Elena De Santis

Brief paper: A structural approach to detectability for a class of hybrid systems

We address detectability of linear switching systems. We show that detectability of a linear switching system reduces to asymptotic stability of a suitable switching system with guards extracted from it. A condition for checking asymptotic stability of linear switching systems with guards is also derived.

On location observability notions for switching systems

Abstract The focus of this paper is on the analysis of initial discrete state distinguishability notions for switching systems, in a discrete time setting. Moreover, the relationship between initial discrete state distinguishability and the problem of reconstructing the current discrete state is addressed.

Techniques of linear programming based on the theory of convex cones

The convex cones approach to linear programming is illustrated. Two methods are introduced. The first, called primal, is based on a tangency condition for nonnegative orthant and an affine set. The second, called dual, uses the extreme rays of a pointed polyhedral cone, given by the intersection of the nonnegative orthant with a subspace, to compute the maximum and than proceeds in the same way as the primal to derive the solution. A complete theory for the extreme rays of any cone of this form is given. Another highlight of the paper is the theory of the strictly tangent relaxation, which is independent of the particular method used, and allows the reduction of the problem to a minimal form, A numerical example is included to give a practical feeling of the dual method. Finally features of the methods, like the possibility of highly parallel implementations, open problems and perspectives are discussed.

Critical Observability of a Class of Hybrid Systems and Application to Air Traffic Management

We present a novel observability notion for switching systems that model safety–critical systems, where a set of states – called critical states – must be detected within a prescribed delay since they correspond to hazards that may yield catastrophic events. Some sufficient and some necessary conditions for critical observability are derived. An observer is proposed for reconstructing the hybrid state evolution of the switching system whenever a critical state is reached. We apply our results to the runway crossing control problem, i.e., the control of aircraft that cross landing or take–off runways. In the hybrid model of the system, five agents are present; four are humans, each modeled as hybrid systems, subject to situation awareness errors.

Communication Control and Driving Assistance to a Platoon of Vehicles in Heavy Traffic and Scarce Visibility

A decentralized communication and control system is presented for driving assistance and automation along designated highway segments. This paper is based on a hybrid dynamical model describing vehicular motion, and the structure of a safe controller is presented. A ranging and communication system provides information for a vehicle and its nearest neighbors. The system is capable of handling sudden changes of regime, overtakes, reentries, as well as a number of maneuvers dictated by safety requirements under partially unpredicted events. A user-friendly interface, based on a palmtop computer, is developed to assist drivers visually and acoustically

On invariant sets for constrained discrete time linear systems with disturbances and parametric uncertainties

We consider discrete time linear systems with disturbances and parametric uncertainties in the matrix A with constraints on both control and state variables. We give the explicit expression of maximal sets of disturbances and/or parameters such that it is possible to control the state trajectory of the system to the given constraining set. The case of static linear state feedback control is analyzed.

Invariant Sets and Control Synthesis for Switching Systems with Safety Specifications

A structural procedure is proposed for solving the problem of maximal safe-set determination based on maximal controlled invariant sets. However, the procedure is not guaranteed to converge in a finite number of steps. The procedure is made computationally appealing first by linearizing and discretizing the dynamical systems and, second, by using an inner approximation of these sets that, together with the classical outer approximation, yields tight bounds for an error due to the truncation of the procedure after a finite number of steps. The theory is applied to idle-speed regulation in engine control.

DIGITAL IDLE SPEED CONTROL OF AUTOMOTIVE ENGINES USING HYBRID MODELS

Abstract Idle speed control for an automotive engine is formulated as the problem of computing a maximal safe set for a hybrid system modeling an SI engine in idle mode. Since this problem is computationally intractable, we exploit the relations between safe sets for a continuous-time switching system S and an appropriate discrete-time switching system associated with S to reduce drastically its complexity. An algorithm in the discrete-time domain is proposed for the determination of the maximal safe set. The methodology is general enough to be easily extended to different hybrid control problems. In particular, we solved the problem of the computation of the maximal safe set in the case of un-synchronized switching and sampling times for idle control, an open problem for quite some time. Simulation results show the efficiency of the proposed approach.

Engine idle speed control via maximal safe set computation in the crank-angle domain

In this paper, the idle speed control problem is addressed via maximal safe set computation. A hybrid model of the engine in idle mode is used. The solution is based on the transformation of the continuous dynamics from the time-domain to the crank-angle domain and on the linearization and discretization of these dynamics. A flexible and portable algorithm in the discrete-time domain is proposed for the determination of the maximal safe set. Simulation results show the efficiency of the proposed approach.

Issues in design and architecture of advanced dynamic model management for decision support systems

Abstract This paper presents some of the research issues that arise when the design of a dynamic model management system oriented to decision support is extended to provide such advanced features as handling of symbolic models, automatic building and manipulation of models, model base management and simultaneous processing of multiple models. In particular it discusses the relationship between system theory and the design of software for model management, with an attempt to individuate research orientations that may foster further progress in the development of decision support systems.