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Nonlinear optimal control of cascaded irrigation canals with conservation law PDEs

control ENGINEERING PRACTICE 2020年 100卷 104407-104407页

作者： Zeng, Ningjun Cen, Lihui Xie, Yongfang Zhang, Shaohui Cent South Univ 932 South Lushan Rd Changsha Peoples R China China Inst Water Resources & Hydropower Res State Key Lab Simulat & Regulat Water Cycle River Beijing 100038 Peoples R China

This paper considers an optimal control problem for cascaded irrigation canals. The aim of the optimal control is to guarantee both the minimum water levels for irrigation demands and avoidance of water overflows even dam collapse. Due to the structural complexities involving control gates and interconnected long-distance water delivery reaches that are modeled by the Saint-Venant PDEs with conservation laws, wave superposition effects, coupling effects and strong nonlinearities made the optimal control be a hard task. A nonlinear optimal control method is proposed to deal with the PDE-constrained optimization problem via a control parameterization approach. control parameterization approximates the time-varying control by a linear combination of basis functions with control parameters. The Hamiltonian function method is used to derive the gradients of the objective function with respect to the control parameters as well as the time scale parameters for providing the search directions of the optimization problem with acceptable amount of computations. Based on the gradient formulas, a gradient-based optimization algorithm is proposed to solve the optimal control problem. The proposed nonlinear optimal control method is validated in two cases: a single reach canal in Yehe Irrigation District in Hebei Province (China) and a cascaded two-reach canal system.

关键词： Partial differential equations Optimal control control parameterization Gradient-based optimization

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A Comparison of Constrained Optimal control Algorithms

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IFAC Proceedings Volumes 1990年第8期23卷 439-447页

作者： S. Strand J.G. Balchen Division of Engineering Cybernetics The Norwegian Institute of Technology Trondheim Norway

he paper compares four different algorithms for the solution of control and state constrained optimal control problems. Three example problems have been chosen to challenge a conjugate gradient function space algorithm, the algorithms due to Sakawa and Shindo and to Goh and Teo, and an implementation of a simultaneous collocation and optimization algorithm. In the last algorithm, the state variables are approximated by Lagrange polynomials, while two different control parameterizations are applied. Piecewise constant control parameterization is applied by Goh and Teo. The results indicate that the algorithms in general should be preferred in the order: simultaneous optimization and collocation, conjugate gradient, Goh and Teo and Sakawa and Shindo.

关键词： Optimal control computational methods nonlinear programming nonlinear systems control parameterization

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Sequential time scaling transformation technique for time-delay optimal control problem

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COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION 2024年 133卷

作者： Chen, Yin Zhu, Xi Yu, Changjun Teo, Kok Lay Shanghai Univ Dept Math Shanghai 200444 Peoples R China Sunway Univ Sch Math Sci Selangor Malaysia

The time-scaling transformation technique used within the computational framework of control parameterization serves as an effective method for the optimization of control switching time as well as the control value for time-delay optimal control problems. However, the conventional time-scaling transformation stipulates that the switching times for all control components must be identical, which may not be feasible in real-world scenarios. To address this limitation, we introduce the sequential time-scaling transformation technique for solving time-delay optimal control problems. By sequentially applying control parameterization and time-scaling transformation to each of the control variable, the new technique enables the configuration of a varying number of segments for the control, and the switching time for each control component can be adaptively selected. Numerical results demonstrate that our approach not only achieves superior cost performance but also offers enhanced flexibility in control strategy.

关键词： Time-delay system control parameterization Time-scaling transformation Switching time optimization

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On the Optimal Placement of Robot Manipulators and Work Stations

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IFAC Proceedings Volumes 1992年第8期25卷 716-720页

作者： Petko Kiriazov Pencho Marinov Institute of Mechanics and Biomechanics Bulgarian Academy of Sciences "Acad.G.Bonchev" Str. bl.4 1113 Sofia

A direct-search control synthesis procedure for robots in point-to-point operation is, at first, proposed. The performance index is the mixed time energy loss functional. The procedure uses a set of simple, linear spline parameterized control functions and a weak conditions given to ensure existence of feasible solutions. On the base of the procedure above proposed, the problem of optimal placement is converted into a problem of nonlinear programming. An illustrative example is given to show how sensitive is the movement execution time with respect to the layout of the manipulator

