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Transformed orthogonal functions for solving infinite horizon fractional optimal control problems

EUROPEAN JOURNAL OF CONTROL 2021年 59卷 13-28页

作者： Shahini, M. Mehrpouya, M. A. Gonbad Kavous Univ Fac Basic Sci Dept Math & Stat Gonbad Kavous Iran Tafresh Univ Dept Math Tafresh *** Iran

In the present paper, an efficient numerical method for solution of infinite horizon fractional optimal con-trol problems is investigated. The fractional derivative in such problems is considered in the Caputo sense. The methodology developed here, is based on utilizing transformed orthogonal functions to approximate the state and control functions directly. Thereby, the original problem is converted to a nonlinear pro-gramming problem which can be solved by the well-developed parameter optimization algorithms. While the present solution procedure provides good results and high rate of convergence is achieved, the infinite horizon fractional optimal control problem is solved on the original time interval of the problem, without transforming it to a finite one. Illustrative examples are included at the end and the effectiveness of the proposed methodology is demonstrated. (c) 2021 European Control Association. Published by Elsevier Ltd. All rights reserved. In the present paper, an efficient numerical method for solution of infinite horizon fractional optimal con-trol problems is investigated. The fractional derivative in such problems is considered in the Caputo sense. The methodology developed here, is based on utilizing transformed orthogonal functions to approximate the state and control functions directly. Thereby, the original problem is converted to a nonlinear pro-gramming problem which can be solved by the well-developed parameter optimization algorithms. While the present solution procedure provides good results and high rate of convergence is achieved, the infinite horizon fractional optimal control problem is solved on the original time interval of the problem, without transforming it to a finite one. Illustrative examples are included at the end and the effectiveness of the proposed methodology is demonstrated. (c) 2021 European Control Association. Published by Elsevier Ltd. All rights reserved.

关键词： Fractional optimal control Orthogonal functions Infinite horizon problems Collocation methods nonlinear programming problem

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A robust pseudospectral method for numerical solution of nonlinear optimal control problems

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2021年第6期98卷 1146-1165页

作者： Mehrpouya, Mohammad Ali Peng, Haijun Tafresh Univ Dept Math Tafresh *** Iran Dalian Univ Technol State Key Lab Struct Anal Ind Equipment Dept Engn Mech Dalian Peoples R China

In the present paper, a robust pseudospectral method for efficient numerical solution of nonlinear optimal control problems is presented. In the proposed method, at first, based on the Pontryagin's minimum principle, the first-order necessary conditions of optimality which are led to the Hamiltonian boundary value problem are derived. Then, utilizing a pseudospectral method for discretization, the nonlinear optimal control problem is converted to a system of nonlinear algebraic equations. However, the need to have a good initial guess may lead to a challenging problem for solving the obtained system of nonlinear equations. So, an optimization approach is introduced to simplify the need of a good initial guess. Numerical findings of some benchmark examples are presented at the end and computational features of the proposed method are reported.

关键词： Optimal control Hamiltonian boundary value problem Pontryagin's minimum principle pseudospectral methods nonlinear programming problem

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A Low-Dimensional Optimization Method for Parallel Parking Path Planning

A Low-Dimensional Optimization Method for Parallel Parking P...

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2025 International Conference on Electrical Automation and Artificial Intelligence, ICEAAI 2025

作者： Hu, Qiuxia Zhan, Guanglun Gao, Feng Liu, Hongwei College of Mechanical and Vehicle Engineering Chongqing University Chongqing China Co. Ltd. Chongqing China

ISBN: (纸本)9798331506797

Optimization-based parking path planner can make full use of parking space, but its extensive computational consumption limits its practical application. This paper proposes a low-dimensional optimization path planning method, which accelerates the numerical computation process by reducing the number of the optimization variables and obstacle avoidance constraints. Since differential equations in the optimization-based planner require many discretize points to ensure numerical accuracy, the geometric characteristic of the optimal path is analyzed from a large amount of optimization results and further used to describe the parallel parking mission as a low-dimensional nonlinear programming problem that only consists of algebraic equations. As adjacent points on the parking path are connected by analytical curves, a simplified obstacle avoidance constraint is designed based on relative geometric position relationship between these curves and obstacle boundary lines. Based on this, a collision-free parking path can be optimized by verifying obstacle avoidance constraints only at the endpoints. Simulation results show that the optimized path is collision-free and the optimization process is accelerated by these techniques. © 2025 IEEE.

