A mathematical optimal-control tumor therapy framework consisting of radio- and anti-angiogenesis control strategies that are included in a tumor growth model is investigated. The governing system, resulting from the ...A mathematical optimal-control tumor therapy framework consisting of radio- and anti-angiogenesis control strategies that are included in a tumor growth model is investigated. The governing system, resulting from the combination of two well established models, represents the differential constraint of a non-smooth optimal control problem that aims at reducing the volume of the tumor while keeping the radio- and anti-angiogenesis chemical dosage to a minimum. Existence of optimal solutions is proved and necessary conditions are formulated in terms of the Pontryagin maximum principle. Based on this principle, a so-called sequential quadratic Hamiltonian (SQH) method is discussed and benchmarked with an “interior point optimizer—a mathematical programming language” (IPOPT-AMPL) algorithm. Results of numerical experiments are presented that successfully validate the SQH solution scheme. Further, it is shown how to choose the optimisation weights in order to obtain treatment functions that successfully reduce the tumor volume to zero.展开更多
The zinc oxide rotary kiln,as an essential piece of equipment in the zinc smelting industrial process,is presenting new challenges in process control.China’s strategy of achieving a carbon peak and carbon neutrality ...The zinc oxide rotary kiln,as an essential piece of equipment in the zinc smelting industrial process,is presenting new challenges in process control.China’s strategy of achieving a carbon peak and carbon neutrality is putting new demands on the industry,including green production and the use of fewer resources;thus,traditional stability control is no longer suitable for multi-objective control tasks.Although researchers have revealed the principle of the rotary kiln and set up computational fluid dynamics(CFD)simulation models to study its dynamics,these models cannot be directly applied to process control due to their high computational complexity.To address these issues,this paper proposes a multi-objective adaptive optimization model predictive control(MAO-MPC)method based on sparse identification.More specifically,with a large amount of data collected from a CFD model,a sparse regression problem is first formulated and solved to obtain a reduction model.Then,a two-layered control framework including real-time optimization(RTO)and model predictive control(MPC)is designed.In the RTO layer,an optimization problem with the goal of achieving optimal operation performance and the lowest possible resource consumption is set up.By solving the optimization problem in real time,a suitable setting value is sent to the MPC layer to ensure that the zinc oxide rotary kiln always functions in an optimal state.Our experiments show the strength and reliability of the proposed method,which reduces the usage of coal while maintaining high profits.展开更多
In this paper, a hybird approximation scheme for an optimal control problem governed by an elliptic equation with random field in its coefficients is considered. The random coefficients are smooth in the physical spac...In this paper, a hybird approximation scheme for an optimal control problem governed by an elliptic equation with random field in its coefficients is considered. The random coefficients are smooth in the physical space and depend on a large number of random variables in the probability space. The necessary and sufficient optimality conditions for the optimal control problem are obtained. The scheme is established to approximate the optimality system through the discretization by using finite volume element method for the spatial space and a sparse grid stochastic collocation method based on the Smolyak approximation for the probability space, respectively. This scheme naturally leads to the discrete solutions of an uncoupled deterministic problem. The existence and uniqueness of the discrete solutions are proved. A priori error estimates are derived for the state, the co-state and the control variables. Numerical examples are presented to illustrate our theoretical results.展开更多
Blind image deblurring is a long-standing ill-posed inverse problem which aims to recover a latent sharp image given only a blurry observation.So far,existing studies have designed many effective priors w.r.t.the late...Blind image deblurring is a long-standing ill-posed inverse problem which aims to recover a latent sharp image given only a blurry observation.So far,existing studies have designed many effective priors w.r.t.the latent image within the maximum a posteriori(MAP)framework in order to narrow down the solution space.These non-convex priors are always integrated into the final deblurring model,which makes the optimization challenging.However,due to unknown image distribution,complex kernel structure and non-uniform noises in real-world scenarios,it is indeed challenging to explicitly design a fixed prior for all cases.Thus we adopt the idea of adaptive optimization and propose the sparse structure control(SSC)for the latent image during the optimization process.In this paper,we only formulate the necessary optiinization constraints in a lightweight MAP model with no priors.Then we develop an inexact projected gradient scheme to incorporate flexible SSC in MAP inference.Besides Zp-norm based SSC in our previous work,we also train a group of denoising convolutional neural networks(CNNs)to learn the sparse image structure automatically from the training data under different noise levels,and we show that CNNs-based SSC can achieve similar results compared with Zp-norm but are more robust to noise.Extensive experiments demonstrate that the proposed adaptive optimization scheme with two types of SSC achieves the state-of-the-art results on both synthetic data and real-world images.展开更多
文摘A mathematical optimal-control tumor therapy framework consisting of radio- and anti-angiogenesis control strategies that are included in a tumor growth model is investigated. The governing system, resulting from the combination of two well established models, represents the differential constraint of a non-smooth optimal control problem that aims at reducing the volume of the tumor while keeping the radio- and anti-angiogenesis chemical dosage to a minimum. Existence of optimal solutions is proved and necessary conditions are formulated in terms of the Pontryagin maximum principle. Based on this principle, a so-called sequential quadratic Hamiltonian (SQH) method is discussed and benchmarked with an “interior point optimizer—a mathematical programming language” (IPOPT-AMPL) algorithm. Results of numerical experiments are presented that successfully validate the SQH solution scheme. Further, it is shown how to choose the optimisation weights in order to obtain treatment functions that successfully reduce the tumor volume to zero.
