A stochastic dynamical system with double singularities driven by non-Gaussian noise is investigated. The Fokker Plank equation of the system is obtained through the path-integral approach and the method of transforma...A stochastic dynamical system with double singularities driven by non-Gaussian noise is investigated. The Fokker Plank equation of the system is obtained through the path-integral approach and the method of transformation. Based on the definition of Shannon＇s information entropy and the Schwartz inequality principle, the upper bound for the time derivative of entropy is calculated both in the absence and in the presence of non-equilibrium constraint. The present calculations can be used to interpret the effects of the system dissipative parameter, the system singularity strength parameter, the noise correlation time and the noise deviation parameter on the upper bound.展开更多
The coupling effect of the flexible joint and the flexible link on the dynamic singularity of the flexible manipulator is addressed. Firstly, the dynamic equations of a flexible manipulator with a flexible joint and a...The coupling effect of the flexible joint and the flexible link on the dynamic singularity of the flexible manipulator is addressed. Firstly, the dynamic equations of a flexible manipulator with a flexible joint and a flexible link are derived. Secondly, the relationship and property between the flexible joint and the flexible link are analyzed. It shows that the flexible joint＇s amplitude will increase abruptly, thereby the dynamic singularity occurs if the frequency of a flexible joint is near or equal to some natural frequency of a flexible link. Finally, some numerical simulations which will verify the correctness of the theoretical analysis, are carded out. The results are fundamental for the design of a flexible manipulator and for the avoidance of the dynamic singularity.展开更多
The ill-conditioned stable inversion is studied for slightly nonminimum phase systems whose zero dynam- ics is singularly perturbed, that is, the relative degree is ill-defined. For these systems, we show that there e...The ill-conditioned stable inversion is studied for slightly nonminimum phase systems whose zero dynam- ics is singularly perturbed, that is, the relative degree is ill-defined. For these systems, we show that there exists an inherent limitation in the bandwidth of a reference trajectory to be tracked when a well-conditioned feedforward input via stable inversion is sought. We assert that, when the violation of this limitation occurs, the so-called reference trajectory redesign is called for. Our analysis results can provide an explicit assessment as well as useful guidance for the reference trajectory redesign if needed.展开更多
We consider the following Hamiltonian system: q″(t)+V′(q(t))=0 q ∈C^2(R,R^n\{0}) (HS) where V ∈C^2(R^n\{0},R)is an even function.By looking for closed geodesics,we prove that (HS)has a nonconstant periodic solutio...We consider the following Hamiltonian system: q″(t)+V′(q(t))=0 q ∈C^2(R,R^n\{0}) (HS) where V ∈C^2(R^n\{0},R)is an even function.By looking for closed geodesics,we prove that (HS)has a nonconstant periodic solution of prescribed energy under suitable assumptions.Our main assumption is related with the strong force condition of Gordon.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No. 10872165)
文摘A stochastic dynamical system with double singularities driven by non-Gaussian noise is investigated. The Fokker Plank equation of the system is obtained through the path-integral approach and the method of transformation. Based on the definition of Shannon＇s information entropy and the Schwartz inequality principle, the upper bound for the time derivative of entropy is calculated both in the absence and in the presence of non-equilibrium constraint. The present calculations can be used to interpret the effects of the system dissipative parameter, the system singularity strength parameter, the noise correlation time and the noise deviation parameter on the upper bound.
基金supported by National Natural Science Foundation of China(No. 50075008)Important Project of Science and Technology Research of Ministry of Education of China (No.307005).
文摘The coupling effect of the flexible joint and the flexible link on the dynamic singularity of the flexible manipulator is addressed. Firstly, the dynamic equations of a flexible manipulator with a flexible joint and a flexible link are derived. Secondly, the relationship and property between the flexible joint and the flexible link are analyzed. It shows that the flexible joint＇s amplitude will increase abruptly, thereby the dynamic singularity occurs if the frequency of a flexible joint is near or equal to some natural frequency of a flexible link. Finally, some numerical simulations which will verify the correctness of the theoretical analysis, are carded out. The results are fundamental for the design of a flexible manipulator and for the avoidance of the dynamic singularity.
基金the National Natural Science Foundation of China (No.60473120)the Natural Science Foundation of Guangdong(No.6023190)the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry of China.
文摘The ill-conditioned stable inversion is studied for slightly nonminimum phase systems whose zero dynam- ics is singularly perturbed, that is, the relative degree is ill-defined. For these systems, we show that there exists an inherent limitation in the bandwidth of a reference trajectory to be tracked when a well-conditioned feedforward input via stable inversion is sought. We assert that, when the violation of this limitation occurs, the so-called reference trajectory redesign is called for. Our analysis results can provide an explicit assessment as well as useful guidance for the reference trajectory redesign if needed.
文摘We consider the following Hamiltonian system: q″(t)+V′(q(t))=0 q ∈C^2(R,R^n\{0}) (HS) where V ∈C^2(R^n\{0},R)is an even function.By looking for closed geodesics,we prove that (HS)has a nonconstant periodic solution of prescribed energy under suitable assumptions.Our main assumption is related with the strong force condition of Gordon.
