reveal the effectiveness of the proposed approach. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Dynamic optimization Multi-objective particle swarm optimization control vector parameterization Multi-objective optimization Region reduction strategy State constrained engineering problems

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Optimal control vector parameterization Approach with a Hybrid Intelligent Algorithm for Nonlinear Chemical Dynamic Optimization Problems

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CHEMICAL ENGINEERING & TECHNOLOGY 2015年第11期38卷 2067-2078页

作者： Zhang, Panpan Liu, Xinggao Ma, Liang Zhejiang Univ Inst Ind Proc Control Control Dept Hangzhou 310027 Zhejiang Peoples R China

A control vector parameterization (CVP)-based hybrid algorithm, HAPSODSA-CVP, is proposed to solve the nonlinear chemical dynamic optimization problems, where adaptive particle swarm optimization (APSO) is applied to enhance the global search ability, while differential search algorithm (DSA) is used to improve the local exploitation ability. Three well-known classic nonlinear chemical dynamic optimization problems are tested as illustration, and detailed comparisons are carried out among PSO-CVP, APSO-CVP, and HAPSODSA-CVP approaches. The research results not only demonstrate the efficiency of the HAPSODSA-CVP approach for this kind of dynamic optimization problems, but also its superiority to both APSO-CVP and PSO-CVP approaches in terms of accuracy as well as convergence rate.

关键词： control vector parameterization Differential search algorithm Dynamic optimization Particle swarm optimization

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

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ENGINEERING OPTIMIZATION 2013年第9期45卷 1129-1146页

作者： Qian, Feng Sun, Fan Zhong, Weimin Luo, Na E China Univ Sci & Technol Key Lab Adv Control & Optimizat Chem Proc Minist Educ Shanghai 200237 Peoples R China

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.

关键词： control vector parameterization iterative genetic algorithm dynamic optimization chemical engineering

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Smooth trajectory generation based on contour error constraint and parameter correction b-spline

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INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY 2022年第7-8期119卷 4359-4373页

作者： Zhao, Kai Li, Shurong Kang, Zhongjian Liu, Zhe China Univ Petr East China Coll Control Sci & Engn Qingdao 266580 Peoples R China Anyang Inst Technol Coll Comp Sci & Informat Engn Anyang 455000 Peoples R China Beijing Univ Posts & Telecommun Sch Artificial Intelligence Beijing 100876 Peoples R China China Univ Petr East China Coll New Energy Qingdao 266580 Peoples R China

In terms of CNC machining task, high feedrate and high accuracy are of great significance. In this paper, an integrated jerk-limited method of minimal time trajectory planning with confined contour error (IJLMTPC) is proposed. Firstly, an optimal control method is utilized to obtain the minimal time feedrate profile. To compensate the contour error, it is added into the optimal control framework as a constraint. Based on the high-order transfer functions of every axis servo model, the contour errors constraint is formulated as the function of tracking errors. However, the optimal control problem (OCP) is difficult to be solved. Hence, the OCP is transformed into two convex subproblems. Since the axial jerk elements are included in the contour error constraint, they are no longer considered as dependent constraints in the two subproblems specially. Afterwards, two subproblems are discretized with control vector parameterization. Consequently, two subproblems are more efficient to be solved with nonlinear programming, and the minimal time feedrate is obtained. Secondly, considering that the OCP is solved on the domain of curve parameter, it is inconvenient for real-time interpolation. The resulting feedrate from solving the OCP is transformed into the corresponding profile on time domain, while the limited tangent jerk is imposed on. Hence, the feedrate is smoothed. Finally, to alleviate the fluctuation of feedrate, the real-time interpolation is performed based on the parameter correction b-spline. Two benchmark tool paths are adopted to test the proposed scheme, and the effectiveness is verified.

