State-multiplicative Noise Research Articles

Stochastic Antiresonance for Systems with Multiplicative Noise and Sector-Type Nonlinearities.

The paradigm of stochastic antiresonance is considered for a class of nonlinear systems with sector bounded nonlinearities. Such systems arise in a variety of situations such as in engineering applications, in physics, in biology, and in systems with more general nonlinearities, approximated by a wide neural network of a single hidden layer, such as the error equation of Hopfield networks with respect to equilibria or visuo-motor tasks. It is shown that driving such systems with a certain amount of state-multiplicative noise, one can stabilize noise-free unstable systems. Linear-Matrix-Inequality-based stabilization conditions are derived, utilizing a novel non-quadratic Lyapunov functional and a numerical example where state-multiplicative noise stabilizes a nonlinear system exhibiting chaotic behavior is demonstrated.

Distributed Optimal Consensus Control of Multiagent Systems Involving State and Control Dependent Multiplicative Noise

This paper aims to solve the multi-objective optimization control problem by investigating the consensus problem of multi-agent simultaneous optimization with state and control dependent multiplicative noise. The main contributions of this work are two-fold. First, the optimal consensus control problem is solved by designing the free item of an optimal controller, and the coefficient of the feedback gain is obtained based on analyzing a parameterized generalized algebraic Riccati equation. Second, we derive a new consensus controller that comprises two parts different from the current consensus. One part minimizes a linear quadratic index with a singular control weighting matrix, and the other affords the multi-agent systems to achieve mean square consensus.

Asynchronous Control for Discrete-Time Markovian Jump Systems With Multiplicative Noise

In this note, the guaranteed cost control problem for discrete-time Markovian jump systems with state and input multiplicative noise is solved. Since the model mismatch problem often exists in system modes and controller modes, an asynchronous controller is presented to make the system stochastically stable in this paper. By using of the linear matrix inequality techniques, an optimization solution can be obtained, such that the quadratic cost function can be minimized, meanwhile the expectation of the state and control can be guaranteed in a constraint set.

Stochastic Linearization of Feedback Systems With Multivariate Nonlinearities and Systems With State-Multiplicative Noise

Stochastic Linearization of Feedback Systems With Multivariate Nonlinearities and Systems With State-Multiplicative Noise

Predictor‐based H∞ leader‐following consensus of stochastic multi‐agent systems with random input delay

AbstractIn this paper, we investigate H∞ leader‐following consensus of multi‐agent systems with state multiplicative noise governed by stochastic differential equations and random time‐varying input delays which satisfy a certain probability. A new predictor‐based controller is designed based on the reduction approach to guarantee H∞ leader‐following consensus is achieved in mean square sense. By designing a Lyapunov function and using stochastic techniques, sufficient conditions are obtained in a form of linear matrix inequalities. Finally, a simulation is given to demonstrate the effectiveness of the obtained theoretical results.

Dynamic Event-Triggered Control of Networked Stochastic Systems With Scheduling Protocols

In the present article, we consider network-based control of linear systems with state multiplicative noise. For the sensor-controller network, round-robin, try-once-discard, and independent and identically distributed protocols are proposed to orchestrate the measurement transmission from multiple sensor nodes. By using the time-delay approach to networked control systems, sufficient conditions for the exponential mean-square stability are obtained in terms of linear matrix inequalities. Moreover, a discrete-time dynamic event-trigger is suggested to reduce the number of sent control signals from controller to actuator. An air vehicle system from the literature illustrates the efficiency of the presented approach.

Exponential stabilization for 1-D linear Itô-type state-dependent stochastic parabolic PDE systems via static output feedback

This paper deals with the problem of exponential stabilization for 1-D linear stochastic parabolic partial differential equation (PDE) systems with state-multiplicative noise in the form of Itô type. A static output feedback (SOF) control scheme is proposed to stabilize the stochastic PDE system in a stochastic framework via locally collocated piecewise uniform actuators and sensors. The closed-loop well-posedness analysis is provided by virtue of the semi-group theory. Based on the infinite-dimensional infinitesimal operator and Lyapunov technique, the SOF controller design is developed to guarantee the exponential stability of the resulting closed-loop system in the mean square sense. Finally, simulation results on a stochastic heat equation are presented to verify the effectiveness of the proposed design method.

