Nonlinear internal models for output regulation

In this paper we show how nonlinear internal models can be effectively used in the design of output regulators for nonlinear systems. This result provides a significant enhancement of the non-equilibrium theory for output regulation, which we have presented in the recent paper entitled "Limit Sets, Zero Dynamics, and Internal Models in the Problem of Nonlinear Output Regulation"

Robust Asymptotic Stabilization of Nonlinear Systems with Non-Hyperbolic Zero Dynamics

In this paper we present a general tool to handle the presence of zero dynamics which are asymptotically but not locally exponentially stable in problems of robust nonlinear stabilization by output feedback. We show how it is possible to design locally Lipschitz stabilizers under conditions which only rely upon a partial detectability assumption on the controlled plant, by obtaining a robust stabilizing paradigm which is not based on design of observers and separation principles. The main design idea comes from recent achievements in the field of output regulation and specifically in the design of nonlinear internal models.Comment: 30 pages. Preliminary versions accepted at the 47th IEEE Conference on Decision and Control, 200

Remote Tracking via Encoded Information for Nonlinear Systems

The problem addressed in this paper is to control a plant so as to have its output tracking (a family of) reference commands generated at a remote location and transmitted through a communication channel of finite capacity. The uncertainty due to the presence of the communication channel is counteracted by a suitable choice of the parameters of the regulator

Structural Analysis and Control of a Model of Two-site Electricity and Heat Supply

This paper introduces a control problem of regulation of energy flows in a two-site electricity and heat supply system, where two Combined Heat and Power (CHP) plants are interconnected via electricity and heat flows. The control problem is motivated by recent development of fast operation of CHP plants to provide ancillary services of power system on the order of tens of seconds to minutes. Due to the physical constraint that the responses of the heat subsystem are not necessary as fast as those of the electric subsystem, the target controlled state is not represented by any isolated equilibrium point, implying that stability of the system is lost in the long-term sense on the order of hours. In this paper, we first prove in the context of nonlinear control theory that the state-space model of the two-site system is non-minimum phase due to nonexistence of isolated equilibrium points of the associated zero dynamics.Instead, we locate a one-dimensional invariant manifold that represents the target controlled flows completely. Then, by utilizing a virtual output under which the state-space model becomes minimum phase, we synthesize a controller that achieves not only the regulation of energy flows in the short-term regime but also stabilization of an equilibrium point in the long-term regime. Effectiveness of the synthesized controller is established with numerical simulations with a practical set of model parameters

Necessary Conditions for Output Regulation with Exosystem Modelled by Differential Inclusions

The problem of output regulation has always been tackled in frameworks in which the references to be tracked and the disturbances to be rejected are generated by an autonomous differential equation, referred to as the exosystem. This assumption, that is routinely used in the design of asymptotic regulators, plays also a fundamental role in the formulation of the regulation problem and in the definition of the basic concepts such as the steady state and the zero dynamics of nonlinear systems. In this paper we show that the concepts of steady state, zero dynamics and the output regulation problem can be equivalently defined in a framework in which the exosystem is generated by a differential inclusion