基金supported in part by the National Key Research and Development Program of China(2022YFB3304900)in part by the National Natural Science Foundation of China(61988101,62073340,and 61860206014)+2 种基金in part by the Major Key Project of Peng Cheng Laboratory(PCL)(PCL2021A09)in part by the Science and Technology Innovation Program of Hunan Province(2022JJ10083,2021RC3018,and 2021RC4054)in part by the Innovation-Driven Project of Central South University,China(2019CX020)。
文摘The zinc oxide rotary kiln,as an essential piece of equipment in the zinc smelting industrial process,is presenting new challenges in process control.China’s strategy of achieving a carbon peak and carbon neutrality is putting new demands on the industry,including green production and the use of fewer resources;thus,traditional stability control is no longer suitable for multi-objective control tasks.Although researchers have revealed the principle of the rotary kiln and set up computational fluid dynamics(CFD)simulation models to study its dynamics,these models cannot be directly applied to process control due to their high computational complexity.To address these issues,this paper proposes a multi-objective adaptive optimization model predictive control(MAO-MPC)method based on sparse identification.More specifically,with a large amount of data collected from a CFD model,a sparse regression problem is first formulated and solved to obtain a reduction model.Then,a two-layered control framework including real-time optimization(RTO)and model predictive control(MPC)is designed.In the RTO layer,an optimization problem with the goal of achieving optimal operation performance and the lowest possible resource consumption is set up.By solving the optimization problem in real time,a suitable setting value is sent to the MPC layer to ensure that the zinc oxide rotary kiln always functions in an optimal state.Our experiments show the strength and reliability of the proposed method,which reduces the usage of coal while maintaining high profits.
基金The work is partly supported by the Natural Science Foundation of China （Grant No. 11271231, 11301300, 61572297）, by the Shandong Province Outstanding Young Scientists Research Award Fhnd Project （Grant No. BS2013DX010）, by the Natural Science Foundation of Shandong Province, China （Grant No. ZR2014FM003）, and by the Shandong Academy of Sciences Youth Fund Project （Grant No. 2013QN007）.
文摘In this paper, a hybird approximation scheme for an optimal control problem governed by an elliptic equation with random field in its coefficients is considered. The random coefficients are smooth in the physical space and depend on a large number of random variables in the probability space. The necessary and sufficient optimality conditions for the optimal control problem are obtained. The scheme is established to approximate the optimality system through the discretization by using finite volume element method for the spatial space and a sparse grid stochastic collocation method based on the Smolyak approximation for the probability space, respectively. This scheme naturally leads to the discrete solutions of an uncoupled deterministic problem. The existence and uniqueness of the discrete solutions are proved. A priori error estimates are derived for the state, the co-state and the control variables. Numerical examples are presented to illustrate our theoretical results.
基金the National Natural Science Foundation of China under Grant Nos.61672125 and 61772108.
文摘Blind image deblurring is a long-standing ill-posed inverse problem which aims to recover a latent sharp image given only a blurry observation.So far,existing studies have designed many effective priors w.r.t.the latent image within the maximum a posteriori(MAP)framework in order to narrow down the solution space.These non-convex priors are always integrated into the final deblurring model,which makes the optimization challenging.However,due to unknown image distribution,complex kernel structure and non-uniform noises in real-world scenarios,it is indeed challenging to explicitly design a fixed prior for all cases.Thus we adopt the idea of adaptive optimization and propose the sparse structure control(SSC)for the latent image during the optimization process.In this paper,we only formulate the necessary optiinization constraints in a lightweight MAP model with no priors.Then we develop an inexact projected gradient scheme to incorporate flexible SSC in MAP inference.Besides Zp-norm based SSC in our previous work,we also train a group of denoising convolutional neural networks(CNNs)to learn the sparse image structure automatically from the training data under different noise levels,and we show that CNNs-based SSC can achieve similar results compared with Zp-norm but are more robust to noise.Extensive experiments demonstrate that the proposed adaptive optimization scheme with two types of SSC achieves the state-of-the-art results on both synthetic data and real-world images.