关键词： nonlinear programming problem Obstacle avoidance Optimization Parallel parking Path planning

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A Shape Optimisation with the Isogeometric Boundary Element Method and Adjoint Variable Method for the Three-Dimensional Helmholtz Equation

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COMPUTER-AIDED DESIGN 2022年 142卷 103126-103126页

作者： Takahashi, Toru Sato, Daisuke Isakari, Hiroshi Matsumoto, Toshiro Nagoya Univ Grad Sch Engn Dept Mech Syst Engn Furo Cho Nagoya Aichi 4648603 Japan

This paper presents a shape optimisation system to design the shape of an acoustically-hard object in the three-dimensional open space. The boundary element method (BEM) is suitable to analyse such an exterior field. However, the conventional BEM, which is based on piecewise polynomial shape and approximate (interpolation) functions, can require many design variables because they are usually chosen as a part of the nodes of the underlying boundary element mesh. In addition, it is not easy for the conventional method to compute the gradient of the sound pressure on the surface, which is necessary to compute the shape derivative of our interest, of a given object. To overcome these issues, we employ the isogeometric boundary element method (IGBEM), which was developed in our previous work. With using the IGBEM, we can design the shape of surfaces through control points of the NURBS surfaces of the target object. We integrate the IGBEM with the nonlinear programming software through the adjoint variable method (AVM), where the resulting adjoint boundary value problem can be also solved by the IGBEM with a slight modification. The numerical verification and demonstration validate our shape optimisation framework. (C) 2021 Elsevier Ltd. All rights reserved.

关键词： Boundary element method Isogeometric analysis Shape optimisation Adjoint variable method nonlinear programming problem

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Hybrid battery-ultracapacitor storage system sizing for renewable energy network integration

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IET RENEWABLE POWER GENERATION 2020年第13期14卷 2367-2375页

作者： Gonzalez-Gonzalez, Jose M. Martin, Sebastian Lopez, Pablo Aguado, Jose A. Univ Malaga Dept Elect Engn C Doctor Ortiz Ramos S-N Malaga 29071 Spain

Wind and Solar photovoltaic power plants outputs are usually highly variable due to gusts of wind and sharp sun irradiance level variations caused by cloud shading effects. These effects negatively impact system security, especially in weak power networks. On the other hand, due to the recent technological progress and cost reductions, electrical energy storage systems are an attractive alternative that can be easily integrated into non-despatchable power plants to compensate for those power output fluctuations. This study proposes a methodology for optimal sizing of a hybrid (lithium-ion battery and ultracapacitor) energy storage system for renewable energy network integration. Special attention is paid to the battery cycling degradation process. It is shown that battery aging due to cycling is a major driver for optimal sizing. The resulting sizing problem is posed as a non-linear programming problem. Finally, real and illustrative case studies are presented for both, wind and photovoltaic power plants integrating a hybrid energy storage system. Results are reported by comparing different energy storage system configurations.

关键词： photovoltaic power systems supercapacitors secondary cells cost reduction energy management systems ageing wind power plants solar power wind power nonlinear programming battery storage plants battery management systems lithium compounds power generation economics power system security hybrid power systems solar photovoltaic power plants hybrid battery-ultracapacitor storage system sizing renewable energy network integration cloud shading effects system security cost reductions electrical energy storage systems nondespatchable power plants power output fluctuations lithium-ion battery battery cycling degradation process nonlinear programming problem sun irradiance level variations wind power plants battery aging

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Pseudo-spectral method for controlling the drug dosage in cancer

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IET SYSTEMS BIOLOGY 2020年第5期14卷 261-270页

作者： Nazari, Mostafa Nazari, Morteza Noori Skandari, Mohammad Hadi Shahrood Univ Technol Fac Mech & Mechatron Engn POB *** Shahrood Iran Shahrood Univ Technol Fac Math Sci POB *** Shahrood Iran

