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

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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The approximation for the boundary optimal control problem of Burgers-Fisher equation with constraints

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APPLIED MATHEMATICS AND COMPUTATION 2014年 243卷 889-898页

作者： Yu, Xin Cheng, Rongjun Jiang, Huachen Zhang, Qian Xu, Chao Zhejiang Univ Ningbo Inst Technol Lab Informat & Control Technol Ningbo 315100 Zhejiang Peoples R China Zhejiang Univ State Key Lab Ind Control Technol Hangzhou 310027 Zhejiang Peoples R China Zhejiang Univ Inst Cyber Syst & Control Hangzhou 310027 Zhejiang Peoples R China

This paper deals with the numerical approximation with meshless method for the boundary optimal control problem with some control and state constraints governed by the Burgers-Fisher equation, which is a nonlinear evolution equation and is the prototype model for the reaction, convection and diffusion phenomena arising in many spatial-temporal processes. By making use of the element-free Galerkin (EFG) method, the original optimal control problem is discretized spatially to a semi-discrete optimal control problem governed by a system of nonlinear ordinary differential equations. Then, by using the control parameterization method, the original problem can be reduced to an optimal parameter selection problem governed by a lumped parameter system, which can be solved as a nonlinear optimization problems by using the Sequential Quadratic Programming (SQP) algorithm. The numerical simulations are given to illustrate the effectiveness of the proposed numerical approximation method. (C) 2014 Elsevier Inc. All rights reserved.

关键词： Meshless method Boundary optimal control Burgers-Fisher equation State and control constraints control parameterization

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OPTIMAL-control COMPUTATION FOR DIFFERENTIAL-ALGEBRAIC PROCESS SYSTEMS WITH GENERAL CONSTRAINTS

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CHEMICAL ENGINEERING COMMUNICATIONS 1990年第1期97卷 9-26页

作者： CHEN, CT HWANG, C Department of Chemical Engineering National Chen Kung University Tainan Taiwan 70101 Republic of China

This paper is concerned with the combined problem of optimal parameter selection and control for differential-algebraic system (DASs) involving various constraints. The control parameterization technique of using piecewise constant functions is used to approximate the original problem into a sequence of finite-dimensional parameter selection problems. Based on characterizing the Hamiltonian function and adjoint system associated with a DAS and transforming different types of constraints into a cononical function which has the same form as the cost functional, a unified gradient computation algorithm for the controls and parameters is derived. This algorithm makes the resulting approximate problems be effectively solved by gradient-based optimization methods. As a specific example, the singular control problem of finding the optimal feeding policy for a fed-batch fermentation process governed by the product and substrate inhibited specific growth and product formation kinetics is solved. The computed results show that such a singular control problem can also be effectively solved by the proposed optimization scheme.

关键词： Differential-algebraic systems Optimal control control parameterization Fed-batch fermentation process Singular control

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A Hybrid Time-Scaling Transformation for Time-Delay Optimal control Problems

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2016年第3期169卷 876-901页

作者： Yu, Changjun Lin, Qun Loxton, Ryan Teo, Kok Lay Wang, Guoqiang Cent S Univ Changsha Hunan Peoples R China Curtin Univ Perth WA 6845 Australia Shanghai Univ Engn Sci Shanghai Peoples R China

In this paper, we consider a class of nonlinear time-delay optimal control problems with canonical equality and inequality constraints. We propose a new computational approach, which combines the control parameterization technique with a hybrid time-scaling strategy, for solving this class of optimal control problems. The proposed approach involves approximating the control variables by piecewise constant functions, whose heights and switching times are decision variables to be optimized. Then, the resulting problem with varying switching times is transformed, via a new hybrid time-scaling strategy, into an equivalent problem with fixed switching times, which is much preferred for numerical computation. Our new time-scaling strategy is hybrid in the sense that it is related to two coupled time-delay systems-one defined on the original time scale, in which the switching times are variable, the other defined on the new time scale, in which the switching times are fixed. This is different from the conventional time-scaling transformation widely used in the literature, which is not applicable to systems with time-delays. To demonstrate the effectiveness of the proposed approach, we solve four numerical examples. The results show that the costs obtained by our new approach are lower, when compared with those obtained by existing optimal control methods.

关键词： Time-delay Optimal control control parameterization Time-scaling transformation Time-delay control system Computational method for optimal control

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A Switching Time Optimization Strategy for Optimal control Problems

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JOURNAL OF THE OPERATIONS RESEARCH SOCIETY OF CHINA 2023年 1-22页

作者： Chen, Yin Yu, Chang-Jun Zhu, Xi Shanghai Univ Dept Math Shanghai 200444 Peoples R China

The time-scaling transformation is a widely used approach within the computational framework of control parameterization for optimizing the switching times of control variables. However, the conventional time-scaling transformation has the limitation that the switching times and the number of switches for each control component must be the same. In this paper, we present a novel technique to solve constrained optimal control problems that allows for adaptively optimizing the switching times for each control component. Numerical results demonstrate that this proposed method provides better flexibility in control strategy and yields improved performance.

