Over the years,practical importance and interesting dynamical features have caused a growing interest in dry friction systems.Nevertheless,an effective approach to capture the non-smooth transition behavior of such sy...Over the years,practical importance and interesting dynamical features have caused a growing interest in dry friction systems.Nevertheless,an effective approach to capture the non-smooth transition behavior of such systems is still lacking.Accordingly,we propose a piecewise radial basis function neural network(RBFNN)strategy to solve the transient response of the randomly excited dry friction system.Within the established framework,the transient probability density function of the dry friction system is expressed in a piecewise form.Each segment of the solution is expressed by the sum of a series of Gaussian activation functions with time-dependent weights.These time dependent weights are solved by minimizing the loss function,which involves the residual of the Fokker-Planck-Kolmogorov equations and constraint conditions.To avoid the singularity of the initial condition being a Dirac delta function,a short-time Gaussian approximation strategy is presented to solve the initiating time-dependent weights.Based on some numerical results,the proposed scheme effectively performs.Moreover,a comparison with other existing methods reveals that the proposed scheme can completely capture the nonlinear characteristic of the dry friction system stochastic response more closely.Noteworthy,we can easily extend the proposed method to other types of non-smooth systems with piecewise response characteristics.Moreover,the semi-analytical solution provides a valuable reference for system optimization.展开更多
This paper presents a study of optimal control design for a single-inverted pendulum(SIP)system with the multi-objective particle swarm optimization(MOPSO)algorithm.The proportional derivative(PD)control algorithm is ...This paper presents a study of optimal control design for a single-inverted pendulum(SIP)system with the multi-objective particle swarm optimization(MOPSO)algorithm.The proportional derivative(PD)control algorithm is utilized to control the system.Since the SIP system is nonlinear and the output(the pendulum angle)cannot be directly controlled(it is under-actuated),the PD control gains are not tuned with classical approaches.In this work,the MOPSO method is used to obtain the best PD gains.The use of multi-objective optimization algorithm allows the control design of the system without the need of linearization,which is not provided by using classical methods.The multi-objective optimal control design of the nonlinear system involves four design parameters(PD gains)and six objective functions(time-domain performance indices).The HausdorfF distances of consecutive Pareto sets,obtained in the MOPSO iterations,are computed to check the convergence of the MOPSO algorithm.The MOPSO algorithm finds the Pareto set and the Pareto front efficiently.Numerical simulations and experiments of the rotary inverted pendulum system are done to verify this design technique.Numerical and experimental results show that the multi-objective optimal controls offer a wide range of choices including the ones that have comparable performances to the linear quadratic regulator(LQR)control.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.12072118)the Natural Science Funds for Distinguished Young Scholar of the Fujian Province of China(Grant No.2021J06024)the Project for Youth Innovation Fund of Xiamen(Grant No.3502Z20206005)。
文摘Over the years,practical importance and interesting dynamical features have caused a growing interest in dry friction systems.Nevertheless,an effective approach to capture the non-smooth transition behavior of such systems is still lacking.Accordingly,we propose a piecewise radial basis function neural network(RBFNN)strategy to solve the transient response of the randomly excited dry friction system.Within the established framework,the transient probability density function of the dry friction system is expressed in a piecewise form.Each segment of the solution is expressed by the sum of a series of Gaussian activation functions with time-dependent weights.These time dependent weights are solved by minimizing the loss function,which involves the residual of the Fokker-Planck-Kolmogorov equations and constraint conditions.To avoid the singularity of the initial condition being a Dirac delta function,a short-time Gaussian approximation strategy is presented to solve the initiating time-dependent weights.Based on some numerical results,the proposed scheme effectively performs.Moreover,a comparison with other existing methods reveals that the proposed scheme can completely capture the nonlinear characteristic of the dry friction system stochastic response more closely.Noteworthy,we can easily extend the proposed method to other types of non-smooth systems with piecewise response characteristics.Moreover,the semi-analytical solution provides a valuable reference for system optimization.
基金the National Natural Science Foundation of China(Nos.11572215 and 11702162)the Natural Science Foundation of Shandong Province(No.ZR2018LA009)。
文摘This paper presents a study of optimal control design for a single-inverted pendulum(SIP)system with the multi-objective particle swarm optimization(MOPSO)algorithm.The proportional derivative(PD)control algorithm is utilized to control the system.Since the SIP system is nonlinear and the output(the pendulum angle)cannot be directly controlled(it is under-actuated),the PD control gains are not tuned with classical approaches.In this work,the MOPSO method is used to obtain the best PD gains.The use of multi-objective optimization algorithm allows the control design of the system without the need of linearization,which is not provided by using classical methods.The multi-objective optimal control design of the nonlinear system involves four design parameters(PD gains)and six objective functions(time-domain performance indices).The HausdorfF distances of consecutive Pareto sets,obtained in the MOPSO iterations,are computed to check the convergence of the MOPSO algorithm.The MOPSO algorithm finds the Pareto set and the Pareto front efficiently.Numerical simulations and experiments of the rotary inverted pendulum system are done to verify this design technique.Numerical and experimental results show that the multi-objective optimal controls offer a wide range of choices including the ones that have comparable performances to the linear quadratic regulator(LQR)control.
