Integral reinforcement learning(IRL)is an effective tool for solving optimal control problems of nonlinear systems,and it has been widely utilized in optimal controller design for solving discrete-time nonlinearity.Ho...Integral reinforcement learning(IRL)is an effective tool for solving optimal control problems of nonlinear systems,and it has been widely utilized in optimal controller design for solving discrete-time nonlinearity.However,solving the Hamilton-Jacobi-Bellman(HJB)equations for nonlinear systems requires precise and complicated dynamics.Moreover,the research and application of IRL in continuous-time(CT)systems must be further improved.To develop the IRL of a CT nonlinear system,a data-based adaptive neural dynamic programming(ANDP)method is proposed to investigate the optimal control problem of uncertain CT multi-input systems such that the knowledge of the dynamics in the HJB equation is unnecessary.First,the multi-input model is approximated using a neural network(NN),which can be utilized to design an integral reinforcement signal.Subsequently,two criterion networks and one action network are constructed based on the integral reinforcement signal.A nonzero-sum Nash equilibrium can be reached by learning the optimal strategies of the multi-input model.In this scheme,the NN weights are constantly updated using an adaptive algorithm.The weight convergence and the system stability are analyzed in detail.The optimal control problem of a multi-input nonlinear CT system is effectively solved using the ANDP scheme,and the results are verified by a simulation study.展开更多
Both auto-power spectrum and cross-power spectrum need to be controlled in multi-input multi-output （MIMO） random vibration test. During the control process with the difference control algorithm （DCA）, a lower tri...Both auto-power spectrum and cross-power spectrum need to be controlled in multi-input multi-output （MIMO） random vibration test. During the control process with the difference control algorithm （DCA）, a lower triangular matrix is derived from Cholesky decomposition of a reference spectrum matrix. The diagonal elements of the lower triangular matrix （DELTM） may become negative. These negative values have no meaning in physical significance and can cause divergence of auto-power spectrum control. A proportional root mean square control algorithm （PRMSCA） provides another method to avoid the divergence caused by negative values of DELTM, but PRMSCA cannot control the cross-power spectrum. A new control algorithm named matrix power control algorithm （MPCA） is proposed in the paper. MPCA can guarantee that DELTM is always positive in the auto-power spectrum control. MPCA can also control the cross-power spectrum. After these three control algorithms are analyzed, three-input three-output random vibration control tests are implemented on a three-axis vibration shaker. The results show the validity of the proposed MPCA.展开更多
A control method for Multi-Input Multi-Output（MIMO） non-Gaussian random vibration test with cross spectra consideration is proposed in the paper. The aim of the proposed control method is to replicate the specified ...A control method for Multi-Input Multi-Output（MIMO） non-Gaussian random vibration test with cross spectra consideration is proposed in the paper. The aim of the proposed control method is to replicate the specified references composed of auto spectral densities, cross spectral densities and kurtoses on the test article in the laboratory. It is found that the cross spectral densities will bring intractable coupling problems and induce difficulty for the control of the multioutput kurtoses. Hence, a sequential phase modification method is put forward to solve the coupling problems in multi-input multi-output non-Gaussian random vibration test. To achieve the specified responses, an improved zero memory nonlinear transformation is utilized first to modify the Fourier phases of the signals with sequential phase modification method to obtain one frame reference response signals which satisfy the reference spectra and reference kurtoses. Then, an inverse system method is used in frequency domain to obtain the continuous stationary drive signals. At the same time, the matrix power control algorithm is utilized to control the spectra and kurtoses of the response signals further. At the end of the paper, a simulation example with a cantilever beam and a vibration shaker test are implemented and the results support the proposed method very well.展开更多
针对存在输入时滞的多智能体系统(multi-agent system,MAS)滞后一致性问题,提出一种基于时基生成器(time base generator,TBG)的二阶MAS预设时间领导跟随滞后一致性控制方法,使得稳定时间与系统初始状态无关且可预先设定。首先,提出一...针对存在输入时滞的多智能体系统(multi-agent system,MAS)滞后一致性问题,提出一种基于时基生成器(time base generator,TBG)的二阶MAS预设时间领导跟随滞后一致性控制方法,使得稳定时间与系统初始状态无关且可预先设定。首先,提出一种误差变换方法,将具有时滞的误差系统转换为无时滞误差系统。然后,利用TBG函数构造误差辅助变量并构造相应滑模面,进而设计预设时间控制器。同时,证明所设计控制器的预设时间稳定性。最后,通过数值仿真验证所提方法的可行性及有效性。仿真结果表明,MAS能够实现精确的预设时间滞后一致性。展开更多
Noises always disturb the control effect of an environment test especially in multi-input multi-output(MIMO) systems. If the frequency response function matrices are ill-conditioned, the noises in the driving forces w...Noises always disturb the control effect of an environment test especially in multi-input multi-output(MIMO) systems. If the frequency response function matrices are ill-conditioned, the noises in the driving forces will be amplified and the response spectral lines may awfully exceed their tolerances. Most of the major biases between the response spectra and the reference spectra are produced by the amplified noises. However, ordinary control algorithms can hardly reduce the level of noises. The influences of the noises on both the auto- and cross-power spectra are analyzed in this paper. As a conventional frequency domain method on the inverse problem, the Tikhonov filter is adopted in the environment test to suppress the exceeding spectral lines. By altering regularization parameters gradually, the auto-power spectra can be improved in a closed control loop. Instead of using the traditional way of selecting regularization parameters, we observe the coherence change to estimate noise eliminations. Incidentally, the requirement of coherence control can be realized. The errors of the phase are then studied and a phase control algorithm is introduced at the end as a supplement of cross-power spectra control. The Tikhonov filter and the proposed phase control algorithm are tested numerically and experimentally. The results show that the noises in the vicinity of lightly damped resonant peaks are more stubborn. The response spectra are able to be greatly improved by the combination of these two methods.展开更多
