This paper proposes a data-driven learning-based approach to predictive control for switched nonlinear systems subject to state and control constraints and external stochastic disturbances.A switched Koopman modeling ...This paper proposes a data-driven learning-based approach to predictive control for switched nonlinear systems subject to state and control constraints and external stochastic disturbances.A switched Koopman modeling framework is developed,where a multi-mode neural network for state lifting is trained simultaneously with Koopman operators and state reconstruction matrices for all modes.This framework facilitates the construction of the switched linear Koopman model in a transformed space and effectively captures the dynamics of the original nonlinear system.A switched predictive control strategy is then designed to regulate the switched Koopman model with constrained states and control inputs against both the stochastic disturbances and the uncertainties introduced by the lifting neural network.The proposed control scheme ensures mean-square stability and guarantees boundedness during the online phase.Furthermore,boundedness analysis is performed to determine the bounded set of the original system state across all admissible switching sequences.The effectiveness of the proposed methodology is demonstrated through a case study of a gene regulatory network.展开更多
【目的】双碳目标下,为加速火电机组从主力型电源向提供调峰调频服务的辅助型电源角色转型,提升机组的负荷响应能力至关重要。传统控制方法在火电机组大范围变负荷运行过程中,容易出现响应不及时、稳态精度差、计算量大等问题。【方法...【目的】双碳目标下,为加速火电机组从主力型电源向提供调峰调频服务的辅助型电源角色转型,提升机组的负荷响应能力至关重要。传统控制方法在火电机组大范围变负荷运行过程中,容易出现响应不及时、稳态精度差、计算量大等问题。【方法】本文以某1 000 MW超超临界火电机组协调控制系统为研究对象,提出了一种基于Koopman算子的模型预测控制(Koopman model predictive control,KMPC)方法。该方法采用4阶龙格库塔法离散化原非线性系统获取数据集,通过扩展动态模态分解法有限维近似Koopman算子构建机组高维线性近似模型,并基于该模型预测系统未来动态,引入滚动时域优化策略,综合考虑控制约束、控制目标和性能指标等约束条件,设计超超临界火电机组的模型预测控制算法。以局部线性MPC(locallinear model predictive control,LMPC)为基准对比算法,通过仿真实验验证本文所提出的KMPC算法的有效性。【结果】研究表明,对应于机组的主蒸汽压力、分离器蒸汽焓值、汽轮机发电功率,(1)在连续阶跃升负荷仿真实验中高维近似系统与原非线性系统输出量相对均方根误差分别为1.00%,0.40%和0.36%;(2)标称工况下,KMPC算法在升负荷实验中输出量的时间加权绝对误差积分(integral of time-weighted absolute error,ITAE)相较LMPC分别减少了46.67%、48.66%和21.46%;(3)在模型失配工况下,相较于LMPC算法,KMPC算法在升负荷实验中输出量的ITAE分别减少了19.57%、22.45%和30.94%。【结论】基于Koopman算子构建的高维线性近似模型可较为精准捕捉原系统非线性动力学特征;与LMPC算法相比,KMPC算法在机组大范围变负荷运行过程中响应更加及时且稳态误差更小,同时表现出更强的鲁棒性,有利于机组现场运行。展开更多
Under the CES production technology, an improved Cass Coopmans model with solvable endogenous fertility is given. We prove that there are multiple growth paths and multiple steady states when CES 0<σ<1 ...Under the CES production technology, an improved Cass Coopmans model with solvable endogenous fertility is given. We prove that there are multiple growth paths and multiple steady states when CES 0<σ<1 and the technology level is high enough; the growth path and the steady state is unique when σ>1 and the ratio of capital is smaller than a constant. So, the dynamic system which describes the model undergoes a bifurcation when σ=1 . We discuss the economic sense of the main results we give.展开更多
基金supported in part by Ministry of EducationSingapore+2 种基金under Ac RF TIER 1 Grant No.RG64/23in part by open project funding of Key Laboratory of Intelligent Control and Optimization for Industrial Equipment of Ministry of Education under Grant No.LICO2023YB01in part by the Eric and Wendy Schmidt AI in Science Postdoctoral Fellowship,a program of Schmidt Sciences。
文摘This paper proposes a data-driven learning-based approach to predictive control for switched nonlinear systems subject to state and control constraints and external stochastic disturbances.A switched Koopman modeling framework is developed,where a multi-mode neural network for state lifting is trained simultaneously with Koopman operators and state reconstruction matrices for all modes.This framework facilitates the construction of the switched linear Koopman model in a transformed space and effectively captures the dynamics of the original nonlinear system.A switched predictive control strategy is then designed to regulate the switched Koopman model with constrained states and control inputs against both the stochastic disturbances and the uncertainties introduced by the lifting neural network.The proposed control scheme ensures mean-square stability and guarantees boundedness during the online phase.Furthermore,boundedness analysis is performed to determine the bounded set of the original system state across all admissible switching sequences.The effectiveness of the proposed methodology is demonstrated through a case study of a gene regulatory network.
文摘【目的】双碳目标下,为加速火电机组从主力型电源向提供调峰调频服务的辅助型电源角色转型,提升机组的负荷响应能力至关重要。传统控制方法在火电机组大范围变负荷运行过程中,容易出现响应不及时、稳态精度差、计算量大等问题。【方法】本文以某1 000 MW超超临界火电机组协调控制系统为研究对象,提出了一种基于Koopman算子的模型预测控制(Koopman model predictive control,KMPC)方法。该方法采用4阶龙格库塔法离散化原非线性系统获取数据集,通过扩展动态模态分解法有限维近似Koopman算子构建机组高维线性近似模型,并基于该模型预测系统未来动态,引入滚动时域优化策略,综合考虑控制约束、控制目标和性能指标等约束条件,设计超超临界火电机组的模型预测控制算法。以局部线性MPC(locallinear model predictive control,LMPC)为基准对比算法,通过仿真实验验证本文所提出的KMPC算法的有效性。【结果】研究表明,对应于机组的主蒸汽压力、分离器蒸汽焓值、汽轮机发电功率,(1)在连续阶跃升负荷仿真实验中高维近似系统与原非线性系统输出量相对均方根误差分别为1.00%,0.40%和0.36%;(2)标称工况下,KMPC算法在升负荷实验中输出量的时间加权绝对误差积分(integral of time-weighted absolute error,ITAE)相较LMPC分别减少了46.67%、48.66%和21.46%;(3)在模型失配工况下,相较于LMPC算法,KMPC算法在升负荷实验中输出量的ITAE分别减少了19.57%、22.45%和30.94%。【结论】基于Koopman算子构建的高维线性近似模型可较为精准捕捉原系统非线性动力学特征;与LMPC算法相比,KMPC算法在机组大范围变负荷运行过程中响应更加及时且稳态误差更小,同时表现出更强的鲁棒性,有利于机组现场运行。
文摘Under the CES production technology, an improved Cass Coopmans model with solvable endogenous fertility is given. We prove that there are multiple growth paths and multiple steady states when CES 0<σ<1 and the technology level is high enough; the growth path and the steady state is unique when σ>1 and the ratio of capital is smaller than a constant. So, the dynamic system which describes the model undergoes a bifurcation when σ=1 . We discuss the economic sense of the main results we give.
