Design Method of High-Order Kalman Filter for Strong Nonlinear System Based on Kronecker Product Transform

In this paper, a novel design idea of high-order Kalman filter based on Kronecker product transform is proposed for a class of strong nonlinear stochastic dynamic systems. Firstly, those augmenting systems are modeled with help of the Kronecker product without system noise. Secondly, the augmented system errors are illustratively charactered by Gaussian white noise. Thirdly, at the expanded space a creative high-order Kalman filter is delicately designed, which consists of high-order Taylor expansion, introducing magical intermediate variables, representing linear systems converted from strongly nonlinear systems, designing Kalman filter, etc. The performance of the proposed filter will be much better than one of EKF, because it uses more information than EKF. Finally, its promise is verified through commonly used digital simulation examples.

Identification and Stochastic Optimizing the UAV Motion Control in Turbulent Atmosphere

In a class of diffusion Markov processes, we formulate a problem of identification of nonlinear stochastic dynamic systems with random parameters, multiplicative and additive noises, control functions, and the state vector at a final time moment. For such systems, the identifiability conditions are being studied, and necessary conditions are formulated in terms of the general theory of extreme problems. The developed engineering methods for identification and optimizing nonlinear stochastic systems are presented as well as their application for unmanned aerial vehicles under wind disturbances caused by atmospheric turbulence, namely, for optimizing the autopilot parameters during a rotary maneuver of an unmanned aerial vehicle in translational motion, taking into account the identification of its angular velocities.

A Reliability-Based Formulation for Simulation-Based Control Co-design Using Generalized Polynomial Chaos Expansion

Combined plant and control design (control co-design, or CCD) methods are often used during product development to address the synergistic coupling between the plant and control parts of a dynamic system. Recently, a few studies have started applying CCD to stochastic dynamic systems. In their most rigorous approach, reliability-based design optimization (RBDO) principles have been used to ensure solution feasibility under uncertainty. However, since existing reliability-based CCD (RBCCD) algorithms use all-at-once (AAO) formulations, only most-probable-point (MPP) methods can be used as reliability analysis techniques. Though effective for linear/quadratic RBCCD problems, the use of such methods for highly nonlinear RBCCD problems introduces solution error that could lead to system failure. A multidisciplinary feasible (MDF) formulation for RBCCD problems would eliminate this issue by removing the dynamic equality constraints and instead enforcing them through forward simulation. Since the RBCCD problem structure would be similar to traditional RBDO problems, any of the well-established reliability analysis methods could be used. Therefore, in this work, a novel reliability-based MDF formulation of multidisciplinary dynamic system design optimization (RB-MDF-MDSDO) has been proposed for RBCCD. To quantify the uncertainty propagated by the random decision variables, Monte Carlo simulation has been applied to the generalized polynomial chaos (gPC) expansion of the probabilistic constraints. The proposed formulation is applied to two engineering test problems, with the results indicating the effectiveness of both the overall formulation as well as the reliability analysis technique for RBCCD.

Relaxation of Some Confusions about Confounders

This work is about observational causal discovery for deterministic and stochastic dynamic systems. We explore what additional knowledge can be gained by the usage of standard conditional independence tests and if the interacting systems are located in a geodesic space.

The Framework of Mechanics for Dynamic Behaviors of Fractional-Order Stochastic Dynamic Systems

The main goal of this paper is to establish a general framework for dynamic behaviors of coupled fractional-order stochastic dynamic systems of particles by using star-coupled models. In particular, the general mechanics on the dynamic behaviors related to the stochastic resonance (SR) phenomenon of a starcoupled harmonic oscillator subject to multiplicative fluctuation and periodic force in viscous media are established by considering couplings, memory effects, the occurring of synchronization linked to the occurring of SR induced. Here the noise is modeled with the fractional power kernel function and analytical expressions for the first moment of the stability between system responses and parameters in the long-time (of asymptotic stability) are also given. The theoretic and simulation results show the non-monotonic dependence between the response output gain and the input signal frequency, noise parameters provided by fractional-order stochastic dynamics are significant different by comparing those exhibited under the traditional integer-order stochastic dynamics, which indicates that the bona fide resonance and the generalized SR phenomena would appear. Furthermore, the fluctuation noise, the number of the particles for the systems, and the fractional order work together, producing more complex dynamic phenomena compared with the traditional integral-order systems. The theoretical analyses are supported by the corresponding numerical simulations, and thus it seems that the results established in this paper would provide a possible fundamental mathematical framework for the study of Schumpeter’s theory on the economic development under the “innovation and capital paradigm” and related disciplines. In particular, the framework established by this paper allows us at the first time logically concluding that “in principle. the ratio of SMEs growing up successfully is less than one third”, this is consistent with what the market has been observed commonly, but similar conclusion not available from the existing literature today. Finally, we like to point out that the framework established in this paper actually shows that under the basic model established in Section 2, through numerical simulation results given in sections 3 and 4, the fractional derivative in the interval (0; 1) as a basic tool, which can provide a new world with a more refined description of the market financial scene, such as in identifying risk factors or describing mechanics for enterprises’ growths more precisely with extra features compared with the traditional integer derivative one.