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Second-order sensitivities of general dynamic systems with application to optimal control problems

CHEMICAL ENGINEERING SCIENCE 1999年第17期54卷 3851-3860页

作者： Vassiliadis, VS Balsa-Canto, E Banga, JR Univ Cambridge Dept Chem Engn Cambridge CB2 3RA England CSIC Inst Invest Marinas Chem Engn Lab Vigo 36208 Spain

The derivation of formulae for second-order parametric sensitivity analysis of differential-algebraic equations is presented in this paper, using tensorial analysis. The proposed formulae derive this information in conjunction with the state and first-order sensitivity evaluation. An original result in this work is the derivation of Hessian matrix-vector product forms which are shown to have the same computational complexity as the evaluation of first-order sensitivities. The theoretical result for second-order sensitivities is shown to be a very effective way to solve optimal control problems. The algorithm constructed is demonstrated to have a fine performance on three standard optimal control problems taken from the chemical engineering literature. (C) 1999 Elsevier Science Ltd. All rights reserved.

关键词： second-order sensitivities first-order sensitivities optimal control control parameterization differential-algebraic equations ordinary differential equations

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

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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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Dynamic optimization of trajectory for ramp-up current profile in tokamak plasma

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ASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERING 2016年第6期11卷 918-929页

作者： Ren, Zhigang Xu, Chao Ou, Yongsheng Zhejiang Univ Ningbo Inst Technol Lab Informat & Control Technol Ningbo Zhejiang Peoples R China Zhejiang Univ State Key Lab Ind Control Technol Hangzhou Zhejiang Peoples R China Zhejiang Univ Inst Cyber Syst & Control Hangzhou Zhejiang Peoples R China Chinese Acad Sci Shenzhen Inst Adv Technol Shenzhen Guangdong Peoples R China

In this paper, we consider an open-loop, finite-time, optimal control problem of attaining a specific desired current profile during the ramp-up phase by finding the best open-loop actuator input trajectories. Average density, total power, and plasma current are used as control actuators to manipulate the profile shape in tokamak plasmas. Based on the control parameterization method, we propose a numerical solution procedure directly to solve the original partial differential equation (PDE)-constrained optimization problem using gradient-based optimization techniques such as sequential quadratic programming. This paper is aimed at proposing an effective framework for the solution of PDE-constrained optimization problem in tokamak plasmas. A more user-friendly and efficient graphical user interface is designed in MATLAB, and the numerical simulation results are verified to demonstrate its applicability. In addition, the proposed framework of combining existing PDE and numerical optimization solvers to solve PDE-constrained optimization problem has the prospective to target challenge advanced control problems arising in more general chemical engineering processes. (C) 2016 Curtin University of Technology and John Wiley & Sons, Ltd.

关键词： nuclear fusion current profile control control parameterization sequential quadratic programming (SQP)

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Dynamic optimization of dual-mode hybrid systems with state-dependent switching conditions

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OPTIMIZATION METHODS & SOFTWARE 2018年第2期33卷 297-310页

作者： Blanchard, Eunice Loxton, Ryan Rehbock, Volker Curtin Univ Dept Math & Stat Perth WA Australia

This paper presents a computational approach for optimizing a class of hybrid systems in which the state dynamics switch between two distinct modes. The times at which the mode transitions occur cannot be specified directly, but are instead governed by a state-dependent switching condition. The control variables, which should be chosen optimally by the system designer, consist of a set of continuous-time input signals. By introducing an auxiliary binary-valued control function to represent the system's current mode, we show that any dual-mode hybrid system with state-dependent switching conditions can be transformed into a standard dynamic system subject to path constraints. We then develop a computational algorithm, based on control parameterization, the time-scaling transformation, and an exact penalty method, for determining the optimal piecewise constant input signals for the original hybrid system. A numerical example on cancer chemotherapy is included to demonstrate the effectiveness of the proposed algorithm.

关键词： dynamic optimization hybrid systems state-dependent switching control parameterization time-scaling transform exact penalty method

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A COMPUTATIONAL METHOD FOR TIME-LAG control-PROBLEMS WITH control AND TERMINAL INEQUALITY CONSTRAINTS

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OPTIMAL control APPLICATIONS & METHODS 1987年第4期8卷 377-395页

作者： TEO, KL WONG, KH UNIV WITWATERSRAND DEPT APPL MATHJOHANNESBURG 2001SOUTH AFRICA

A computational algorithm for a class of time-lag optimal control problems involving control and terminal inequality constraints is presented. The convergence properties of the algorithm are also investigated. To test... 详细信息

关键词： Non-linear time-lag system Linear control constraints Non-linear terminal constraints Feasible direction method control parameterization Initial feasible control Computational scheme Finite convergence

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Optimal control problems with incomplete and different integral time domains in the objective and constraints

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NONLINEAR DYNAMICS 2014年第4期78卷 2883-2895页