A Feedback Nash Equilibrium for Affine-Quadratic Zero-Sum Stochastic Differential Games With Random Coefficients

We study the affine-quadratic zero-sum stochastic differential game with random coefficients, where the coefficients of the stochastic differential equation (SDE) are random processes and both additive and state multiplicative noise are included in the diffusion term of the corresponding SDE. By applying Ito-Kunita’s formula to the quadratic random field, we develop a direct approach, also known as the completion of squares method, to characterize the explicit (feedback) Nash equilibrium and obtain the optimal game value. The characterized Nash equilibrium depends linearly on the state and the additional linear backward SDE. We also verify the optimality of the Nash equilibrium by characterizing the smooth solution of the stochastic Hamilton-Jacobi-Isaacs equation that is the second-order stochastic partial differential equation obtained from dynamic programming.

Gain-scheduled ℋ∞ controller synthesis for LPV systems subject to multiplicative noise

This paper proposes LMI conditions to design parameter-dependent (i.e. gain-scheduled) state-feedback controllers that ensure closed-loop stability with guaranteed ℋ∞ performance for both continuous and discrete-time LPV systems with state multiplicative noise. The state-space matrices and the multiplicative noise matrix are considered polytopic and independent. The time-varying parameters can be considered time-invariant, arbitrarily fast or with bounded rates of variation. The advantages of the proposed technique are illustrated by numerical examples borrowed from the literature.

Containment control of stochastic multiagent systems with semi‐Markovian switching topologies

SummaryThe containment control of stochastic multiagent systems with semi‐Markov switching topologies is investigated in this paper. The general case that the distribution function of the sojourn time is dependent on both the current system mode and the target mode is considered. Taking state multiplicative noise into account and using stochastic techniques, sufficient conditions to achieve the containment control in the asymptotic mean square sense are obtained in a form of linear matrix inequalities and the controller design condition is given. Finally, a simulation is given to demonstrate the effectiveness of the obtained theoretical results.

Stochastic control of state‐dependent jump linear systems with state‐dependent noise

State-dependent jump linear systems (SJLSs) are a set of linear systems whose switching is determined by a finite state random process with state-dependent transition rates. In this study, a SJLS is considered with state multiplicative noise and stochastic perturbations. In particular, the jump process is regarded to have dissimilar transition rates among sets of state evolution space. The aim of this study is to consider stochastic H ∞ control of such systems using state-feedback control input. Sufficient conditions for stochastic H ∞ are obtained by solving linear matrix inequalities, which are validated by a simulation example.

Two-Dimensional Peak-to-Peak Filtering for Stochastic Fornasini–Marchesini Systems

This paper is concerned with the problem of two-dimensional (2-D) stochastic peak-to-peak filter design for Fornasini–Marchesini local state-space (FM LSS) systems with state-multiplicative noise. First, a novel sufficient condition is established, which guarantees that the underlying FM LSS system is stochastically mean-square stable with 2-D stochastic peak-to-peak performance. A deterministic FM LSS system case is also discussed. Subsequently, based on the result, a new 2-D stochastic peak-to-peak filter of general form is designed for FM LSS systems with state-multiplicative noise. Finally, a numerical example is presented to show the effectiveness of the proposed 2-D stochastic peak-to-peak filter.

Predictor-Based Control of Systems With State Multiplicative Noise

Linear, continuous-time systems with state-multiplicative noise and time-delayed input are considered. The problems of \(H_{\infty }\) state-feedback and output-feedback control are solved for these systems when uncertainty in their deterministic parameters is encountered. Cascaded sub-predictors of the Luenberger-type are applied that considerably increase the size of the input time delay that can be solved for. Two examples are given. The first is a practical control engineering design and the second is an illustrative example that compares several solution methods for the stochastic state-feedback control.

Control design for discrete-time state-multiplicative noise stochastic systems

Design conditions for existence of the H∞ linear state feedback control for discretetime stochastic systems with state-multiplicative noise and polytopic uncertainties are presented in the paper. Using an enhanced form of the bounded real lemma for discrete-time stochastic systems with state-multiplicative noise, the LMI-based procedure is provided for computation of the gains of linear, as well as nonlinear, state control law. The approach is illustrated on an example demonstrating the validity of the proposed method.

