M.D. Di Benedetto

Hamiltonian adaptive control of spacecraft

A new approach to the accurate attitude tracking control of rigid spacecraft handling large loads of unknown mass properties is proposed. The method, based on the construction of a physically motivated Lyapunov-like function, is inspired by the adaptive robot control algorithm of J.J.E. Slotine and W. Li (Int. J. Robot. Res., vol.6, no.3, 1987), and presents similar advantages over techniques based on inverse dynamics in terms of simplicity, easier approach to robustness issues, and adaptive capabilities. The approach is illustrated in simulations. >

On observability and detectability of continuous-time linear switching systems

The notion of observability and detectability for a particular class of hybrid systems, linear continuous-time switching systems, is investigated. We compare some of the definitions of observability previously offered and we analyze their drawbacks. A novel definition of observability is proposed corresponding to the possibility of reconstructing the state of the system from the knowledge of the discrete and continuous outputs and inputs. The notion of detectability is also introduced. Sufficient and necessary conditions for these properties to hold for switching systems are presented.

Necessary conditions for asymptotic tracking in nonlinear systems

In the literature, it has been shown that if a single-input single-output analytic nonlinear plant 1) has a well-defined relative degree and 2) is minimum-phase, it is possible to achieve asymptotic tracking for an open set of output trajectories containing the origin in C/sup N/ [0, /spl infin/), the space of N-times continuously differentiable functions taking values in R. When either of these sufficient conditions is not met, various authors have investigated approximate analytic solutions, discontinuous solutions and solutions for restricted sets of trajectories. In this paper, it is shown that conditions 1) and 2) are necessary for the existence of an analytic compensator which yields asymptotic tracking for an open set of output trajectories. Analogous results are established for multi-input multi-output systems. >

Stochastic Hybrid Models: An Overview

Abstract An overview of Stochastic Hybrid Models developed in the literature is presented. Attention is concentrated on three classes of models: Piecewise Deterministic Markov Processes, Switching Diffusion Processes and Stochastic Hybrid Systems. The descriptive power of the three classes is compared and conditions under which the classes coincide are developed. The theoretical analysis is motivated by modelling problelns in Air Traffic Management.

Computation of maximal safe sets for switching systems

The problem of determining maximal safe sets and hybrid controllers is computationally intractable because of the mathematical generality of hybrid system models. Given the practical and theoretical relevance of the problem, finding implementable procedures that could at least approximate the maximal safe set is important. To this end, we begin by restricting our attention to a special class of hybrid systems: switching systems. We exploit the structural properties of the graph describing the discrete part of a switching system to develop an efficient procedure for the computation of the safe set. This procedure requires the computation of a maximal controlled invariant set. We then restrict our attention to linear discrete-time systems for which there is a wealth of results available in the literature for the determination of maximal controlled invariant sets. However, even for this class of systems, the computation may not converge in a finite number of steps. We then propose to compute inner approximations that are controlled invariant and for which a procedure that terminates in a finite number of steps can be obtained. A tight bound on the error can be given by comparing the inner approximation with the classical outer approximation of the maximal controlled invariant set. Our procedure is applied to the idle-speed regulation problem in engine control to demonstrate its efficiency.

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.

Model matching for finite-state machines

The problem of model matching for finite state machines (FSMs) consists of finding a controller for a given open-loop system so that the resulting closed-loop system matches a desired input-output behavior. In this paper, a set of model matching problems is addressed: strong model matching (where the reference model and the plant are deterministic FSMs and the initial conditions are fixed), strong model matching with measurable disturbances (where disturbances are present in the plant), and strong model matching with nondeterministic reference model (where any behavior out of those in the reference model has to be matched by the closed-loop system). Necessary and sufficient conditions for the existence of controllers for all these problems are given. A characterization of all feasible control laws is derived and an efficient synthesis procedure is proposed. Further, the well-known supervisory control problem for discrete-event dynamical systems (DEDSs) formulated in its basic form is shown to be solvable as a strong model matching problem with measurable disturbances and nondeterministic reference model.

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.

Inversion of nonlinear time-varying systems

A procedure for inverting nonlinear systems that presents some computational advantages when applied to flexible robot arms or, more generally, to mechanical structures, is given. The procedure is presented in a general setting, for nonlinear time-varying systems. An iterative algorithm that computes a smooth controlled invariant time-varying manifold, the mathematical properties of which are illustrated and exploited, is also proposed. An application to a flexible two-link manipulator illustrates the algorithm and its computational advantages. >

Individual cylinder characteristic estimation for a spark injection engine

Engine control policies are mostly based on the assumption that all injectors have the same behavior independent of location and aging. In reality, injectors do vary and age. To contain variations around a nominal value, tight tolerances are imposed on the manufacturing process. Even if the manufacturing process is tightly controlled, the air-to-fuel (A/F) ratio needed to satisfy emission constraints is difficult to achieve due to aging and even slight mismatch among different injectors. To devise control policies that take into account behavior differences among injectors, we need to estimate injector characteristics from measurements that are taken on the engine during its life time. In this paper, we present an estimation technique for injector characteristics based on a set of measurements that can be carried out using the sensors present in the car, i.e., intake manifold pressure, crank-shaft speed, throttle-valve plate angle, injection timings and exhaust A/F ratio, which is measured by a single UEGO sensor placed at the exhaust pipe output.