关键词： robot manipulators time-energy loss minimization control parameterization shooting technique

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A new computational approach for optimal control of switched systems

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JOURNAL OF INEQUALITIES AND APPLICATIONS 2024年第1期2024卷 53页

作者： Zhu, Xi Bai, Yanqin Yu, Changjun Teo, Kok Lay Shanghai Univ Dept Math Shanghai Peoples R China Sunway Univ Sch Math Sci Sunway Malaysia

The combination of the time-scaling transformation and control parameterization has proven to be an effective approach in addressing optimal control problems involving switching systems with predefined subsystem sequences. However, this approach has certain limitations. First, the number of control switchings is required to be no less than the number of subsystem switchings. Second, the switching of the subsystem must be accompanied by the switching of the control. Third, this scheme introduces many hyperparameters, leading to combinatorial explosion. To address these drawbacks, we introduce a novel computational approach such that the control switching can be independent of subsystem switching. The superiority of this novel approach can be clearly observed from the solutions obtained using the proposed method for solving two illustrative examples.

关键词： Switched system Optimal control Switching time optimization control parameterization Time-scaling transformation

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Energy-efficient Medium-speed Maglev Train control Based on Resistance Fitting

Energy-efficient Medium-speed Maglev Train Control Based on ...

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第40届中国控制会议

作者： Junyu Shi Wenjin Yue Yiwei Wang Weifeng Zhong Beijing Jiaotong University

Compared with traditional rail transit systems with the same transport capacity, the maglev transport has great advantages in terms of safety, energy conservation and environmental protection. Since the maglev train is driven by the electromagnetic force and does not touch the rail when it is running, the form of basic resistance acting on the maglev train is more complex than that of the traditional train. This imposes extra challenges to obtain the energy-efficient control strategies for maglev trains. In this paper, we consider the energy-efficient control problem for medium-speed maglev trains whose basic resistance is a piecewise-quadratic function of train speed. Firstly, the piecewise-quadratic function is approximated as a single quadratic function by using the least square fitting method. Then, by applying control parameterization and time-scaling transformation technique, the traction and braking forces of the maglev train are approximated as piecewise-constant values at each track segment, and the energy-efficient maglev train control problem is transformed into a finite-dimensional optimization problem which is then solved by using the gradient-based sequential quadratic programming（SQP） algorithm. Finally, the effectiveness and performance of the proposed method are demonstrated by two numerical examples. The simulation results show that the proposed algorithm can fit the original resistance function well, and the obtained control strategy based on the fitted resistance results in lower energy consumption with higher computation efficiency.

关键词： Medium-speed Maglev Train Energy-efficient Train control Resistance Fitting control parameterization Time-scaling Transformation

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Pigeon-Inspired Optimization Approach to Multiple UAVs Formation Reconfiguration controller Design

Pigeon-Inspired Optimization Approach to Multiple UAVs Forma...

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2014中国制导、导航与控制学术会议

作者： Xiaomin Zhang Haibin Duan Chen Yang School of Advanced Engineering Beihang UniversityBeijingChina Science and Technology on Aircraft Control LaboratorySchool of Automation Science and Electrical EngineeringBeihang UniversityBeijingChina

ISBN: (纸本)9781479946983

This article introduces a controller for solving the problem of multiple unmanned aerial vehicles (UAVs) formation *** the constraints of terminal status and of control action energy,the controller aims to find the best values of UAV's inputs (including thrust,load factor,bank angle) to accomplish the *** basis of our controller is a method which combines PIO with ***-Inspired optimization (PIO) is a novel *** has been proposed and applied in engineering problems by following the inspirational precious *** is a method called control parameterization and time ***,we use a mathematical model to get a function which can evaluate the reconfiguration ***,to verify the validity of our controller,comparative experiments between PIO and particle swarm optimization (PSO) are *** comparative results demonstrate that our proposed controller embedded with PIO is much better than the one with PSO.

