Compensating Operator and Weak Convergence of Semi-Markov Process to the Diffusion Process without Balance Condition

Weak convergence of semi-Markov processes in the diffusive approximation scheme is studied in the paper. This problem is not new and it is studied in many papers, using convergence of random processes. Unlike other studies, we used in this paper concept of the compensating operator. It enables getting sufficient conditions of weak convergence under the conditions on the local characteristics of output semi-Markov process.

Research of Dynamic Compensation for Hysteresis Nonlinear

The hysteresis nonlinearity reduces the accuracy of precision instrument..In order to mitigate the effect of the hysteresis, it is necessary to build hysteresis model and compensate hysteresis nonlinearity.The Krasnosel’skii–Pokrovkii （KP） operator is used to build hysteresis model, which the model is divided into linear part and nonlinear part. The KP compensating operator is proposed to compensate nonlinear part of hysteresis model. The Sliding model adaptive control law for the control method is deduced from the Lyapunov stability theorem. The emulational results confirmed the availability of hysteresis nonlinear compensation control.