Approximate dynamic programming for stochastic systems with additive and multiplicative noise

We derive an optimum filter function to detect a target degraded by multiplicative noise and additive overlapping noise and placed in background noise. The filter is designed to maximize the metric peak-to-output energy, which is the ratio of the expected value squared of the output peak at the target position to the expected value of the average output energy. The optimum filter provides improved discrimination as well as robustness to input noise. One advantage of the filter described here over the homomorphic filters is that the additional preprocess on the input image, that is, the input logarithmic operation, is not required for reducing the effects of multiplicative noise. The performance of the filter is examined in terms of discrimination against background noise and robustness to multiplicative and additive input noise. Both multiplicative amplitude noise and multiplicative complex noise are considered.

Analysis of noise-induced transitions for Hopf system with additive and multiplicative random disturbances

Current reversal in a continuously periodic system driven by an additive noise and a multiplicative noise

The issues are considered, associated with the estimation of the measurement accuracy of the information parameters of the useful signal in the conditions of simultaneous action of multiplicative and additive noise, which in general have non-Gaussian character of the distribution. Two approaches to representation of the multiplicative noise are analyzed. It is shown that when considering of multiplicative noise in the form of deterministic or quasideterministic process the measurement accuracy is affected as non-Gaussian nature of the additive noise and average power of the multiplicative noise. It is shown that with the increase of the average power of the multiplicative noise effect of non-Gaussian nature of the additive noise on the measurement accuracy is reduced. It is shown that if the multiplicative noise is a random process, then the potential measurement accuracy under its influence can be reduced by more than an order of magnitude. Accounting non-Gaussian character of equivalent noise formed by additive noise and a multiplicative part, leads to a significant reduction in the potential loss of measurement accuracy.

Rotational Motion Control by Feedback with Minimum L1-Norm

Adaptive cubature Kalman filter with the estimation of correlation between multiplicative noise and additive measurement noise

In this study, we investigate the dynamic mechanisms of tumor progression in response to fluctuations and uncertainties within the tumor-immune microenvironment. Utilizing temporal single-cell data, we develop a novel stochastic reaction-convection model that captures the spatiotemporal dynamics of macrophage responses to tumor cells subjected to both multiplicative and additive noise generated by non-homologous microenvironmental fluctuations. We prove the existence and uniqueness of a global positive solution for the proposed stochastic model. Then, by combining the stochastic Lyapunov analysis and the comparison theorem, we explore the moment boundaries for cell populations, as well as the asymptotic behavior at the boundary equilibrium points; sufficient conditions for driving sustained tumor growth and clearance are derived by employing the ergodicity theorem and are interestingly found to be only related to multiplicative noise. Furthermore, we employ an upwind finite difference scheme to simulate the effects of different noise types on a cell population distribution and the persistence of tumor growth. Results show that while additive noise influences the multimodal distribution of early tumor cell phenotypes, it has minimal impact on the mean density of tumor cells, indicating that additive noise acts primarily as a diffusion factor. In contrast, increasing multiplication noise effectively inhibits the development without altering the number of peaks in a phenotypic distribution. Interestingly, when additive and multiplicative noises are correlated, stronger additive noise can have dual effects on the steady-state distribution of tumor cells, with increased correlation positively influencing tumor cell elimination. These results provide novel insight into the tumor-immune microenvironment dynamics.

In this paper, the stochastic optimal control problems, which frequently occur in economic and finance are investigated. First, using Bellman’s dynamic programming method the stochastic optimal control problems are converted to Hamilton-Jacobi-Bellman (HJB) equation. Then, obtained HJB equation is solved through the method of separation of variables by guessing a solution via its terminal condition. Also, the non-linear optimal feedback control law is constructed. Finally, the solution procedure is illustrated for solving some examples that two of them are financial models. In fact, to highlight the applications of stochastic optimal control problems in financial mathematics, some financial models are presented.

The problem of distributed parameter estimation from binary quantized observations is studied when the unquantized observations are corrupted by combined multiplicative and additive Gaussian noise. These results are applicable to sensor networks where the sensors observe a parameter in combined additive and nonadditive noise and to a case where dispersed receivers are employed with analog communication over fading channels where the receivers employ binary quantization before noise-free digital communications to a fusion center. We first discuss the case in which all the quantizers use an identical threshold. The parameter identifiability condition is given, and, surprisingly, it is shown that unless the common threshold is chosen properly and the parameter lies in an open interval, the parameter will not generally be identifiable, in contrast to the additive noise case. The best achievable mean square error (MSE) performance is characterized by deriving the corresponding Cramer-Rao Lower Bound (CRLB). A closed-form expression describing the corresponding maximum likelihood (ML) estimator is presented. The stability of the performance of the ML estimators is improved when a nonidentical threshold strategy is utilized to estimate the unknown parameter. The thresholds are designed by maximizing the minimum asymptotic relative efficiency (ARE) between quantized and unquantized ML estimators. Although the ML estimation problem is nonconvex, it is shown that one can relax the optimization to make it convex. The solution to the relaxed problem is used as an initial solution in a gradient algorithm to solve the original problem. Next, the case where both the variances of the additive noise and multiplicative noise are unknown is studied. The corresponding CRLB is obtained, and the ML estimation problem is transformed to a convex optimization, which can be solved efficiently. Finally, numerical simulations are performed to substantiate the theoretical analysis.

A stochastic control problem is formulated and we get the explicit form of the optimal control for initial-data-parameterized linear quadratic stochastic optimal control problems with random jumps. The optimal control can be proved to be unique. A stochastic Riccati equation is rigorous derived from the stochastic Hamilton system, which provides an optimal feedback control. This completes the the interrelationship between the stochastic Riccati equation and stochastic Hamilton system as two different but equivalent tools for the stochastic linear quadratic problem.

In this paper, the state estimation problem for discrete-time linear systems influenced by multiplicative and time-correlated additive measurement noises is considered where the multiplicative noises are zero-mean white noise sequences, and the time-correlated additive noise is described by a linear system model with white noise. An optimal linear estimator for the system under consideration is proposed, which does not require computing the inverse of state transition matrix. The proposed estimator has a recursive structure, and has time-independent computation and storage load. Computer simulations are carried out to demonstrate the performance of the proposed estimator. The simulation results show the superiority of the proposed estimator.

Signal-to-noise analysis of FM demodulation in the presence of multiplicative and additive noise

Tails in the probability distribution of stochastic processes with power law multiplicative noise

In this paper, the localization accuracy of range-only sensors is investigated. Being different from most previous studies, we consider a more general measurement model with both additive and multiplicative noise other than with only additive noise. The main contributions lie in twofold. First, a CRLB(Cramer-Rao Lower Bound)-based metric is proposed to evaluate the localization accuracy. In addition, the analytical relationships between target-sensor distance and localization accuracy, and between noise and localization accuracy are derived. Second, numerical analysis is executed to evaluate the localization accuracy for three important regular patterns of sensor deployment, i.e., triangle, square and hexagon. Two aspects have been examined and discussed, including (a) the geometric distribution of localization accuracy, (b) the average localization accuracy. Both theoretical and numerical results show that the multiplicative noise will influence significantly the localization accuracy. This study also provides important guidelines for optimal sensor deployment.

Output-feedback adaptive optimal control of interconnected systems based on robust adaptive dynamic programming