关键词： Parameter correction b-spline Computer numerical control control vector parameterization Interpolation Smooth trajectory planning Contour error constraint

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Chaos Elite Harris Hawk Optimization Algorithm to Solve Chemical Dynamic Optimization Problems

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IEEE ACCESS 2022年 10卷 65833-65853页

作者： Hong, Lila Mo, Yuanbin Bao, Dongxue Gong, Rong Guangxi Minzu Univ Inst Artificial Intelligence Nanning 530006 Peoples R China Guangxi Minzu Univ Guangxi Key Lab Hybrid Computat & IC Design Anal Nanning 530006 Peoples R China

Dynamic optimization problems in chemical engineering are often described by complex differential equations, In general, Due to the complexity of the model established in practice, it is not easy to solve it with an accurate algorithm, so the study of numerical methods to solve such problems has received much attention. As a new computing model, intelligent optimization algorithm has attracted more attention in solving dynamic optimization problems because of their easy operation. Based on the analysis of the Harris Hawk Optimization algorithm, this paper proposes the Chaos Elite Harris Hawk Optimization algorithm (CEHHO), which is used to improve the performance of CEHHO using control vector parameterization to solve dynamic optimization problems of the chemical industry. First of all, when the population is initialized, the population is initialized by Opposition-based learning Logistic chaos, which improves the diversity of the population and the quality of the solution. Second, the linear decreasing escape energy factor is changed to a nonlinear decreasing escape energy factor to balance the exploration and exploitation capabilities of the algorithm. Finally, through the mutation strategy guided by elite individuals, the algorithm can jump out of the local optimum. We use 8 test functions and 5 classical chemical optimization problems to evaluate the feasibility of the algorithm and compare and analyze the research results with other solving methods, showing the superiority of the CEHHO algorithm.

关键词： Optimization Heuristic algorithms Rabbits Chemicals Dynamic programming Statistics Sociology Chaos Elite Harris Hawk opposition-based learning elite individual mutation strategy chemical optimization control vector parameterization

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Stochastic state-feedback control using homotopy optimization and particle filtering

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INTERNATIONAL JOURNAL OF DYNAMICS AND control 2022年第3期10卷 942-955页

作者： Polisetty, Venkata Goutham Varanasi, Santhosh Kumar Jampana, Phanindra Indian Inst Technol Hyderabad Dept Chem Engn Hyderabad 502285 India Univ Alberta Dept Chem & Mat Engn Edmonton AB T6G 1H9 Canada

In this paper, a method of designing control inputs for stochastic nonlinear processes under state-feedback is proposed. The objective is to determine a control input that minimizes the expected value of the integral of error between the set-point and the states. Since the states may not be measured, they are estimated using a particle filtering algorithm. The optimal control design is then reformulated as a parameter estimation problem using control vector parameterization where the inputs are considered as a nonlinear function of the error between the state estimates and the set-point. The parameters are then computed through a homotopy based optimization method. The control performance resulting from proposed homotopy based optimization method is compared with that of direct optimization and an existing nonlinear control method on a Solid Oxide Fuel Cell (SOFC) stack model.

关键词： Stochastic dynamic systems Particle filtering control vector parameterization Homotopy optimization

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Process control of chemical dynamic system based on multi-strategy mayfly optimization algorithm

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2024年第3期46卷 7327-7352页

作者： Li, Jingyan Mo, Yuanbin Hong, Lila Gong, Rong Guangxi Minzu Univ Sch Artificial Intelligence Nanning Peoples R China Guangxi Minzu Univ Guangxi Key Lab Hybrid Computat & IC Design Anal Nanning Peoples R China Guizhou Police Coll Guiyang Peoples R China Aba Teachers Coll Sch Comp Sci & Technol Wenchuan Peoples R China

Dynamic optimization problems exist widely in chemical industry, and its operational variables change with the evolution of both space and time. Therefore, dynamic optimization problems have important research significance and challenges. To solve this problem, a multi-strategy mayfly optimization algorithm (MMOA) combined with control variable parameterization method(CVP) is proposed in this paper. MMOA introduces three improvements on the basis of the original algorithm, namely, circle chaos crossover strategy, center wandering strategy and boundary correction strategy. The hybrid strategy can better balance the exploration and exploitation ability of the algorithm. Based on MATLAB simulation environment, MMOA was evaluated. The experimental results show that MMOA has excellent performance in solving precision, convergence speed and stability for the benchmark function. For the six classical chemical dynamic optimization problems, MMOA obtained the performance indexes of 0.61071, 0.4776, 0.57486, 0.73768, 0.11861 and 0.13307, respectively. Compared with the data in the previous literature, MMOA can obtain more accurate control trajectory and better performance indicators. It provides an effective way to solve the dynamic optimization problem.

关键词： Chemical dynamic system process control dynamic optimization mayfly optimization algorithm control vector parameterization

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