Salvatore Monaco

Issues on Nonlinear Digital Control

The purpose of this work is to show the real need to motivate theoretical research in nonlinear digital control not only for solving control problems which are specific to the context, but also for giving the intuition of new control methodologies. Digital control methods can, indeed, be used either for the design of piecewice constant feedback strategies or for the design of discontinuous and hybrid controllers.

On the observer design in discrete-time

Abstract The paper deals with the equivalence, under coordinates change and output transformation, of a discrete-time nonlinear system to observer canonical forms. Necessary and sufficient conditions for local equivalence to these forms are given.

Advanced tools for nonlinear sampled-data systems' analysis and control

It is shown that the formalism of asymptotic series expansions recently developed by the authors for computing the solutions of non autonomous differential equations, can be profitably employed to obtain the equivalent model to a nonlinear continuous system under generalized sampling procedures. Tools and insights for the design of sampled-data control systems are derived.

Nonlinear regulation for a class of discrete-time systems

Abstract This paper deals with nonlinear discrete-time regulation for multi-input, multi-output plants. Conditions involving solvability of nonlinear transcendental equations are set. Following the approach recently developed by Isidori and Byrnes (1990) for continuous time systems, the existence of solutions to the posed problem is proved by investigating the properties of the zero dynamics. Finally a condition is given for the existence of an arbitrary approximation of the nonlinear solution.

Invariant distributions for discrete-time nonlinear systems

The purpose of this paper is to introduce some notions of invariant distributions, for the class of linear analytic discrete-time systems, and to give an algebraic characterization of them. A brief final discussion motivates the usefulness of the notions introduced in the study of the geometric properties of the system.

Sampled-Data Stabilization; A PBC Approach

Two sampled-data design procedures ensuring stabilization of passive systems are described in the general framework of passivity-based control (PBC) strategies. The first one makes reference to some modified output with respect to which passivity under sampling can be preserved. The second one can be interpreted as the sampled-data equivalent to the celebrated continuous-time stabilizing and damping Lg V-controller. A simulated example illustrates the performances.

From Chronological Calculus to Exponential Representations of Continuous and Discrete-Time Dynamics: A Lie-Algebraic Approach

In this paper, formal exponential representations of the solutions to nonautonomous nonlinear differential equations are derived. It is shown that the chronological exponential admits an ordinary exponential representation, the exponent being given by an explicitly computable Lie series expansion. The results are then used to describe controlled dynamics, dynamics under sampling and forced discrete-time dynamics. The study emphasizes the role of Lie algebra techniques in nonlinear control theory and specifies structural similarities between nonautonomous differential equations, dynamics under sampling and forced discrete-time dynamics up to hybrid ones.

Nonlinear discrete-time control of systems with a Naimark-Sacker bifurcation

In this paper we study the problem of the stabilization of nonlinear control system with one complex uncontrollable mode. We find normal forms and quadratic invariants; then we compute center manifolds, and use bifurcation theory to synthesize quadratic controllers.

Control Lyapunov stabilization of affine discrete-time systems

Based on integral Lyapunov inequality associated to discrete-time dynamics, some preliminary results on control Lyapunov design are set.

Quadratic forms and approximate feed back linearization in discrete time

Quadratic feedback linearization is discussed for discrete-time systems, i.e. approximate feedback linearization up to the second order with respect to input and state variables. After introducing in discrete time two equivalence classes, invariant under quadratic static state feedback and diffeomorphism, two canonical quadratic representations are proposed. Then it is shown that any nonlinear discrete-time dynamics, which are controllable in their first approximations, can be linearized up to the second order under dynamic feedback. The results stated here can be considered as the general discrete-time analogues of the continuous-time ones (Kang and Krener 1992).