Miloš S. Stanković

Consensus based overlapping decentralized estimation with missing observations and communication faults

In this paper a new algorithm for discrete-time overlapping decentralized state estimation of large scale systems is proposed in the form of a multi-agent network based on a combination of local estimators of Kalman filtering type and a dynamic consensus strategy, assuming intermittent observations and communication faults. Under general conditions concerning the agent resources and the network topology, conditions are derived for the convergence to zero of the estimation error mean and for the mean-square estimation error boundedness. A centralized strategy based on minimization of the steady-state mean-square estimation error is proposed for selection of the consensus gains; these gains can also be adjusted by local adaptation schemes. It is also demonstrated that there exists a connection between the network complexity and efficiency of denoising, i.e., of suppression of the measurement noise influence. Several numerical examples serve to illustrate characteristic properties of the proposed algorithm and to demonstrate its applicability to real problems.

Decentralized Parameter Estimation by Consensus Based Stochastic Approximation

In this paper, an algorithm for decentralized multi-agent estimation of parameters in linear discrete-time regression models is proposed in the form of a combination of local stochastic approximation algorithms and a global consensus strategy. An analysis of the asymptotic properties of the proposed algorithm is presented, taking into account both the multi-agent network structure and the probabilities of getting local measurements and implementing exchange of inter-agent messages. In the case of non-vanishing gains in the stochastic approximation algorithms, an asymptotic estimation error covariance matrix bound is defined as the solution of a Lyapunov-like matrix equation. In the case of asymptotically vanishing gains, the mean-square convergence is proved and the rate of convergence estimated. In the discussion, the problem of additive communication noise is treated in a methodologically consistent way. It is also demonstrated how the consensus scheme in the algorithm can contribute to the overall reduction of measurement noise influence. Some simulation results illustrate the obtained theoretical results.

Consensus Based Overlapping Decentralized Estimator

In this technical note a new algorithm for state estimation is proposed in the form of a multi-agent network based on a synergy between local Kalman filters and a dynamic consensus strategy between the agents. It is shown that it is possible, under general conditions concerning local resources and the network topology, to achieve asymptotic stability of the whole estimation algorithm by a proper choice of the consensus gains. It is demonstrated that the consensus gains can be obtained by minimizing the total mean-square estimation error. Capabilities of the network to achieve reduction of the measurement noise influence are also discussed.

Extremum seeking under stochastic noise and applications to mobile sensors

In this paper the extremum seeking algorithm with sinusoidal perturbations has been extended and modified in two ways: (a) the output of the system is corrupted with measurement noise; (b) the amplitudes of the perturbation signals, as well as the gain of the integrator block, are time varying and tend to zero at a pre-specified rate. Convergence to the extremal point, with probability one, has been proved. Also, as a consequence of being able to cope with a stochastic environment, it has been shown how the proposed algorithm can be applied to mobile sensors as a tool for achieving the optimal observation positions. The proposed algorithm has been illustrated through several simulations.

Decentralized parameter estimation by consensus based stochastic approximation

In this paper, an algorithm for decentralized multi-agent estimation of parameters in linear discrete-time regression models is proposed in the form of a combination of local stochastic approximation algorithms and a global consensus strategy. An analysis of the asymptotic properties of the proposed algorithm is presented, taking into account both the multi-agent network structure and the probabilities of getting local measurements and implementing exchange of inter-agent messages. In the case of non-vanishing gains in the stochastic approximation algorithms, an asymptotic estimation error covariance matrix bound is defined as the solution of a Lyapunov-like matrix equation. In the case of asymptotically vanishing gains, the mean-square convergence is proved and the rate of convergence estimated. In the discussion, the problem of additive communication noise is treated in a methodologically consistent way. It is also demonstrated how the consensus scheme in the algorithm can contribute to the overall reduction of measurement noise influence. Some simulation results illustrate the obtained theoretical results.

Lie bracket approximation of extremum seeking systems

Extremum seeking feedback is a powerful method to steer a dynamical system to an extremum of a partially or completely unknown map. It often requires advanced system-theoretic tools to understand the qualitative behavior of extremum seeking systems. In this paper, a novel interpretation of extremum seeking is introduced. We show that the trajectories of an extremum seeking system can be approximated by the trajectories of a system which involves certain Lie brackets of the vector fields of the extremum seeking system. It turns out that the Lie bracket system directly reveals the optimizing behavior of the extremum seeking system. Furthermore, we establish a theoretical foundation and prove that uniform asymptotic stability of the Lie bracket system implies practical uniform asymptotic stability of the corresponding extremum seeking system. We use the established results in order to prove local and semi-global practical uniform asymptotic stability of the extrema of a certain map for multi-agent extremum seeking systems.

Discrete time extremum seeking by autonomous vehicles in a stochastic environment

In this paper, discrete time extremum seeking algorithms with sinusoidal perturbations have been developed for three different problems involving autonomous vehicle planar control: a) control of velocity actuated vehicles; b) control of force actuated vehicles; c) control of nonholonomic vehicles (unicycles). The algorithms assume time varying gains and are able to cope with stochastic perturbations. Convergence to the extremal point, with probability one, has been demonstrated for all three cases. It is also shown how the proposed algorithms can be applied to mobile sensors as a tool for achieving optimal observation positions. The proposed algorithms have been illustrated with several simulations.

Stochastic extremum seeking with applications to mobile sensor networks

In this paper the extremum seeking algorithm with sinusoidal perturbation has been modified and extended in two ways: a) the amplitudes of the perturbation signals, as well as the gain of the integrator block, are time varying and tend to zero at a pre-specified rate; b) the output of the system is corrupted with measurement noise. Local convergence to the extremal point, with probability one and in the mean square sense, has been proved. Also, it has been shown how the proposed algorithm can be applied to mobile sensor networks as a tool for achieving the optimal observation positions. The proposed algorithms have been illustrated through several simulations.

Consensus based overlapping decentralized fault detection and isolation

In this paper a new distributed fault detection and isolation (FDI) methodology is proposed in the form of a multi-agent network representing a combination of a consensus based FDI observer for residual generation and a consensus based decision making strategy for change detection, applicable in real time. The proposed observer is based on overlapping system decomposition and a combination between the local optimal stochastic FDI observers and a dynamic consensus strategy. It is shown how the proposed algorithm can generate residuals which provide, under general conditions concerning local models and the network topology, high efficiency, scalability and robustness. The proposed decision making strategy provides solutions for two particular cases: a) local detection for non-overlapping parts of the identified subsystems; b) a consensus based strategy for FDI in the overlapping parts. One selected example illustrates the applicability of the proposed methodology in practice.

A Lie Bracket Approximation for Extremum Seeking Vehicles

Abstract In this paper we propose a novel methodology for the analysis of autonomous vehicles seeking the extremum of an arbitrary smooth nonlinear map in the plane. By interpreting the extremum seeking schemes as input-affine systems with periodic excitations and by using the methodology of Lie brackets, we calculate a simplified system which approximates the qualitative behavior of the original one better than existing methods. By examining this approximate Lie bracket system, we are able to directly derive properties of the original one. Thus, by showing that the Lie bracket direction is directly related to the unknown gradient of the objective function we prove global uniform practical asymptotic stability of the extremum point for vehicles modeled as single integrators and non-holonomic unicycles. We illustrate the proposed method through simulations.