Optimal Kalman-like filter for a class of nonlinear stochastic systems

This paper deals with an optimal Kalman-like filter for nonlinear discrete-time systems aided with auto and cross-correlated noises and stochastic parameter matrices involved in state and measurement equa-tions,and random nonlinearity.The random variables are proposed by their statistical characteristics while the inquiry is focused on stochastic multivariate analysis and calculation.For the nonlinear sys-tem with the auto and cross-correlated noises and stochastic parameter matrices,an equivalent system is first reconstructed by decomposing stochastic parameter matrices and introducing uncorrelated pseudo-noises.Then a recursive filter that ensures unbiasedness and minimizes the error variance is designed for the newly transformed equivalent system.Finally,the filter is verified by applying it to some numerical simulations.

Seismic response analysis of damper-connected adjacent structures with stochastic parameters

Dynamic response analysis of damper connected adjacent multi-story structures with uncertain parameters is carried out.A formula of the multi degree of freedom(MDOF) for the structure-damper system with stochastic parameters is derived.The uncertainties of mass and stiffness are taken into consideration firstly.The ground acceleration is represented by Kanai-Tajimi filtered non-stationary process.The mean square random responses of structural displacement and story drift are chosen as the optimization objective.The variations of mean square responses of top floor displacements and bottom story drifts in neighboring structures with the damper stiffness and damping coefficient are analyzed in detail.Through the parametric study,the acquiring optimum parameters of damper are regarded as numerical results.Then,a reducing order model of the MDOF system for adjacent structures with mean parameters is presented.The explicit expressions for determining optimal parameters of Kelvin model-defined damper which is used to connect adjacent single degree of freedom(SDOF) structures subjected to a white-noise excitation are employed to achieve the appropriate damper parameters,which are called theory results.Through a comparative study,it can be found that the theory values of damper parameters are consistent with the results based on extensive parametric studies.The analytical results can be obtained by using the first natural frequencies and the total mass of the adjacent deterministic structures with mean parameters.The analytical formulas can be used to find appropriate parameters of damper between adjacent structures for engineering applications.The performance of damper is investigated on the basis of mitigations of mean square random responses of inter-story drifts,displacements and accelerations in adjacent structures.The numerical results demonstrate the robustness of coupled building control strategies.

Advances in structural vibration control application of magneto-rheological visco-elastomer

Magneto-rheological visco-elastomer （MRVE） as a new smart material developed in recent years has several significant advantages over magneto-rheological liquid. The adjustability of structural dynamics to random environmental excitations is required in vibration control. MRVE can supply considerably adjustable damping and stiffness for structures, and the adjustment of dynamic properties is achieved only by applied magnetic fields with changeless structure design. Increasing researches on MRVE dy- namic properties, modeling, and vibration control application are presented. Recent advances in MRVE dynamic properties and structural vibration control application including composite structural vibration mitigation under uniform magnetic fields, vibration response characteristics improvement through harmonic parameter distribution, and optimal bounded parametric control design based on the dynamical programming principle are reviewed. Relevant main methods and results introduced are beneficial to understanding and researches on MRVE application and development.

ADAPTIVE TRACKING OF A CLASS OF FIRST-ORDER SYSTEMS WITH BINARY-VALUED OBSERVATIONS AND FIXED THRESHOLDS

This paper considers the adaptive tracking problem for a class of first-order systems with binary-valued observations generated via fixed thresholds. A recursive projection algorithm is proposed for parameter estimation based on the statistical properties of the system noise. Then, an adaptive control law is designed via the certainty equivalence principle. By use of the conditional expectations of the innovation and output prediction with respect to the estimates, the closed-loop system is shown to be stable and asymptotically optimal. Meanwhile, the parameter estimate is proved to be both almost surely and mean square convergent, and the convergence rate of the estimation error is also obtained. A numerical example is given to demonstrate the efficiency of the adaptive control law.