A form of iterative learning control (ILC) is used to update the set-point for the local controller. It is referred to as set-point-related (SPR) indirect ILC. SPR indirect ILC has shown excellent performance: as a su...A form of iterative learning control (ILC) is used to update the set-point for the local controller. It is referred to as set-point-related (SPR) indirect ILC. SPR indirect ILC has shown excellent performance: as a supervision module for the local controller, ILC can improve the tracking performance of the closed-loop system along the batch direction. In this study, an ILC-based P-type controller is proposed for multi-input multi-output (MIMO) linear batch processes, where a P-type controller is used to design the control signal directly and an ILC module is used to update the set-point for the P-type controller. Under the proposed ILC-based P-type controller, the closed-loop system can be transformed to a 2-dimensional (2D) Roesser s system. Based on the 2D system framework, a sufficient condition for asymptotic stability of the closed-loop system is derived in this paper. In terms of the average tracking error (ATE), the closed-loop control performance under the proposed algorithm can be improved from batch to batch, even though there are repetitive disturbances. A numerical example is used to validate the proposed results.展开更多
Lookup table is widely used in automotive industry for the design of engine control units(ECU).Together with a proportional-integral controller,a feed-forward and feedback control scheme is often adopted for automotiv...Lookup table is widely used in automotive industry for the design of engine control units(ECU).Together with a proportional-integral controller,a feed-forward and feedback control scheme is often adopted for automotive engine management system(EMS).Usually,an ECU has a structure of multi-input and single-output(MISO).Therefore,if there are multiple objectives proposed in EMS,there would be corresponding numbers of ECUs that need to be designed.In this situation,huge efforts and time were spent on calibration.In this work,a multi-input and multi-out(MIMO) approach based on model predictive control(MPC) was presented for the automatic cruise system of automotive engine.The results show that the tracking of engine speed command and the regulation of air/fuel ratio(AFR) can be achieved simultaneously under the new scheme.The mean absolute error(MAE) for engine speed control is 0.037,and the MAE for air fuel ratio is 0.069.展开更多
文摘Integral reinforcement learning(IRL)is an effective tool for solving optimal control problems of nonlinear systems,and it has been widely utilized in optimal controller design for solving discrete-time nonlinearity.However,solving the Hamilton-Jacobi-Bellman(HJB)equations for nonlinear systems requires precise and complicated dynamics.Moreover,the research and application of IRL in continuous-time(CT)systems must be further improved.To develop the IRL of a CT nonlinear system,a data-based adaptive neural dynamic programming(ANDP)method is proposed to investigate the optimal control problem of uncertain CT multi-input systems such that the knowledge of the dynamics in the HJB equation is unnecessary.First,the multi-input model is approximated using a neural network(NN),which can be utilized to design an integral reinforcement signal.Subsequently,two criterion networks and one action network are constructed based on the integral reinforcement signal.A nonzero-sum Nash equilibrium can be reached by learning the optimal strategies of the multi-input model.In this scheme,the NN weights are constantly updated using an adaptive algorithm.The weight convergence and the system stability are analyzed in detail.The optimal control problem of a multi-input nonlinear CT system is effectively solved using the ANDP scheme,and the results are verified by a simulation study.
基金National Natural Science Foundation of China （10972104） The Fundamental Research Funds for NUAA（NS2010007）
文摘Both auto-power spectrum and cross-power spectrum need to be controlled in multi-input multi-output （MIMO） random vibration test. During the control process with the difference control algorithm （DCA）, a lower triangular matrix is derived from Cholesky decomposition of a reference spectrum matrix. The diagonal elements of the lower triangular matrix （DELTM） may become negative. These negative values have no meaning in physical significance and can cause divergence of auto-power spectrum control. A proportional root mean square control algorithm （PRMSCA） provides another method to avoid the divergence caused by negative values of DELTM, but PRMSCA cannot control the cross-power spectrum. A new control algorithm named matrix power control algorithm （MPCA） is proposed in the paper. MPCA can guarantee that DELTM is always positive in the auto-power spectrum control. MPCA can also control the cross-power spectrum. After these three control algorithms are analyzed, three-input three-output random vibration control tests are implemented on a three-axis vibration shaker. The results show the validity of the proposed MPCA.