关键词： autonomous aerial vehicles control system synthesis evolutionary computation multi-robot systems particle swarm optimisation position control PIO algorithm PSO UAV formation reconfiguration controller design control action energy constraint control parameterization multiple unmanned aerial vehicles particle swarm optimization pigeon-inspired optimization approach reconfiguration effect terminal status constraint time discretization Compass Educational institutions Equations Linear programming Mathematical model Solid modeling Three-dimensional displays

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Optimal Orbit Transfer of Spacecraft under Constant Thrust

Optimal Orbit Transfer of Spacecraft under Constant Thrust

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第28届中国控制与决策会议

作者： Dake Gu Houqing Zhu School of Automation Engineering Northeast Dianh University

ISBN: (纸本)9781467397155

This paper considers the optimal orbit transfer problem of spacecraft under constant *** main purpose is to design the optimal control law to ensure the orbit transfer of the spacecraft with the least time *** is formulated as a constrained optimal control problem,where specific requirements of this orbit transfer problem are all incorporated in the problem ***,by utilizing the specific features of the problem,this optimal orbit transfer problem is transformed into an equivalent standard optimal control problem subject to continuous state inequality constraints.A computational method is developed,based on the control parameterization in conjunction with a time scaling transform and the constraint transcription method,to design the optimal controller for this new constrained optimal control *** simulation results are presented in the *** shows the feasibility and effectiveness of the proposed method.

关键词： Minimum-time Orbit Transfer control parameterization Time Scaling Transform Constraint Transcription

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Optimal Operation for Medium-speed Maglev Trains

Optimal Operation for Medium-speed Maglev Trains

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第三十九届中国控制会议

作者： Weifeng Zhong Hongze Xu Wenjing Zhang Ryan Loxton Yang Zhang Beijing Jiaotong University Curtin University CRCC Zhuzhou Locomotive Co.Ltd.

The maglev transportation system has obvious advantages in safety, reliability, and energy efficiency compared with other rail transit systems with the same carrying capacity. Research topics concerning optimal operations for maglev trains have attracted much attention in recent years. Since the basic resistance acting on the maglev train is more complex than that on the conventional train, it is more challenging to solve the time-optimal and energy-optimal problems, especially considering the operational and safety constraints, such as fluctuating track gradients, varying speed limits, and speed-dependent control bound constraints. This paper considers the time-optimal control problem for medium-speed maglev trains with operational and safety constraints. By expressing the basic resistance of the medium-speed maglev train as a piecewise-quadratic function of the train’s speed, we formulate the time-optimal control problem as an optimal switching control problem with free terminal time and state-dependent switching conditions. To solve this problem, we first transform the optimal switching control problem with free terminal time into one with fixed terminal time. Then, we introduce a binary-valued function to govern the switching condition, and further replace the binary constraints with equivalent continuous constraints. The resulting optimal control problem is converted into a finite-dimensional optimization problem by applying the control parameterization and time-scaling transformation techniques. The speed limit and speed-dependent control bound constraints are then transformed into a set of point and integral constraints. Furthermore, the equivalent continuous constraints involving the binary-valued function are tackled using the exact penalty method. Finally, we obtain a nonlinear programming problem which can be solved using gradient-based optimization algorithms. A numerical example using data for a real line is given to demonstrate the effectiveness of the

关键词： Medium-speed Maglev Train Time-optimal Operation State-dependent Switching control parameterization Time-scaling Transformation

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基于控制参数化多时滞线性系统的优化控制方法

基于控制参数化多时滞线性系统的优化控制方法

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湖南省第三届研究生创新论坛——信息与控制工程的新理论和新技术分论坛

作者：陈宁沈晓瑜桂卫华阳春华王凌云中南大学信息科学与工程学院长沙 410083

针对具有连续状态不等式约束的多时滞线性系统的优化控制问题，研究基于控制参数化的最优设计方法。通过把时滞系统动态模型中的控制量表示成关于时间的分段常数函数，把每个控制参数看作决策变量，从而将多时滞系统的控制问题转化为数... 详细信息

针对具有连续状态不等式约束的多时滞线性系统的优化控制问题，研究基于控制参数化的最优设计方法。通过把时滞系统动态模型中的控制量表示成关于时间的分段常数函数，把每个控制参数看作决策变量，从而将多时滞系统的控制问题转化为数学规划问题。推导出在连续状态不等式约束条件下的目标函数和约束函数对于待求参数的梯度公式，并用序列二次规划算法求出其最优控制量。最后，将该优化算法应用于湿法炼锌净化过程中。仿真结果说明，添加的锌粉量可以有效地减少，从而避免了资源的浪费。

关键词： multiple time-delays system control parameterization continuous state inequality constraints SQP algorithm

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