Andrea Balluchi

Design of Observers for Hybrid Systems

A methodology for the design of dynamical observers for hybrid plants is proposed. The hybrid observer consists of two parts: a location observer and a continuous observer. The former identifies the current location of the hybrid plant, while the latter produces an estimate of the evolution of the continuous state of the hybrid plant. A synthesis procedure is offered when a set of properties on the hybrid plant is satisfied. The synthesized hybrid observer identifies the current location of the plant after a finite number of steps and converges exponentially to the continuous state.

Path tracking control for Dubin's cars

The problem of driving a Dubins car (1957) along a given path is considered. In order to model a realistic road-following problem, the car is supposed to move forward only and to have bounds on the turning radius (Dubins car). We propose a discontinuous control scheme on the angular velocity of the vehicle, based on the theory of sliding modes, that achieves the goal of tracking an unknown path relying on measurements of the current distance from the path and of the heading angle error.

Cut-off in engine control: a hybrid system approach

A novel approach to the control of an automotive engine in the cut-off region is presented. First, a hybrid model which describes the torque generation mechanism and the power-train dynamics is developed. Then, the cut-off control problem is formulated as a hybrid optimization problem, whose solution is obtained by relaxing it to the continuous domain and mapping its solution back into the hybrid domain. A formal analysis as well as simulation results demonstrate the properties and the quality of the control law.

Hybrid control in automotive applications: the cut-off control

A novel approach to the control of an automotive engines in the cut-off region is presented. First, a hybrid model which describes the torque generation mechanism and the powertrain dynamics is developed. Then, the cut-off control problem is formulated as a hybrid optimal control problem, whose solution is obtained by relaxing it to the continuous domain and mapping its solution back into the hybrid domain. A formal analysis as well as experimental results demonstrate the properties and the quality of the control law.

Brief Steering of a class of nonholonomic systems with drift terms

In the present paper nonholonomic systems with drift terms are studied. The discussion is focused on a class of Lagrangian systems with a cyclic coordinate. We present an approach to open-loop path planning in which the system evolution is studied on manifolds of dimension equal to the number of control inputs. A control procedure is derived and it is applied to the planar diver.

Controller synthesis on non-uniform and uncertain discrete–time domains

The problem of synthesizing feedback controllers that perform sensing and actuation actions on non–uniform and uncertain discrete time domains is considered. This class of problems is relevant to many application domains. For instance, in engine control a heterogenous and, to some extent, uncertain event–driven time domain is due to the behavior of the 4-stroke internal combustion engine, with which the controller has to synchronize to operate the engine properly. Similar problems arise also in standard discrete–time control systems when considering the behavior of the system with controller implementation and communication effects. The design problem is formalized in a hybrid system framework; synthesis and verification methods, based on robust stability and robust performance results, are presented. The effectiveness of the proposed methods is demonstrated in an engine control application.

Maximal Safe Set Computation for Idle Speed Control of an Automotive Engine

The specification for the idle control problem for automotive engines is to maintain the crankshaft speed within a given range in the presence of load changes. A new cycle-detailed hybrid model of the engine that captures well the interactions between the discrete phenomena of torque generation and spark ignition, and the continuous evolution of the power-train and air dynamics, is proposed. The idle control problem is formalized as a safety specification problem on the hybrid system. The Tomlin-Lygeros-Sastry procedure [12] is applied to compute the maximal controlled invariant set that satisfies the safety specification.

Hybrid Control for Automotive Engine Management: The Cut-Off Case

A novel approach to the control of an automotive engine in the cut-off region is presented. First, a hybrid model which describes the torque generation mechanism and the power-train dynamics is developed. Then, the cut-off control problem is formulated as a hybrid optimization problem, whose solution is obtained by relaxing it to the continuous domain and mapping its solution back into the hybrid domain. A formal analysis as well as simulation results demonstrate the properties and the quality of the control law.

The design of dynamical observers for hybrid systems: Theory and application to an automotive control problem

A design methodology is presented for dynamical observers of hybrid systems with linear continuous-time dynamics that reconstruct the complete state (discrete location and continuous state) from the knowledge of the inputs and outputs of a hybrid plant. Given a current-location observable living hybrid system with minimum dwell-time, we prove that exponential ultimate boundedness for an hybrid observer can always be achieved. We also prove that the observer correctly identifies (apart from an initial finite number of transitions) the sequence of hybrid system locations even when the complementary outputs are generated with some delay with respect to the corresponding transitions in the plant.We then present the application of the theory to the problem of on–line identification of the actual engaged gear for a car, an important contribution. The relevance of this problem is related to engine control strategies achieving high performance and efficient emissions control which depend critically on the knowledge of the engaged gear. The performance of the observer was tested with (real and not simulated) experimental data obtained in Magneti Marelli Powertrain using an Opel Astra equipped with a Diesel engine and a robotized gearbox SeleSpeed.

Hybrid Feedback Control for Path Tracking by a Bounded-Curvature Vehicle

In this paper, we consider the problem of stabilizing the kinematic model of a car to a general path in the plane, subject to very mild restrictions. The car model, although rather simplified, contains some of the most relevant limitations that make application of existing results in the literature impossible: namely, the car can only move forward, and turn with a bounded steering radius; also, only limited sensory information is available. The approach we follow to stabilization is to adapt to the present general case an optimal synthesis approach successfully applied in our previous work to tracking rectilinear paths. Due to both the nature of the problem, and the solution technique used, the analysis of the controlled system involves a rather complex switching logic. Hybrid formalism and verification techniques prove extremely useful in this context to formally proof stability of the resulting system, and are described in detail in the paper.