General nonlinear control systems are studied in this paper with the goal to transform them into the so-called controllability canonteal form via state transformation only. The conditions of transformability are given...General nonlinear control systems are studied in this paper with the goal to transform them into the so-called controllability canonteal form via state transformation only. The conditions of transformability are given for both single input and multiple input cases. Besides, by an algebraic approach the procedure for constructing the state transformation is established. This paper is formulated in the framework of calculus rather than differential geometry approach.展开更多
This paper discusses the conformal invariance by infinitesimal transformations of canonical Hamilton systems. The necessary and sufficient conditions of conformal invarianee being Lie symmetrical simultaneously by the...This paper discusses the conformal invariance by infinitesimal transformations of canonical Hamilton systems. The necessary and sufficient conditions of conformal invarianee being Lie symmetrical simultaneously by the action of infinitesimal transformations are given. The determining equations of the conformal invariance are gained. Then the Hojman conserved quantities of conformal invariance by special infinitesimal transformations are obtained. Finally an illustrative example is given to verify the results.展开更多
Semi-linear n x n systems of the form Aδu/δ＋Bδ/δy=f can generally be solved, at least locally, provided data are imposed on non-characteristic curves. There are at most n characteristic curves and they are determ...Semi-linear n x n systems of the form Aδu/δ＋Bδ/δy=f can generally be solved, at least locally, provided data are imposed on non-characteristic curves. There are at most n characteristic curves and they are determined by the coefficient matrices on the left-hand sides of the equations. We consider cases where such problems become degenerate as a result of ambiguity associated with the definition of characteristic curves. In such cases, the existence of solutions requires restrictions on the data and solutions might not be unique.展开更多
文摘General nonlinear control systems are studied in this paper with the goal to transform them into the so-called controllability canonteal form via state transformation only. The conditions of transformability are given for both single input and multiple input cases. Besides, by an algebraic approach the procedure for constructing the state transformation is established. This paper is formulated in the framework of calculus rather than differential geometry approach.
基金supported by the National Natural Science Foundation of China (Grant Nos 10472040,10572021 and 10772025)the Outstanding Young Talents Training Found of Liaoning Province of China (Grant No 3040005)
文摘This paper discusses the conformal invariance by infinitesimal transformations of canonical Hamilton systems. The necessary and sufficient conditions of conformal invarianee being Lie symmetrical simultaneously by the action of infinitesimal transformations are given. The determining equations of the conformal invariance are gained. Then the Hojman conserved quantities of conformal invariance by special infinitesimal transformations are obtained. Finally an illustrative example is given to verify the results.
文摘Semi-linear n x n systems of the form Aδu/δ＋Bδ/δy=f can generally be solved, at least locally, provided data are imposed on non-characteristic curves. There are at most n characteristic curves and they are determined by the coefficient matrices on the left-hand sides of the equations. We consider cases where such problems become degenerate as a result of ambiguity associated with the definition of characteristic curves. In such cases, the existence of solutions requires restrictions on the data and solutions might not be unique.