Linear quadratic regulation for discrete-time systems with state delays and multiplicative noise

In this paper, the linear quadratic regulation problem for discrete-time systems with state delays and multiplicative noise is considered. The necessary and sufficient condition for the problem admitting a unique solution is given. Under this condition, the optimal feedback control and the optimal cost are presented via a set of coupled difference equations. Our approach is based on the maximum principle. The key technique is to establish relations between the costate and the state.

H∞ Control of Discrete-Time Stochastic State-multiplicative Systems Constrained in State by Equality Constraints

Design conditions for the existence of the H∞ state feedback control for discrete-time stochastic systems with state-multiplicative noise stabilizing the closed-loop in such a way that the state variables satisfy equality constraints in the mean are presented in the paper. Using an enhanced form of the bounded real lemma for discrete-time stochastic systems with state-multiplicative noise, the LMI-based procedure is provided for computation of the gain matrix of state control law and the influence of equality constraints is explained. The approach is illustrated on example demonstrating the validity of the proposed method.

H∞Enhanced Control Design of Discrete-Time Takagi-Sugeno State-Multiplicative Noisy Systems

Design conditions for existence of theH∞state feedback control for Takagi-Sugeno fuzzy discrete-time stochastic systems with state-multiplicative noise, stabilizing the closed-loop in such way that the quadratic performance in the mean is satisfied, are presented in the paper. Using newly introduced enhanced form of the bounded real lemma for such stochastic systems, the LMI-based procedure is provided for computation of gain matrices of the state control law, realized in the parallel distributed compensation structure. The approach is illustrated on an example, demonstrating the validity of the proposed method.

Spectral Perspective on the Stability of Discrete-Time Markov Jump Systems with Multiplicative Noise

We apply the spectrum analysis approach to address the stability of discrete-time Markov jump systems with state-multiplicative noise. In terms of the spectral distribution of a generalized Lyapunov operator, spectral criteria are presented to testify three different kinds of stochastic stabilities: asymptotic mean square stability, critical stability, and essential instability.

Quaternion Estimation from Vector Observations using a Matrix Kalman Filter

A novel two-stage quaternion estimator from vector observations that is a synthesis between Wahba's approach and the Kalman filtering approach is presented. The first stage features an optimal denoising procedure of the elements of a time-varying noisy K-matrix. The second stage produces a quaternion estimate from the filtered K-matrix via any eigenvalue-eigenvector solver. This work's contribution consists in performing the denoising via Kalman filtering. For that purpose, a matrix Kalman filter (MKF) is developed, which has the advantage of preserving the natural formulation of the matrix plant equations. As a result, two aspects of a previous algorithm, called Optimal-REQUEST (OPREQ), are improved: the K-matrix update estimation stage uses a matrix gain rather than a scalar gain, and that gain is optimized with respect to the classical minimum-variance cost. This work assumes that the sensed lines of sight (LOS) are time invariant as seen in the chosen reference frame. This assumption fits in various operational mission architectures. An exact Kalman filter is developed that accounts for the state-multiplicative noise in the process equation. A reduced estimator is also developed assuming simple expressions for the filter covariance matrices. A constrained estimator, which enforces the symmetry and null-trace of the estimated matrix, is designed using the pseudomeasurement (PM) technique. Extensive Monte-Carlo simulations illustrate the performance of the novel filters with a spinning and nutating spacecraft (SC) as a case study. Extensive Monte-Carlo simulations show that the proposed estimator outperforms OPREQ. As illustrated by additional Monte-Carlo simulations, the constrained MKF exhibits a better transient and a better steady-state accuracy than the unconstrained filter for large initial disturbances in the symmetry and null-trace properties.

Infinite horizon [formula omitted] control for discrete-time time-varying Markov jump systems with multiplicative noise

In this paper we consider the infinite horizon H2/H∞ control problem for discrete-time time-varying linear systems subject to Markov jump parameters and state-multiplicative noise. A stochastic version of a bounded real lemma is firstly developed for a general class of discrete-time time-varying Markov jump systems with state- and disturbance-multiplicative noise. By which we present a necessary and sufficient condition for the solvability of the H2/H∞ control problem in terms of four coupled discrete-time Riccati equations. Moreover, the obtained design is applied to a macroeconomic problem to verify its effectiveness.