Variance-constrained H∞ filtering for a class of nonlinear time-varying systems with multiple missing measurements: The finite-horizon case

Copyright [2010] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This paper is concerned with the robust H ∞ finite-horizon filtering problem for a class of uncertain nonlinear discrete time-varying stochastic systems with multiple missing measurements and error variance constraints. All the system parameters are time-varying and the uncertainty enters into the state matrix. The measurement missing phenomenon occurs in a random way, and the missing probability for each sensor is governed by an individual random variable satisfying a certain probabilistic distribution in the interval . The stochastic nonlinearities under consideration here are described by statistical means which can cover several classes of well-studied nonlinearities. Sufficient conditions are derived for a finite-horizon filter to satisfy both the estimation error variance constraints and the prescribed H ∞ performance requirement. These conditions are expressed in terms of the feasibility of a series of recursive linear matrix inequalities (RLMIs). Simulation results demonstrate the effectiveness of the developed filter design scheme.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. by Grant GR/S27658/01, the Royal Society of the U.K., National Natural Science Foundation of China by Grants 60825303 and 60834003, National 973 Project of China by Grant 2009CB320600, Fok Ying Tung Education Foundation by Grant 111064, the Youth Science Fund of Heilongjiang Province of China by Grant QC2009C63, and by the Alexander von Humboldt Foundation of Germany

Variance-constrained multiobjective control and filtering for nonlinear stochastic systems: A survey

The multiobjective control and filtering problems for nonlinear stochastic systems with variance constraints are surveyed. First, the concepts of nonlinear stochastic systems are recalled along with the introduction of some recent advances. Then, the covariance control theory, which serves as a practical method for multi-objective control design as well as a foundation for linear system theory, is reviewed comprehensively. The multiple design requirements frequently applied in engineering practice for the use of evaluating system performances are introduced, including robustness, reliability, and dissipativity. Several design techniques suitable for the multi-objective variance-constrained control and filtering problems for nonlinear stochastic systems are discussed. In particular, as a special case for the multi-objective design problems, the mixed H 2 / H ∞ control and filtering problems are reviewed in great detail. Subsequently, some latest results on the variance-constrained multi-objective control and filtering problems for the nonlinear stochastic systems are summarized. Finally, conclusions are drawn, and several possible future research directions are pointed out

Robust filtering for a class of stochastic uncertain nonlinear time-delay systems via exponential state estimation

Copyright [2001] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.We investigate the robust filter design problem for a class of nonlinear time-delay stochastic systems. The system under study involves stochastics, unknown state time-delay, parameter uncertainties, and unknown nonlinear disturbances, which are all often encountered in practice and the sources of instability. The aim of this problem is to design a linear, delayless, uncertainty-independent state estimator such that for all admissible uncertainties as well as nonlinear disturbances, the dynamics of the estimation error is stochastically exponentially stable in the mean square, independent of the time delay. Sufficient conditions are proposed to guarantee the existence of desired robust exponential filters, which are derived in terms of the solutions to algebraic Riccati inequalities. The developed theory is illustrated by numerical simulatio

Discrete-time neural network based state observer with neural network based control formulation for a class of systems with unmatched uncertainties

An observer is a dynamic system that estimates the state variables of another system using noisy measurements, either to estimate unmeasurable states, or to improve the accuracy of the state measurements. The Modified State Observer (MSO) is a technique that uses a standard observer structure modified to include a neural network to estimate system states as well as system uncertainty. It has been used in orbit uncertainty estimation and atmospheric reentry uncertainty estimation problems to correctly estimate unmodeled system dynamics. A form of the MSO has been used to control a nonlinear electrohydraulic system with parameter uncertainty using a simplified linear model. In this paper an extension of the MSO into discrete-time is developed using Lyapunov stability theory. Discrete-time systems are found in all digital hardware implementations, such as that found in a Martian rover, a quadcopter UAV, or digital flight control systems, and have the added benefit of reduced computation time compared to continuous systems. The derived adaptive update law guarantees stability of the error dynamics and boundedness of the neural network weights. To prove the validity of the discrete-time MSO (DMSO) simulation studies are performed using a two wheeled inverted pendulum (TWIP) robot, an unstable nonlinear system with unmatched uncertainties. Using a linear model with parameter uncertainties, the DMSO is shown to correctly estimate the state of the system as well as the system uncertainty, providing state estimates orders of magnitude more accurate, and in periods of time up to 10 times faster than the Discrete Kalman Filter. The DMSO is implemented on an actual TWIP robot to further validate the performance and demonstrate the applicability to discrete-time systems found in many aerospace applications. Additionally, a new form of neural network control is developed to compensate for the unmatched uncertainties that exist in the TWIP system using a state variable as a virtual control input. It is shown that in all cases the neural network based control assists with the controller effectiveness, resulting in the most effective controller, performing on average 53.1% better than LQR control alone --Abstract, page iii

Latent state estimation in a class of nonlinear systems

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The problem of estimating latent or unobserved states of a dynamical system from observed data is studied in this thesis. Approximate filtering methods for discrete time series for a class of nonlinear systems are considered, which, in turn, require sampling from a partially specified discrete distribution. A new algorithm is proposed to sample from partially specified discrete distribution, where the specification is in terms of the first few moments of the distribution. This algorithm generates deterministic sigma points and corresponding probability weights, which match exactly a specified mean vector, a specified covariance matrix, the average of specified marginal skewness and the average of specified marginal kurtosis. Both the deterministic particles and the probability weights are given in closed form and no numerical optimization is required. This algorithm is then used in approximate Bayesian filtering for generation of particles and the associated probability weights which propagate higher order moment information about latent states. This method is extended to generate random sigma points (or particles) and corresponding probability weights that match the same moments. The algorithm is also shown to be useful in scenario generation for financial optimization. For a variety of important distributions, the proposed moment-matching algorithm for generating particles is shown to lead to approximation which is very close to maximum entropy approximation. In a separate, but related contribution to the field of nonlinear state estimation, a closed-form linear minimum variance filter is derived for the systems with stochastic parameter uncertainties. The expressions for eigenvalues of the perturbed filter are derived for comparison with eigenvalues of the unperturbed Kalman filter. Moment-matching approximation is proposed for the nonlinear systems with multiplicative stochastic noise

Trajectory Synthesis for Fisher Information Maximization

Estimation of model parameters in a dynamic system can be significantly improved with the choice of experimental trajectory. For general, nonlinear dynamic systems, finding globally "best" trajectories is typically not feasible; however, given an initial estimate of the model parameters and an initial trajectory, we present a continuous-time optimization method that produces a locally optimal trajectory for parameter estimation in the presence of measurement noise. The optimization algorithm is formulated to find system trajectories that improve a norm on the Fisher information matrix. A double-pendulum cart apparatus is used to numerically and experimentally validate this technique. In simulation, the optimized trajectory increases the minimum eigenvalue of the Fisher information matrix by three orders of magnitude compared to the initial trajectory. Experimental results show that this optimized trajectory translates to an order of magnitude improvement in the parameter estimate error in practice.Comment: 12 page