A mixed chemotherapy-immunotherapy treatment protocol is developed for cancer treatment. Chemotherapy pushes the trajectory of the system towards the desired equilibrium point, and then immunotherapy alters the dynamics of the system by affecting the parameters of the system. A co-existing cancerous equilibrium point is considered as the desired equilibrium point instead of the tumour-free equilibrium. Chemotherapy protocol is derived using the pseudo-spectral (PS) controller due to its high convergence rate and simple implementation structure. Thus, one of the contributions of this study is simplifying the design procedure and reducing the controller computational load in comparison with Lyapunov-based controllers. In this method, an infinite-horizon optimal control problem is proposed for a non-linear cancer model. Then, the infinite-horizon optimal control of cancer is transformed into a non-linear programming problem. The efficient Legendre PS scheme is suggested to solve the proposed problem. Then, the dynamics of the system is modified by immunotherapy is another contribution. To restrict the upper limit of the chemo-drug dose based on the age of the patients, a Mamdani fuzzy system is designed, which is not present yet. Simulation results on four different dynamics cases how the efficiency of the proposed treatment strategy.

关键词： patient treatment cancer convergence linear programming optimal control nonlinear programming nonlinear control systems Lyapunov methods drugs tumours nonlinear programming problem efficient Legendre PS scheme chemo-drug dose Mamdani fuzzy system treatment strategy pseudospectral method drug dosage mixed chemotherapy-immunotherapy treatment protocol cancer treatment desired equilibrium point immunotherapy alters cancerous equilibrium point tumour-free equilibrium chemotherapy protocol pseudospectral controller high convergence rate simple implementation structure controller computational load Lyapunov-based controllers infinite-horizon optimal control problem nonlinear cancer model

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Risk-constrained offering strategies for a large-scale price-maker electric vehicle demand aggregator

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IET SMART GRID 2020年第6期3卷 860-869页

作者： Hossein Abbasi, Mohammad Taki, Mehrdad Rajabi, Amin Li, Li Zhang, Jiangfeng Univ Qom Dept Elect Engn Qom Iran Univ Technol Dept Elect & Data Engn Sydney NSW Australia Clemson Univ Dept Automot Engn Clemson SC 29631 USA

In this study, the problem of an electric vehicle (EV) aggregator participating in a three-settlement pool-based market is presented. In addition to energy procurement, it is assumed that EVs can sell electricity back to the markets. In order to obtain optimised solutions, the aggregator is considered as a price-maker agent who tries to minimise the cost of purchasing energy from the markets by offering price-energy bids in the day-ahead market and only energy bids in both adjustment and balancing markets. Since the problem is heavily constrained by equality constraints, the number of binary variables for a 24-hour market horizon is too large which leads to intractability when solved by traditional mathematical algorithms like the interior point. Therefore, an evolutionary metaheuristic algorithm based on genetic algorithms (GAs) is proposed to deal with the intractability. In this regard, first, the stochastic problem is formulated as a mixed-integer linear programming problem, and as a non-linear programming problem to be solved by CPLEX and GA, respectively. The former is used to ensure that the GA is tuned properly, and helps to avoid converging to local extremums. Furthermore, the solutions of the two formulations are compared in simulations to demonstrate GA could be faster in obtaining better results.

关键词： power generation economics genetic algorithms pricing linear programming optimisation power markets integer programming 24-hour market horizon intractability traditional mathematical algorithms evolutionary metaheuristic algorithm genetic algorithms stochastic problem mixed-integer linear programming problem nonlinear programming problem risk-constrained offering strategies large-scale price-maker electric vehicle demand aggregator electric vehicle aggregator EV three-settlement pool-based market energy procurement electricity optimised solutions price-maker agent purchasing energy price-energy bids day-ahead market balancing markets

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Optimisation of the duplex D2D network: a deep learning approach

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IET NETWORKS 2020年第3期9卷 139-144页

作者： Liu, Xian Univ Arkansas Little Rock Dept Syst Engn Little Rock AR 72204 USA

For wireless networks, it is highly desirable to design a quality-of-service-promotion strategy to allocate the transmission power. In this study, the authors apply the deep learning methodology to solve such a problem in a duplex device-to-device network. The model is formulated as a constrained non-linear programming problem. The training data are generated by a standard optimisation tool. Then, an artificial neural network is designed to learn the system from the training data. Simulation results show the effectiveness of deep leaning.

