Daniela Selvi

Adaptive disturbance attenuation via logic-based switching

Abstract The problem of attenuating unknown and possibly time-varying disturbances acting on a linear time-invariant dynamical system is addressed by means of an adaptive switching control approach. Given a family of pre-designed stabilizing controllers, a supervisory unit infers in real-time the potential behavior of each candidate controller and selects the one providing the best potential performance. To this aim, a set of test functionals is defined, which is shown to enjoy favorable inference properties under certain assumptions on the nature of the disturbances. Both persistent-memory and finite-memory test functionals are analyzed. Further, an implementation of the switching controller is proposed which always guarantees stability of the feedback loop, even if the disturbance characteristics are such that the switching is persistent. Simulation results are provided to show the effectiveness of the proposed method.

Unfalsified approach to data-driven control design

The paper deals with the problem of designing controllers from experimental data. We propose a non-iterative direct approach in which the parameters of a controller of a prescribed order and structure are optimized with respect to a relevant performance criterion. The proposed approach builds upon the so-called unfalsified control theory. This is the key point which makes it possible to derive simple and intuitive relations between the choice of the performance criterion to optimize and closed-loop stability conditions, thus making it possible to derive a data-driven controller tuning procedure incorporating simple stability tests. An example is presented to substantiate the analysis.

Distributed Averaging of Exponential-Class Densities With Discrete-Time Event-Triggered Consensus

The paper addresses discrete-time event-driven consensus on exponential-class probability densities (including Gaussian, binomial, Poisson, Rayleigh, Wishart, Inverse Wishart, and many other distributions of interest) completely specified by a finite-dimensional vector of so-called natural parameters. First, it is proved how such exponential classes are closed under Kullback-Leibler fusion (average), and how the latter is equivalent to a weighted arithmetic average over the natural parameters. Then, a novel event-driven transmission strategy is proposed in order to trade off the data-communication rate and, hence, energy consumption, versus consensus speed and accuracy. A theoretical analysis of the convergence properties of the proposed algorithm is provided by exploiting the Fisher metric as a local approximation of the Kullback-Leibler divergence. Some numerical examples are presented in order to demonstrate the effectiveness of the proposed event-driven consensus. It is expected that the latter can be successfully exploited for energy- and/or bandwidth-efficient networked state estimation.

Event-triggered consensus on exponential families

The paper deals with discrete-time event-triggered consensus on exponential families of probability distributions (including Gaussian, binomial, Poisson and many other distributions of interest) completely characterized by a finite-dimensional vector of so called natural parameters. It is first shown how such exponential families are closed under Kullback-Leibler fusion (average), and that the latter is equivalent to a weighted arithmetic average over the natural parameters. Then, a novel event-triggered transmission strategy is proposed so as to tradeoff data communication rate versus consensus speed and accuracy. Some numerical examples are worked out to demonstrate the effectiveness of the proposed method. It is expected that eventtriggered consensus can be successfully exploited for bandwidthefficient networked state estimation.

A hierarchical approach to adaptive disturbance attenuation combining switching and tuning

In this paper, an algorithm combining switching and tuning is proposed as a solution to the problem of adaptive disturbance attenuation. A high-level switching logic selects the controller providing the best potential performance within a pre-designed family; then a tuning procedure aims at finding a local refinement of the selected controller in order to improve its attenuation capabilities, and a low-level switching logic is used to decide whether to substitute the controller with its refinement or not. The control architecture is designed by adopting a particular implementation which ensures stability under any arbitrary switching sequence. It is shown that an arbitrary attenuation level can be achieved by adopting appropriately defined functionals. Simulation results are provided to show the validity of the proposed algorithm.

A distributed Kalman filter with event-triggered communication and guaranteed stability

The paper addresses Kalman filtering over a peer-to-peer sensor network with a careful eye towards data transmission scheduling for reduced communication bandwidth and, consequently, enhanced energy efficiency and prolonged network lifetime. A novel consensus Kalman filter algorithm with event-triggered communication is developed by enforcing each node to transmit its local information to the neighbors only when this is considered as particularly significant for estimation purposes, in the sense that it notably deviates from the information that can be predicted from the last transmitted one. Further, it is proved how the filter guarantees stability (mean-square boundedness of the estimation error in each node) under network connectivity and system collective observability. Finally, numerical simulations are provided to demonstrate practical effectiveness of the distributed filter for trading off estimation performance versus transmission rate.

Robust Switching Control: Stability Analysis and Application to Active Disturbance Attenuation

This note deals with the problem of controlling an uncertain discrete-time linear system by means of a hybrid controller in the form of a linear system whose parameters switch among a finite number of possible configurations, called modes. We suppose that each single controller is designed in order to individually ensure robust stability for a dual-Youla uncertainty model. Then, we show that robust stability of the switching controller can be directly related to robust stability of each single controller mode, in that it is possible to implement the switching controller so that robust stability is guaranteed for any possible switching sequence. This allows one to freely select the switching signal so as to enhance performance, for instance by selecting in real time the control mode displaying the best potential performance with respect to the current operating conditions. An application of the ideas to the problem of active disturbance attenuation is presented and simulation results are shown to validate the proposed solution.

Energy-efficient distributed state estimation via event-triggered consensus on exponential families

The paper addresses distributed state estimation over a peer-to-peer sensor network with an eye to communication/energy efficiency. In particular, consensus on exponential families of probability distributions is first introduced and shown to be equivalent to iteratively performing convex linear combinations on the natural parameters of such distributions. Then, an event-triggered consensus strategy is presented and exploited to derive a novel energy-efficient consensus Kalman filter algorithm for distributed state estimation. Simulation results are provided to demonstrate the effectiveness of the proposed algorithm.

Design of a switching controller for adaptive disturbance attenuation with guaranteed stability

In this paper, a new algorithm is proposed for the design of a family of controllers to be used within an adaptive switching control scheme. The resulting switching controller is able to attenuate the effects of disturbances having uncertain and possibly time-varying characteristics, as well as to ensure stability under arbitrary switching sequences. Specifically, the stability requirement is addressed within the synthesis of the set of controllers by imposing some constraints in LMI form. The overall synthesis algorithm is formulated in terms of convex optimization problems, which can be solved by means of standard tools. The validity of the proposed solution is underlined by showing simulation results on an adaptive optics case study.

Switching-based adaptive disturbance attenuation with guaranteed robust stability

The paper deals with the problem of adaptive attenuation of disturbances with uncertain and possibly time-varying characteristics when the plant model is also affected by a non-negligible uncertainty. The proposed solution is based on the Adaptive Switching Control paradigm and relies on a family of pre-synthesized controllers, such that, for any possible operating condition, at least one controller is able to ensure desired attenuation capabilities. Then, a supervisory unit selects the controller providing the best potential performance on the basis of appropriately defined test functionals. We show that, when each of the candidate controllers robustly stabilizes the uncertain plant, it is possible to implement the switching controller so that robust stability is guaranteed for any possible switching sequence. Further, we study the properties of the proposed test functionals by analyzing the effects of the plant/model mismatch on their inference capabilities. Simulation results are shown to validate the proposed control solution.