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Perimeter control With State-Dependent Delays: Optimal control Model and Computational Method

IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 2022年第11期23卷 20614-20627页

作者： Yuan, Jinlong Wu, Changzhi Teo, Kok Lay Zhao, Shuang Meng, Lixia Dalian Maritime Univ Dept Appl Math Sch Sci Dalian 116026 Peoples R China Guangzhou Univ Sch Management Guangzhou 510006 Peoples R China Sunway Univ Sch Math Selangor Darul Ehsan 47500 Malaysia

Perimeter control is to manipulate traffic flows in different regions through adjusting traffic signals at the border of the regions. Traditionally, the complete trips in a region are assumed to be dependent on the current accumulated vehicles in this region. This assumption is invalid because the vehicle needs time to complete its trip in a region. In order to solve this shortcoming, some recent studies have introduced a time-delay dynamical system to describe the dynamical behaviour of the accumulated vehicles in a region. However, in these studies, the perimeter control problem is formulated as a tracking problem with a given optimal reference point. In reality, such an optimal reference point is unavailable in advance. This paper will fill this gap through formulating perimeter control as an optimal control problem governed by a state-dependent time delay system. The control parametrization technique and an exact penalty method are introduced to solve such a challenging optimal control problem. Model predictive control is applied to obtain close-loop solution through solving a series of online optimal control problems. Some experiments are performed to demonstrate the effectiveness of our method.

关键词： control systems Mathematical models Delays Optimal control Dynamical systems Vehicle dynamics Routing Macroscopic fundamental diagram optimal perimeter control state-dependent delays control parameterization model predictive control

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A NEW GRADIENT COMPUTATIONAL FORMULA FOR OPTIMAL control PROBLEMS WITH TIME-DELAY

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JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 2022年第4期18卷 2469-2482页

作者： Yu, Changjun Yuan, Lei Su, Shuxuan Shanghai Univ Shanghai 200444 Peoples R China

In this paper, we consider a class of time-delay optimal control problem (TDOCP) with canonical equality and inequality constraints. By applying control parameterization method together with time-scaling transformation, a TDOCP can be readily solved by gradient-based optimization methods. The partial derivative of the cost as well as the constraint functions with respect to the decision variables are obtained by variational approach, which is inefficient when the discretization for the control function is relatively dense. For general optimal control problem without time-delay, co-state approach is an effective way to compute the gradients, however, when time-delay is involved in the dynamic system, the co-state system is not known. In this paper, we derive the co-state system for TDOCP to compute the gradients of the cost and constraints. Numerical results show that the computational efficiency is much higher when compared with the traditional variational approach.

关键词： Time-delay system optimal control co-state system control parameterization time-scaling transformation

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A Hybrid Offline Optimization Method for Reconfiguration of Multi-UAV Formations

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IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS 2021年第1期57卷 506-520页

作者： Li, Bin Zhang, Jiangwei Dai, Li Teo, Kok Lay Wang, Song Sichuan Univ Sch Aeronaut & Astronaut Chengdu 610065 Peoples R China Sichuan Univ Coll Elect Engn Chengdu 610065 Peoples R China Beijing Inst Technol Sch Automat Beijing 100811 Peoples R China Sunway Univ Sch Math Sci Selangor Darul Ehsan 47500 Malaysia Tianjin Univ Finance & Econ Sch Management Sci & Engn Tianjin 300222 Peoples R China Curtin Univ Perth WA Australia Shenzhen Univ Shenzhen Audencia Business Sch Shenzhen 518060 Peoples R China Curtin Univ Sch Elect Engn Comp & Math Sci Bentley WA 6102 Australia

Formation reconfiguration of multiple unmanned aerial vehicles (UAVs) is a challenging problem. Mathematically, this problem is an optimal control problem subject to continuous state inequality constraints and terminal state equality constraints. The first challenge is that there are an infinite number of constraints to be satisfied for the continuous state inequality constraints, which makes the problem extremely difficult to be solved. The second challenge is that the control and state are usually both been discretized. This will result in noncontinuous control input. In addition, the discretized system may not always accurately approximate the original system. In this article, a hybrid offline optimization scheme is proposed to tackle these problems. Unlike the existing methods, the state variables are not required to be discretized and continuous control inputs can be obtained. In addition, the continuous state inequality constraints are tackled without increasing the total number of constraints. Simulation results show that the proposed hybrid optimization method outperforms the state-of-the-art method-the hybrid particle swarm optimization and genetic algorithm.

关键词： Optimal control Genetic algorithms Electronic mail Optimization methods Mathematical model Particle swarm optimization Continuous state inequality constraints control parameterization formation reconfiguration hybrid optimization simulated annealing unmanned aerial vehicle (UAV)

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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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Optimal train control via switched system dynamic optimization

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OPTIMIZATION METHODS & SOFTWARE 2021年第2-3期36卷 602-626页

作者： Zhong, Weifeng Lin, Qun Loxton, Ryan Teo, Kok Lay Beijing Jiaotong Univ Sch Elect & Informat Engn Beijing Peoples R China Curtin Univ Sch Elect Engn Comp & Math Sci Perth WA Australia

This paper considers an optimal train control problem with two challenging, non-standard constraints: a speed constraint that is piecewise-constant with respect to the train's position, and control constraints that are non-smooth functions of the train's speed. We formulate this problem as an optimal switching control problem in which the mode switching times are decision variables to be optimized, and the track gradient and speed limit in each mode are constant. Then, using control parameterization and time-scaling techniques, we approximate the switching control problem by a finite-dimensional optimization problem, which is still subject to the challenging speed limit constraint (imposed continuously during each mode) and the non-smooth control constraints. We show that the speed constraint can be transformed into a finite number of point constraints. We also show that the non-smooth control constraints can be approximated by a sequence of conventional (smooth) inequality constraints. The resulting approximate problem can be viewed as a nonlinear programming problem and solved using gradient-based optimization algorithms, where the gradients of the cost and constraint functions are computed via the sensitivity method. A case study using data for a real subway line shows that the proposed method yields a realistic optimal control profile without the undesirable control fluctuations that can occur with the pseudospectral method.