关键词： learning (artificial intelligence) neural nets optimisation nonlinear programming linear programming cellular radio duplex D2D network deep learning approach wireless networks quality-of-service-promotion strategy transmission power deep learning methodology device-to-device network nonlinear programming problem training data standard optimisation tool artificial neural network deep leaning

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Optimal control problem of multi-vehicle cooperative autonomous parking trajectory planning in a connected vehicle environment

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IET INTELLIGENT TRANSPORT SYSTEMS 2019年第11期13卷 1677-1685页

作者： Wu, Bing Qian, Lijun Lu, Meiling Qiu, Duoyang Liang, Haiqin Hefei Univ Technol Coll Automot & Transportat Engn Dept Vehicle Engn Hefei 230009 Anhui Peoples R China Nanjing Univ Aeronaut & Astronaut Coll Automat Engn Dept Elect Engn Nanjing 210016 Jiangsu Peoples R China

The development of intelligent network and intelligent vehicle technology makes it possible for multi-vehicle cooperative driving. In this study, the multi-vehicle cooperative autonomous parking condition is addressed by establishing a vehicle kinematics model combined with dynamic constraints and endpoint and collision avoidance constraints. The autonomous parking trajectory planning problem is transformed into an optimal control problem. The shortest parking completion time is set as the optimal cost function, and the optimal control problem is discretised by using the Gauss pseudo-spectral method. Then, the non-linear programming problem is solved. Moreover, an initial guess generation strategy is proposed, and the iteration method is used to solve the problem by adding collision avoidance constraints to the collision situation of the vehicle to improve the convergence and robustness of the problem. The simulation model is built in MATLAB/Simulink to simulate multi-vehicle cooperative autonomous parking under different working conditions. The simulation results show that the proposed method can solve the multi-vehicle cooperative autonomous parking trajectory planning problem uniformly and effectively. Compared with the traditional pseudo-spectral method, the proposed method has a faster convergence speed.

关键词： optimisation nonlinear programming path planning iterative methods optimal control mathematics computing mobile robots collision avoidance trajectory control linear programming optimal control problem connected vehicle environment intelligent vehicle technology autonomous parking condition vehicle kinematics model collision avoidance constraints autonomous parking trajectory planning problem shortest parking completion time optimal cost function nonlinear programming problem

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A framework of shape optimisation based on the isogeometric boundary element method toward designing thin-silicon photovoltaic devices

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ENGINEERING WITH COMPUTERS 2019年第2期35卷 423-449页

作者： Takahashi, Toru Yamamoto, Tatsuro Shimba, Yuta Isakari, Hiroshi Matsumoto, Toshiro Nagoya Univ Grad Sch Engn Dept Mech Syst Engn Furo Cho Nagoya Aichi 4648603 Japan Nagoya Univ Grad Sch Engn Dept Micronano Syst Engn Furo Cho Nagoya Aichi 4648603 Japan

We propose a gradient-based optimisation framework to design the shape of the interfaces in periodic layered structures, which can model photovoltaic devices, optical gratings, etc., according to a desired electromagnetic property. To this end, we first develop an isogeometric boundary element method (IGBEM) to analyse singly periodic boundary value problems for 2D Helmholtz equation in layered media. By nature, the IGBEM is not only numerically accurate but also suitable for the shape optimisation in comparison with the conventional boundary- and domain-type solvers. Next, we derive the shape derivative (or shape sensitivity) of the objective function in terms of the magnetic field strength or energy absorption rate on the basis of the adjoint variable method. The shape derivative can be computed by solving the primal and adjoint problems with the IGBEM. Subsequently, we map our shape optimisation problems to nonlinear programming problems in order to exploit a general-purpose software for the latter problems. After verifying our optimisation framework rigorously by comparing with the exact solutions, we demonstrate a shape optimisation of the silicon-metal interface in a model of thin-silicon photovoltaic devices: it is crucial to determine the interface so that the energy of the incident light can be confined in the silicon layer as much as possible when the thickness of the layer is unconventionally small;one micrometre in our model. The optimal shape achieved 8.6 times higher absorption rate than the reference (flat) shape. This simulation shows that the proposed framework is capable of making a fundamental contribution to analysing and designing photovoltaic devices as well as photonic and plasmonic devices that consist of singly periodic layers.

关键词： Boundary element method Isogeometric analysis Periodic structure Shape optimisation Adjoint variable method nonlinear programming problem Quasi-Newton method Photovoltaic device Surface plasmon Plasmonics

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