Stochastic Modeling Of Mechanical Systems, Controls And Applications

It is well known that mechanical systems are often subjected to random disturbances,which significantly affects the performance in a uncertain manner. With the development ofstochastic stability, the research on stochastic mechanics and control has been an active field.In this paper, for several important problems on stochastic modeling, tracking control and theapplication of mechanical systems, some basic analysis tools are developed, and based on sometools, these problems are deeply investigated and solved. The main results include:1. By reasonably introducing random noise, a class of stochastic Lagrangian control sys-tems and a class of stochastic Hamiltonian control systems are constructed to describe the mo-tion of the mechanical systems subjected to random disturbance.2. For a class of stochastic Lagrangian control systems with unknown parameters, undersome milder assumptions, an adaptive tracking controller is designed such that the mean squareof the tracking error converges to an arbitrarily small neighborhood of zero by tuning design pa-rameters. The reasonability of assumptions and the efficiency of the controller are demonstratedby a mechanics model in random vibration environment.3. For a class of stochastic Lagrangian systems with the unmeasurable velocity, undersome milder assumptions, using the structural properties of Lagrangian systems, a reduced-order observer is skillfully constructed to estimate the velocity. Based on the observer, anoutput feedback tracking controller is designed such that the mean square of the tracking er-ror converges to an arbitrarily small neighborhood of zero by tuning design parameters. Theefficiency of the controller is demonstrated by a stochastic mechanical model.4. For a class of stochastic Hamiltonian control systems with unknown drift and diffusionfunctions, a vector form of adaptive backstepping controller is designed such that the closed-loop stochastic Hamiltonian system has a unique solution that is globally bounded in probabilityand the tracking error converges to an arbitrarily small neighborhood of zero. As application,the modeling and the control for spring pendulum in stochastic surroundings are researched.5. For a two-link planar rigid robot manipulator, a stochastic Lagrangian model is con-structed to describe the motion of the manipulator in random vibration environment. Based on the constructed model, for the case that all states are measurable, a state feedback controller isdesigned such that the error system is4-th moment exponentially practically stable. When thevelocity is unmeasurable, a output feedback controller is designed such that the configurationof the closed-loop system can track a given smooth reference signal as close as possible.6. For the manipulator with multi-revolute joints in random vibration environment, byanalyzing the effect of environment to the mass points and introducing an equivalent stochasticnoise process, a stochastic Hamiltonian dynamic model is constructed to describe the motionof the manipulator. Based on the constructed model, a state feedback controller is designedsuch that the configuration of the closed-loop system can approximatively track a given smoothreference signal.7. For stochastic nonlinear systems with state-dependent switching, when the given active-region set can be replaced by its interior, the local solution of the switched system is constructedby defining a series of stopping times as switching instants, and the criteria on global existenceand stability of solution are presented by Lyapunov approach. For the case where the active-region set can not be replaced by its interior, the switched systems do not necessarily havesolutions, thereby quasi-solution to the underlying problem is constructed and the boundednesscriterion is proposed.