Paolo Caravani

Constrained control of switching systems: a positive invariant approach

This paper presents conditions for the stabilization of switching discrete-time linear systems with constrained control by using a positive invariance approach. A state feedback control law is used to construct the stabilizing controller. A numerical example is presented to illustrate the technique.

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

Optimal Location of a Measurement Point in a Diffusion Process

Abstract In this paper a criterion is proposed for the optimal selection of a measurement point in order to get an approximate recovery of the initial state for a distributed parameter system described by a one dimensional parabolic equation. A numerical procedure is established which allows to determine the location of the optimal point up to a desired accuracy. Numerical values of the optimal sensor location are obtained. An application example which shows the effectiveness of the criterion is reported.

Brief Doubly invariant equilibria of linear discrete-time games

In this paper the notion of doubly invariant (DI) equilibrium is introduced. The concept extends controlled and robustly controlled invariance notions to the context of two-person dynamic games. Each player tries to keep the state in a region of state space independently of the actions of the rival player. The paper gives existence conditions, criteria and algorithms for the determination of DI equilibria of linear dynamic games in discrete time. Two examples illustrate the results. The first one is in the area of fault-tolerant controller synthesis. The second is an application to macroeconomics.

Invariant Equilibria of Polytopic Games via Optimized Robust Control Invariance

In the context of non-cooperative linear discrete- time games, invariant equilibria are introduced as an extension to many players of the corresponding concept for two-player games (doubly invariant equilibria). It is established that the set of equilibrium control amplitudes is convex. An efficient computational procedure for the computation of piecewise affine equilibrium strategies based on the recent concept of optimized robust control invariance is proposed. The procedure makes use of a simple linear programming formulation when constraints are polytopic, thus avoiding recursive projection of convex sets. A numerical example for three player game is presented.

On the approximation of invariant sets for constrained LDT systems

Abstract An algorithm is given for the computation of the maximal invariant subset of a given set for linear discrete-time systems subject to hard constraints on state, control and disturbance inputs. At each iteration the algorithm provides an inner invariant approximation of the maximal invariant set.

On distributed mode-observability of multimodal systems

Given a set of autonomous discrete-time LTI systems, one element - the current mode - is active. A number of agents identified to the nodes of a directed graph have different incomplete observations of the systems state, partial knowledge of the systems parameters and no knowledge of the initial state. A distributed scheme based on local communication among agents is studied to identify the current mode. Centralized and de-centralized distinguishability conditions are derived as well as a tight estimate of the number of steps required for the convergence of a distributed mode observer. Contingent on the information available to the agents, robustness to faulty or malicious communication is discussed. A distributed mode observer with a degree of robustness is proposed.

Output stabilization of switching systems with linear discrete-time modes

The discrete component of the hybrid state of a discrete-time linear switching system is assumed uncontrolled and unobserved. Conditions of stabilizability for this class of systems are given in terms of a new definition of control invariance, based on the realization of a discrete observer that permits reconstruction of the discrete state in certain intervals of the time basis. The paper highlights the relationship between the minimum dwell time of the system and its stabilizability. An almost complete characterization of stabilizability is offered in terms of certain subsets of the continuous state space. These sets are amenable to tractable parametric procedures for controller synthesis.

A robust invariance approach to idle speed control of a spark ignited engine

Abstract Idle speed control of a spark ignition engine is studied via a control invariant approach. A hybrid system describes torque generation at cycle–level. The continuous–time dynamics is reset at prescribed crankshaft angles. Time-discretization allows to handle delays in the control loop and constraints on state and control variables in a simple form by means of a control invariant technique. The synchronization problem is solved by a robust extension of the same technique. Controller implements a piecewise–linear state–feedback law.

Introduction to the Control Problem

We deal with linear time-invariant (LTI) systems. A discrete-time LTI system has general form