Giorgio Battistelli

Moving-horizon state estimation for nonlinear discrete-time systems: New stability results and approximation schemes

A moving-horizon state estimation problem is addressed for a class of nonlinear discrete-time systems with bounded noises acting on the system and measurement equations. As the statistics of such disturbances and of the initial state are assumed to be unknown, we use a generalized least-squares approach that consists in minimizing a quadratic estimation cost function defined on a recent batch of inputs and outputs according to a sliding-window strategy. For the resulting estimator, the existence of bounding sequences on the estimation error is proved. In the absence of noises, exponential convergence to zero is obtained. Moreover, suboptimal solutions are sought for which a certain error is admitted with respect to the optimal cost value. The approximate solution can be determined either on-line by directly minimizing the cost function or off-line by using a nonlinear parameterized function. Simulation results are presented to show the effectiveness of the proposed approach in comparison with the extended Kalman filter.

Unfalsified Virtual Reference Adaptive Switching Control of Plants with Persistent Disturbances

Abstract This paper addresses virtual reference adaptive switching control whereby a data-driven supervisor aims at stabilizing an unknown time-invariant dynamic system by switching at any time in feedback with system one element from a finite family of candidate controllers. Under the only assumption of problem feasibility, viz. the controller family contains a stabilizing controller, the resulting switched system is shown to be stable against arbitrary exogenous persistent bounded disturbances.

Receding-horizon estimation for discrete-time linear systems

The problem of estimating the state of a discrete-time linear system can be addressed by minimizing an estimation cost function dependent on a batch of recent measure and input vectors. This problem has been solved by introducing a receding-horizon objective function that includes also a weighted penalty term related to the prediction of the state. For such an estimator, convergence results and unbiasedness properties have been proved. The issues concerning the design of this filter are discussed in terms of the choice of the free parameters in the cost function. The performance of the proposed receding-horizon filter is evaluated and compared with other techniques by means of a numerical example.

Kullback-Leibler average, consensus on probability densities, and distributed state estimation with guaranteed stability

This paper addresses distributed state estimation over a sensor network wherein each node-equipped with processing, communication and sensing capabilities-repeatedly fuses local information with information from the neighbors. Estimation is cast in a Bayesian framework and an information-theoretic approach to data fusion is adopted by formulating a consensus problem on the Kullback-Leibler average of the local probability density functions (PDFs) to be fused. Exploiting such a consensus on local posterior PDFs, a novel distributed state estimator is derived. It is shown that, for a linear system, the proposed estimator guarantees stability, i.e. mean-square boundedness of the state estimation error in all network nodes, under the minimal requirements of network connectivity and system observability, and for any number of consensus steps. Finally, simulation experiments demonstrate the validity of the proposed approach.

Model-Free Adaptive Switching Control of Uncertain Time-Varying Plants

Abstract This paper addresses the problem of controlling an uncertain time-varying plant by means of a finite family of linear candidate controllers supervised by an appropriate switching logic. It is shown that global stability of the closed-loop system can be guaranteed provided that (i) at every time there is at least one candidate controller that would stabilize the current time-invariant “frozen” plant model, and (ii) the changes in the plant model are infrequent.

Consensus CPHD Filter for Distributed Multitarget Tracking

The paper addresses distributed multitarget tracking over a network of heterogeneous and geographically dispersed nodes with sensing, communication and processing capabilities. The contribution has been to develop a novel consensus Gaussian Mixture-Cardinalized Probability Hypothesis Density (GM-CPHD) filter that provides a fully distributed, scalable and computationally efficient solution to the problem. The effectiveness of the proposed approach is demonstrated via simulation experiments on realistic scenarios.

On estimation error bounds for receding-horizon filters using quadratic boundedness

Quadratic boundedness is used to deal with stability and design of receding-horizon estimators. Upper bounds on the norm of the estimation error have been found by means of invariant sets that can be constructed by using quadratic boundedness. Moreover, these bounds are expressed in terms of linear matrix inequalities and are well-suited to being minimized for the purpose of design.

Technical communique: Design of state estimators for uncertain linear systems using quadratic boundedness

The notion of quadratic boundedness, which allows one to address the stability of a dynamic system in the presence of bounded disturbances, is applied to the design of state estimators for discrete-time linear systems with polytopic uncertainties. Necessary and sufficient stability conditions are stated and upper bounding sequences on the estimation error are derived. For the purpose of design, such conditions can be expressed in terms of linear matrix inequalities (LMIs), thus guaranteeing the numerical tractability. Simulation results are reported to show the effectiveness of the approach.

Consensus-Based Linear and Nonlinear Filtering

This note addresses Distributed State Estimation (DSE) over sensor networks. Two existing consensus approaches for DSE, i.e., consensus on information (CI) and consensus on measurements (CM), are combined to provide a novel class of hybrid consensus filters (named Hybrid CMCI) which enjoy the complementary benefits of CM and CI. Novel theoretical results, limitedly to linear systems, on the guaranteed stability of the Hybrid CMCI filters under collective observability and network connectivity are proved. Finally, the effectiveness of the proposed class of consensus filters is evaluated on a target tracking case study with both linear and nonlinear sensors.

Brief paper: Data-driven communication for state estimation with sensor networks

This paper deals with the problem of estimating the state of a discrete-time linear stochastic dynamical system on the basis of data collected from multiple sensors subject to a limitation on the communication rate from the sensors. More specifically, the attention is devoted to a centralized sensor network consisting of: (1) multiple remote nodes which collect measurements of the given system, compute state estimates at the full measurement rate and transmit data (either raw measurements or estimates) at a reduced communication rate; (2) a fusion node that, based on received data, provides an estimate of the system state at the full rate. Local data-driven transmission strategies are considered and issues related to the stability and performance of such strategies are investigated. Simulation results confirm the effectiveness of the proposed strategies.