Alessandro D'Innocenzo

Approximate Abstractions of Stochastic Hybrid Systems

We present a constructive procedure for obtaining a finite approximate abstraction of a discrete-time stochastic hybrid system. The procedure consists of a partition of the state space of the system and depends on a controllable parameter. Given proper continuity assumptions on the model, the approximation errors introduced by the abstraction procedure are explicitly computed and it is shown that they can be tuned through the parameter of the partition. The abstraction is interpreted as a Markov set-Chain. We show that the enforcement of certain ergodic properties on the stochastic hybrid model implies the existence of a finite abstraction with finite error in time over the concrete model, and allows introducing a finite-time algorithm that computes the abstraction.

Modeling and Analysis of Multi-hop Control Networks

We propose a mathematical framework, inspired by the Wireless HART specification, for modeling and analyzing multi-hop communication networks. The framework is designed for systems consisting of multiple control loops closed over a multi-hop communication network. We separate control, topology, routing, and scheduling and propose formal syntax and semantics for the dynamics of the composed system. The main technical contribution of the paper is an explicit translation of multi-hop control networks to switched systems. We describe a Mathematica notebook that automates the translation of multihop control networks to switched systems, and use this tool to show how techniques for analysis of switched systems can be used to address control and networking co-design challenges.

Fault Tolerant Control of Multi-Hop Control Networks

A multi-hop control network (MCN) consists of a plant where the communication between sensors, actuators, and computational units is supported by a (wireless) multi-hop communication network, and data flow is performed using scheduling and routing of sensing and actuation data. We address the control design problem on a MCN where the plant is a SISO LTI system and links are subject to permanent failures. We first characterize controllability and observability of a MCN: we provide necessary and sufficient conditions on the plant dynamics and on the communication scheduling, and we provide a design methodology to satisfy such conditions for any failure configuration. Then we address the problem of detecting the failure of links of the radio connectivity graph: we provide necessary and sufficient conditions on the plant dynamics and on the communication protocol, and we provide a design methodology to satisfy the above conditions.

Scalable scheduling algorithms for wireless networked control systems

In this paper, we address the problem of designing scalable scheduling and routing policies over a time-triggered multi-hop control network, when closing a considerable number of control loops on the same network. The key idea is to formally define by means of regular languages the set of schedules for each control loop that satisfy a given control specification, and to exploit operators on regular languages to compute the set of schedules for the whole system. In order to test our methodology, we address a mineral floatation control problem derived from the Boliden (a swedish mining company) mine in Garpenberg, and propose a scheduling solution that can be implemented on systems compliant with communication protocols for wireless networks (e.g. the WirelessHART specification).

Approximate equivalence and synchronization of metric transition systems

a b s t r a c t In this paper, we consider metric transition systems which are transition systems equipped with metrics for observation and synchronization labels. The existence of metrics leads to the introduction of two new concepts, (i) (, ) -approximate (bi)simulation of transition systems and (ii) approximate synchronization of transition systems. We show that the notion of (, ) -approximate (bi)simulation can be thought of as a generalization or relaxation of the earlier work on -approximate (bi)simulation by Girard and Pappas. We demonstrate the link between reachability verification and approximate (bi)simulation, and we also provide a characterization of (bi)simulation relations using a tool similar to the (bi)simulation function. Approximate synchronization can be thought of as a generalization of synchronization of transition systems in the usual sense. In fact, the usual synchronization and interleaving synchronization are two special cases of the notion of approximate synchronization developed in this paper. Furthermore, we present a result on the compositional properties of the approximate (bi)simulation with respect to the approximate synchronization. In addition to the theoretical presentation of approximate bisimulation and synchronization, we also discuss the application of this framework in analyzing control systems over digital communication networks.

Error Detection within a Specific Time Horizon and Application to Air Traffic Management

We propose a novel concept of observability for hybrid systems, critical observability, for estimating and mitigating the probability of errors in Air Traffic Management. Critical observability refers to states that are characterized by the existence of an evolution that may yield catastrophic situations. Detecting these states is an important element of a safety critical environment and we design a critical observer that we apply to the runway crossing problem. We also present an extension of this theory to a class of stochastic hybrid systems and apply it to a clearance changing the flight plan.

Feedback stabilization of dynamical systems with switched delays

We analyze a classification of two main families of controllers that are of interest when the feedback loop is subject to switching propagation delays due to routing via a wireless multi-hop communication network. We show that we can cast this problem as a subclass of classical switching systems, which is a non-trivial generalization of classical LTI systems with time-varying delays. We consider both cases where delay-dependent and delay-independent controllers are used, and show that both can be modeled as switching systems with unconstrained switchings. We provide NP-hardness results for the stability verification problem, and propose a general methodology for approximate stability analysis with arbitrary precision. We finally give evidence that non-trivial design problems arise for which new algorithmic methods are needed.

Digital self triggered robust control of nonlinear systems

In this paper we develop novel results on self triggering control of nonlinear systems, subject to perturbations and actuation delays. First, considering an unperturbed nonlinear system with bounded actuation delays, we provide conditions that guarantee the existence of a self triggering control strategy stabilizing the closed-loop system. Then, considering parameter uncertainties, disturbances, and bounded actuation delays, we provide conditions guaranteeing the existence of a self triggering strategy, that keeps the state arbitrarily close to the equilibrium point. In both cases, we provide a methodology for the computation of the next execution time. We show on an example the relevant benefits obtained with this approach, in terms of energy consumption, with respect to control algorithms based on a constant sampling, with a sensible reduction of the average sampling time.

Fault Tolerant Stabilizability of Multi-Hop Control Networks

Abstract A MIMO Multi-hop Control Network (MCN) consists of a MIMO LTI plant where the communication between sensors, actuators and computational units is supported by a (wireless) multi-hop communication network and data flow is performed using scheduling and routing of sensing and actuation data. We explicitly characterize by means of necessary and sufficient conditions the set of network configurations that invalidate controllability and observability of the plant. We show that checking such necessary and sufficient conditions can be solved with a complexity that is combinatorial with respect to the number of input and output signals. To overcome this difficulty, we propose an efficient algorithm to design the network configuration in linear time still guaranteeing controllability and observability.

Verification of Hybrid Automata Diagnosability by Abstraction

A notion of diagnosability for hybrid systems is defined, which generalizes the common notion of observability. We propose an abstraction procedure to translate a hybrid automaton into a timed automaton, in order to verify observability and diagnosability properties. We introduce a procedure to check diagnosability, and show that for the system class of our abstraction (namely for a subclass of timed automata: the durational graphs) the verification problem belongs to the complexity class P. We apply our procedure to an electromagnetic valve system for camless engines.