关键词： Optimal control control parameterization Time-scaling transformation Sequential adaptive switching time optimization technique Co-state method

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Constrained optimal control of switched systems and its application

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OPTIMIZATION 2015年第3期64卷 539-557页

作者： Wu, Xiang Zhang, Kanjian Sun, Changyin Southeast Univ Sch Automat Nanjing Jiangsu Peoples R China

In this paper, we consider an optimal co with state and control constraints, where a prespecified sequence of active subsystems is given. Both the switching instants and the control function are to be chosen such that the cost functional is minimized. Firstly, we convert the problem into a conventional optimal control problem based on parameterization of the switching instants. Next, through discretizing the control space, applying a time-scaling transformation and using the smoothing technique, the optimal control problem is approximated by a non-linear optimization problem with linear constraints and bounds on the variables. Furthermore, an algorithm that finds a suboptimal solution to the original problem is proposed. One major advantage with the new algorithm implementation is the only need to solve a non-linear optimization problem with linear constraints and bounds on the variables. The gradients of these linear constraints and the objective function can be easily obtained. Therefore, the original optimization problem can be solved efficiently using any gradient-based method, such as sequential quadratic programming algorithm. Finally, a flight planning example illustrates the efficiency of the proposed approach.

关键词： control parameterization flight planning smoothing technique optimal control switched systems

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Optimal operation processes of discrete-continuous biochemical processes

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COMPUTERS & CHEMICAL ENGINEERING 2000年第2-7期24卷 1167-1173页

作者： Chekhova, E Barton, PI Gorak, A MIT Dept Chem Engn Cambridge MA 02139 USA Univ Dortmund Dept Chem Engn D-44221 Dortmund Germany

Biohemical processes and so-called hybrid biochemical processes, carried out in integrated unit operations such as membrane bioreactors, have found numerous applications in food and pharmaceutical process industries. However, such processes have hardly been investigated comprehensively. Dynamic modeling and especially dynamic optimization attempts were restricted because these unit operations combine continuous and discrete dynamic behavior and contain time and state events. In this paper we present a robust model of a process of high industrial significance, namely citric acid production in a membrane bioreactor, as well as a successful application of control parameterization numerical optimal control techniques to the fed-batch bioreactor and a membrane bioreactor. In order to evaluate the advantages and disadvantages of the design alternatives, the incremental objective function between batch and fed-batch, batch and different operations in a membrane bioreactor was formulated in terms of profit maximization. The determination of the optimal performance for the fed-batch fermenter and membrane bioreactor requires the solution of multiple optimal control problems, namely determining optimal feed and inlet concentration profiles, initial conditions and a production time. We show how the systematic combination of rigorous mathematical modeling: the integration of design and operational decisions and innovative discrete-continuous dynamic optimization techniques allow the generation of optimal designs and operating policies for hybrid biochemical processes that increase the profit of important production processes such as citric acid production. (C) 2000 Elsevier Science Ltd. All rights reserved.

关键词： optimal operation discrete-continuous biochemical processes citric acid production design alternatives control parameterization membrane bioreactor

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Optimal operation processes of discrete-continuous biochemical processes

Optimal operation processes of discrete-continuous biochemic...

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7th International Symposium on Process Systems Engineering

作者： Chekhova, E Barton, PI Gorak, A MIT Dept Chem Engn Cambridge MA 02139 USA Univ Dortmund Dept Chem Engn D-44221 Dortmund Germany

关键词： optimal operation discrete-continuous biochemical processes citric acid production design alternatives control parameterization membrane bioreactor

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Optimal Operation for Medium-speed Maglev Trains 39

Optimal Operation for Medium-speed Maglev Trains

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39th Chinese control Conference (CCC)

作者： Zhong, Weifeng Xu, Hongze Zhang, Wenjing Loxton, Ryan Zhang, Yang Beijing Jiaotong Univ Beijing 100044 Peoples R China Curtin Univ Perth WA 6845 Australia CRCC Zhuzhou Locomot Co Ltd Zhuzhou 412001 Peoples R China

ISBN: (纸本)9789881563903

The magic 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 hound 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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Compact lossless synthetic network drive/controllers for active devices technologies

Compact lossless synthetic network drive/controllers for act...

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Conference on Smart Electronics and MEMS - Smart Structures and Materials 1997

作者： Murray, JJ Knowles, GJ Bower, BL Spangler, BL EMF Industries Inc. and SUNY/Stony Brook (United States) EMF Industries Inc. (United States)

ISBN: (纸本)0819424595

EMF has demonstrated the emergence of an internal structure within the power system and drive electronics for discrete and continuous piezo-coupled systems which leads to the underlying theory of quasi-active controllers (i.e. operates at high voltage, but with no net energy consumption). If the control is lossless, then it should be possible to implement control in a way which, while it requiring a power source, consumes no net energy from the power source. That is a drive/control mechanism which needs a reservoir of stored energy rather than a continuous source of power. This paper is devoted to presenting a complete solution to the implementation of this new concept which is termed a synthetic lossless realization. The synthetic circuitry implements a lossless realization of quasi-active control. The synthetic concepts and circuitry are introduced and the analog and digital microcontrollers of the controlled coupled parameters are discussed.

关键词： piezoelectronics elastodynamic response plate structures transductive systems control parameterization vibration damping admittance design generalized impedance

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