关键词： Optimal train control switched system control parameterization time-scaling transformation state-dependent control constraint

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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 40

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

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40th Chinese control Conference (CCC)

作者： Shi, Junyu Yue, Wenjin Wang, Yiwei Zhong, Weifeng Beijing Jiaotong Univ Beijing 100044 Peoples R China

ISBN: (纸本)9789881563804

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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Optimal setting strategy of electrocoagulation process in heavy metal wastewater treatment plant

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JOURNAL OF ENVIRONMENTAL MANAGEMENT 2022年 310卷 114724-114724页

作者： Zhang, Fengxue Yang, Chunhua Zhu, Hongqiu Li, Yonggang Gui, Weihua Cent South Univ Sch Automat Changsha 410083 Peoples R China

With the increasingly stringent environmental protection policies of various countries, the contradiction between the treatment cost and the purification degree of environmental pollutants has become increasingly significant, which has become a major factor restricting the efficient operation of wastewater treatment plants. Hence, keeping the ion concentration at the outlet as low as possible while reducing the cost are the main objectives of treating heavy metal wastewater by electrocoagulation (EC) process. However, due to the complicated mechanism and uncertain production conditions, it is difficult to achieve those goals by manually setting the current through operators' experience. In this paper, we develop a dynamic multi-objective optimization strategy for EC process to balance these two conflicting production targets. First, we define the removal efficiency (RE) to measure the effectiveness of the EC process. Due to the anodic passivation and cathodic polarization in the EC process, the current reversing period (CRP) is proposed and optimized to ensure the stable performance of the electrodes. Then the current setting problem is formulated as a constrained multi-objective optimization problem with competing objectives of RE and cost. An interval-adjustable control parameterization (CP) approach is developed to reduce the complexity of this optimization problem. To compute this optimization problem, a heuristic method named multi-objective state transition algorithm (MOSTA) with evaluation value is investigated. The effectiveness of our model and optimization strategy is demonstrated by a successful implementation in an EC process of a wastewater treatment plant in Chenzhou, China.

关键词： Electrocoagulation process Dynamic multiobjective optimization Current reversing period control parameterization Power consumption Removal efficiency

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Optimal state-delay control in nonlinear dynamic systems

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AUTOMATICA 2022年 135卷 109981-109981页

作者： Liu, Chongyang Loxton, Ryan Teo, Kok Lay Wang, Song Shandong Technol & Business Univ Sch Math & Informat Sci Yantai 264005 Peoples R China Curtin Univ Sch Elect Engn Comp & Math Sci Perth WA 6845 Australia Sunway Univ Sch Math Sci Kuala Lumpur 47500 Malaysia

This paper considers a class of nonlinear systems in which the control function is a time-varying state-delay. The optimal control problem is to optimize the time-varying delay and a set of time-invariant system parameters subject to lower and upper bounds. To solve this problem, we first parameterize the delay in terms of piecewise-quadratic basis functions, thus yielding a finite-dimensional approximate problem with continuous-time inequality constraints induced by the delay bounds. We then exploit the quadratic structure of the delay to convert these continuous-time constraints into a finite set of canonical point constraints. We also develop an efficient numerical method for computing the gradients of the system cost function. This method, which involves integrating an auxiliary impulsive system with time-varying advance backwards in time, can be combined with any existing gradient-based optimization algorithm to generate approximate solutions for the optimal control problem. (C) 2021 Elsevier Ltd. All rights reserved.

关键词： Delay systems Optimal control control parameterization Numerical optimization

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DYNAMIC OPTIMIZATION WITH A NON-SMOOTH LPV SYSTEM IN AERO-ENGINE TRANSITION STATE ACCELERATION PROCESS

JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS

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JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS 2022年第2期6卷 113-124页

作者： Teng, Jiao Guo, Ke Wang, Lei Dalian Univ Technol Sch Math Sci Dalian Peoples R China China West Normal Univ Sch Math & Informat Nanchong Peoples R China Shihezi Univ Sch Sci Dept Math Shihezi Xinjiang Peoples R China Dalian Univ Technol Key Lab Intelligent Control & Optimizat Ind Equip Dalian Peoples R China

In this paper, we study the dynamic optimization of the acceleration process in the engine transition state. It is difficult for general linear and nonlinear models to portray the complex mechanical characteristics of an aero-engine. We consider a non-smooth linear parameter variation (LPV) system with nonlinear terms as a mathematical model for this acceleration process. First, a control parameterization method is used to transform the problem into a parameter selection problem. Then, a smoothing technique is used to deal with the non-smooth state constraints. Finally, in order to obtain the global optimal solution of this dynamic optimization problem, an optimization algorithm based on a combination of a gradient descent method and a modified particle swarm optimization is designed to solve the equivalent nonlinear programming problem. The effectiveness and superiority of the proposed algorithm is computationally verified by using the LPV model identified from the actual data.

关键词： control parameterization Dynamic optimization LPV system Particle swarm optimization

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