Daniele Carnevale

Explicit Computation of the Sampling Period in Emulation of Controllers for Nonlinear Sampled-Data Systems

The purpose of this note is to apply recent results on stabilization of networked control systems to obtain an explicit formula for the maximum allowable sampling period (MASP) that guarantees stability of a nonlinear sampled-data system with an emulated controller. Such formulas are of great value to control practitioners.

Invariant Manifold Based Reduced-Order Observer Design for Nonlinear Systems

The problem of constructing globally convergent, reduced-order observers for general nonlinear systems is addressed. It is shown that an asymptotic estimate of the unknown states can be obtained by rendering attractive an appropriately selected (invariant) manifold in the extended state space. Current results on nonlinear observer design require that the nonlinearities appearing in the system equations are either linear functions of the unmeasured states or monotonic functions of a linear combination of the states. In this paper we relax these two assumptions by allowing for a wider class of nonlinearities to appear in the system equations. The proposed approach is applied on several examples including a perspective vision system and a general two-degrees-of-freedom mechanical system.

Further results on stability of networked control systems: a Lyapunov approach

Simple Lyapunov proofs are given for an improved (relative to previous results that have appeared in the literature) bound on the maximum allowable transfer interval to guarantee global asymptotic or exponential stability in networked control systems and also for semiglobal practical asymptotic stability with respect to the length of the maximum allowable transfer interval. We apply our results to emulation of nonlinear controllers in sampled-data systems.

Output regulation for a class of linear hybrid systems. Part 1: trajectory generation

In this paper the problem of generating zero error steady-state responses is addressed for a class of hybrid linear systems whose jumps are determined by time only. The procedure for the design of an automatic device generating the steady-state response and input is described. Once such device and a compensator ensuring incremental stability (see the companion paper) are available, the classical output regulation problem for the same class of hybrid linear systems can be immediately solved. Compared with previously available results, no assumption is needed on the plant about minimum phaseness, relative degree or squareness (same number of inputs and outputs). The key role of the zero dynamics and of the additional inputs (when the plant is fat) is highlighted.

Reduced-order observer design for nonlinear systems

This work is a geometric study of reducedorder observer design for nonlinear systems. Our reduced order observer design is applicable for Lyapunov stable nonlinear systems with a linear output equation and is a generalization of Luenberger’s reduced order observer design for linear systems. We establish the error convergence for the reduced order estimator for nonlinear systems using the center manifold theory for flows. We illustrate our re duced order observer construction for nonlinear systems with a physical example, namely a nonlinear pendulum without friction. c

Output regulation for a class of linear hybrid systems. Part 2: stabilization

This paper reports some stabilization results for a class of hybrid linear systems whose jumps are determined by time only. Linearity of the resulting closed-loop system implies that global asymptotic and incremental stability are achieved at the same time. In turn, incremental stability allows for the solution of a recently considered output regulation problem by coupling a suitable steady state generator (described in a companion paper) and the stabilizer from this paper. It is remarked that stabilization and regulation are achieved for general MIMO plants without relying on minimum phase, relative degree or squareness assumptions.

Necessary and sufficient conditions for output regulation in a class of hybrid linear systems

In this paper, the problem of output regulation for a class of hybrid linear systems is considered. Necessary and sufficient conditions for its solution are provided, both in the full information and error feedback case, under the additional constraint that the regulator is a hybrid linear time invariant system from the same class. A stronger version of the internal model principle is also shown, requiring that the regulator must contain a copy of the zero dynamics of the plant in addition to the usual copy of the exosystem dynamics.

Hybrid Output Regulation for Linear Systems With Periodic Jumps: Solvability Conditions, Structural Implications and Semi-Classical Solutions

The problem of output regulation for a class of hybrid linear systems characterized by periodic jumps is considered in this paper. Necessary and sufficient conditions for its solution are provided both in the full information and error feedback case. By a detailed analysis of such conditions, several interesting properties are derived, including the fact that the regulator must contain a (suitably defined) copy of the flow zero dynamics of the plant in addition to the usual copy of the exosystem dynamics, and the fact that the output regulation problem is generically solvable for fat plants (having more inputs than outputs) and generically not solvable for square plants. In addition, semi-classical solutions to the hybrid output regulation problem are introduced and discussed. Such solutions are characterized by the property that the required steady-state input can be generated as a simple linear function of the state of the exosystem (as in the non-hybrid case), although the associated steady-state response has a genuinely hybrid structure.

A case study for hybrid regulation: Output tracking for a spinning and bouncing disk

In this paper, a spinning and bouncing disk is used to illustrate some issues in regulation for a class of hybrid systems. The use of variables having a clear physical meaning allows to give a nice interpretation of the mechanism that can be used, for fat plants, to generate admissible trajectories.

On semiclassical solutions of hybrid regulator equations

In this paper, a special class of hybrid regulation problems is considered, which can be solved by using a class of steady-state inputs essentially coinciding with the class used in standard output regulation problems (for non hybrid systems), although the corresponding state evolution happens on a genuinely hybrid invariant manifold; hence the name “semiclassical”. The main advantage of using such solutions lies in easier implementation and the possibility of robust design.