作者： Li, Guodong Liu, Xinggao Zhejiang Univ Dept Control Sci & Engn State Key Lab Ind Control Technol Hangzhou 310027 Zhejiang Peoples R China

Optimal control problem with incomplete and different integral time domains is a class of very common practical engineering problems. In traditional way, the integral items are transformed to the transient items and treated as artificial states to reduce the complexity of programming. However, its main disadvantage is time wasting for the considered problems. In this paper, an efficient computational method is therefore proposed for this type of problem, where the integral time domains can be either fixed or variable. By employing the control vector parameterization and a timescaling transformation, the original problem is converted to an approximate optimal parameter selection problem. Moreover, new gradient formulae for the cost and constraint functions are derived. With these gradient formulae, standard gradient-based optimization methods can be easily applied to solve the generated approximate problem. For illustration, three classical numerical examples are tested. The research results, which save 10-22 % of time, show the effectivity of the proposed approach.

关键词： Nonlinear optimal control Optimal control computation Constrained optimal control control parameterization

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OPTIMAL-control COMPUTATION FOR LINEAR TIME-LAG SYSTEMS WITH LINEAR TERMINAL CONSTRAINTS

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1984年第3期44卷 509-526页

作者： TEO, KL WONG, KH CLEMENTS, DJ UNIV NEW S WALES SCH MATHKENSINGTONNSW 2033AUSTRALIA UNIV NEW S WALES SCH ELECT ENGN & COMP SCIKENSINGTONNSW 2033AUSTRALIA

A computational scheme using the technique of control parameterization is developed for solving a class of optimal control problems involving linear hereditary systems with bounded control region and linear terminal c... 详细信息

关键词： control parameterization piecewise constant functions linear time-lag systems linear terminal constraints computational schemes

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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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Optimization of hybrid systems

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COMPUTERS & CHEMICAL ENGINEERING 2006年第10-12期30卷 1576-1589页

作者： Barton, Paul I. Lee, Cha Kun Yunt, Mehmet MIT Proc Syst Engn Lab Dept Chem Engn Cambridge MA 02139 USA MIT Dept Mech Engn Cambridge MA 02139 USA

An overview of dynamic optimization problems with hybrid systems embedded is presented. The control parameterization approach is examined in detail, where the possibility of mode switching within the hybrid system causes nonsmoothness in the Master problem, thus invalidating gradient based solvers. To handle this, a decomposition approach is proposed that divides the general problem into smooth subproblems. The subproblem of determining the optimal mode sequence given fixed transition times is considered for continuous time linear time varying hybrid systems. A mixed-integer reformulation of the problem is proposed that retains the linear structure of the embedded hybrid system. A deterministic branch-and-cut framework incorporating outer approximation cuts and a dynamic bounds tightening heuristic is then employed to solve the nonconvex mixed-integer problem to guaranteed global optimality with a finite number of iterations. It is shown that the dynamic bounds tightening heuristic can have a dramatic effect on accelerating convergence of the algorithm. Future directions for research are also discussed, including the application of recent developments in semi-infinite programming for the formal safety verification of processes under uncertainty. (c) 2006 Elsevier Ltd. All rights reserved.

关键词： dynamic optimization optimal mode sequences control parameterization

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Vehicle Collision Avoidance Maneuvers With Limited Lateral Acceleration Using Optimal Trajectory control

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JOURNAL OF DYNAMIC SYSTEMS MEASUREMENT AND control-TRANSACTIONS OF THE ASME 2013年第4期135卷 041006-1-041006-12页

作者： Soudbakhsh, Damoon Eskandarian, Azim Chichka, David MIT Dept Mech Engn Act Adapt Control Lab Cambridge MA 02139 USA George Washington Univ Sch Engn & Appl Sci Ctr Intelligent Syst Res Washington DC 20052 USA George Washington Univ Dept Mech Engn Washington DC 20052 USA

In this paper, the possibility of performing severe collision avoidance maneuvers using trajectory optimization is investigated. A two degree of freedom vehicle model was used to represent dynamics of the vehicle. First, a linear tire model was used to calculate the required steering angle to perform the desired evasive maneuver, and a neighboring optimal controller was designed. Second, direct trajectory optimization algorithm was used to find the optimal trajectory with a nonlinear tire model. To evaluate the results, the calculated steering angles were fed to a full vehicle dynamics model. It was shown that the neighboring optimal controller was able to accommodate the introduced disturbances. Comparison of the resultant trajectories with other desired trajectories showed that it results in a lower lateral acceleration profile and a smaller maximum lateral acceleration;thus the time to perform an obstacle avoidance maneuver can be reduced using this method. A simulation case study of a limited lateral acceleration with constrained direct trajectory optimization shows that using the proposed trajectory optimization technique requires less time than that of trapezoidal acceleration profile for a lane change maneuver.

关键词： road vehicle trajectory optimization control parameterization neighboring extremal optimal control shooting method

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