基金supported by the Priority Academic Program Development of Jiangsu Higher Education Institutionsthe Postgraduate Research & Practice Innovation Program of Jiangsu Province (No. KYCX17_0234)
文摘A control method for Multi-Input Multi-Output（MIMO） non-Gaussian random vibration test with cross spectra consideration is proposed in the paper. The aim of the proposed control method is to replicate the specified references composed of auto spectral densities, cross spectral densities and kurtoses on the test article in the laboratory. It is found that the cross spectral densities will bring intractable coupling problems and induce difficulty for the control of the multioutput kurtoses. Hence, a sequential phase modification method is put forward to solve the coupling problems in multi-input multi-output non-Gaussian random vibration test. To achieve the specified responses, an improved zero memory nonlinear transformation is utilized first to modify the Fourier phases of the signals with sequential phase modification method to obtain one frame reference response signals which satisfy the reference spectra and reference kurtoses. Then, an inverse system method is used in frequency domain to obtain the continuous stationary drive signals. At the same time, the matrix power control algorithm is utilized to control the spectra and kurtoses of the response signals further. At the end of the paper, a simulation example with a cantilever beam and a vibration shaker test are implemented and the results support the proposed method very well.
文摘针对存在输入时滞的多智能体系统(multi-agent system,MAS)滞后一致性问题,提出一种基于时基生成器(time base generator,TBG)的二阶MAS预设时间领导跟随滞后一致性控制方法,使得稳定时间与系统初始状态无关且可预先设定。首先,提出一种误差变换方法,将具有时滞的误差系统转换为无时滞误差系统。然后,利用TBG函数构造误差辅助变量并构造相应滑模面,进而设计预设时间控制器。同时,证明所设计控制器的预设时间稳定性。最后,通过数值仿真验证所提方法的可行性及有效性。仿真结果表明,MAS能够实现精确的预设时间滞后一致性。
基金supported by the Fundamental Research Funds for the Central Universities (No. NS2015008)the corresponding work was performed in the State Key Laboratory of Mechanics and Control of Mechanical Structures
文摘Noises always disturb the control effect of an environment test especially in multi-input multi-output(MIMO) systems. If the frequency response function matrices are ill-conditioned, the noises in the driving forces will be amplified and the response spectral lines may awfully exceed their tolerances. Most of the major biases between the response spectra and the reference spectra are produced by the amplified noises. However, ordinary control algorithms can hardly reduce the level of noises. The influences of the noises on both the auto- and cross-power spectra are analyzed in this paper. As a conventional frequency domain method on the inverse problem, the Tikhonov filter is adopted in the environment test to suppress the exceeding spectral lines. By altering regularization parameters gradually, the auto-power spectra can be improved in a closed control loop. Instead of using the traditional way of selecting regularization parameters, we observe the coherence change to estimate noise eliminations. Incidentally, the requirement of coherence control can be realized. The errors of the phase are then studied and a phase control algorithm is introduced at the end as a supplement of cross-power spectra control. The Tikhonov filter and the proposed phase control algorithm are tested numerically and experimentally. The results show that the noises in the vicinity of lightly damped resonant peaks are more stubborn. The response spectra are able to be greatly improved by the combination of these two methods.
基金supported by National Natural Science Foundation of China (No. 60874116)Natural Science Foundation of Hebei Province (No. F2009000857)
文摘A form of iterative learning control (ILC) is used to update the set-point for the local controller. It is referred to as set-point-related (SPR) indirect ILC. SPR indirect ILC has shown excellent performance: as a supervision module for the local controller, ILC can improve the tracking performance of the closed-loop system along the batch direction. In this study, an ILC-based P-type controller is proposed for multi-input multi-output (MIMO) linear batch processes, where a P-type controller is used to design the control signal directly and an ILC module is used to update the set-point for the P-type controller. Under the proposed ILC-based P-type controller, the closed-loop system can be transformed to a 2-dimensional (2D) Roesser s system. Based on the 2D system framework, a sufficient condition for asymptotic stability of the closed-loop system is derived in this paper. In terms of the average tracking error (ATE), the closed-loop control performance under the proposed algorithm can be improved from batch to batch, even though there are repetitive disturbances. A numerical example is used to validate the proposed results.
基金Project supported by the Centre for Smart Grid and Information Convergence(CeSGIC)at Xi’an Jiaotong-Liverpool University,China
文摘Lookup table is widely used in automotive industry for the design of engine control units(ECU).Together with a proportional-integral controller,a feed-forward and feedback control scheme is often adopted for automotive engine management system(EMS).Usually,an ECU has a structure of multi-input and single-output(MISO).Therefore,if there are multiple objectives proposed in EMS,there would be corresponding numbers of ECUs that need to be designed.In this situation,huge efforts and time were spent on calibration.In this work,a multi-input and multi-out(MIMO) approach based on model predictive control(MPC) was presented for the automatic cruise system of automotive engine.The results show that the tracking of engine speed command and the regulation of air/fuel ratio(AFR) can be achieved simultaneously under the new scheme.The mean absolute error(MAE) for engine speed control is 0.037,and the MAE for air fuel ratio is 0.069.
