Generalized controlled invariance for discrete-time nonlinearsystems with an application to the dynamic disturbance decouplingproblem

In analogy with the continuous-time case, a general notion of controlled invariance with respect to quasi-static-state feedback is introduced for discrete-time nonlinear systems which incorporates the earlier definition of controlled invariance with respect to regular static-state feedback. This new notion is used to derive a geometric solution to the dynamic disturbance decoupling problem. The proposed solution is a natural generalization of the geometric solution to the static disturbance decoupling problem     

Invariant codistributions and the feedforward form for discrete-time nonlinear systems

The goal of this paper is two-fold. First, given an arbitrary n-dimensional discrete-time nonlinear dynamical system, necessary and sufficient conditions for the existence of a one-dimensional invariant codistribution are obtained. Second, it is shown that the previous conditions can be used iteratively to obtain a nested sequence of n invariant codistributions with the properties that each codistribution contains the previous one and the last one coincides with the cotangent bundle of the state manifold. As a byproduct, necessary and sufficient conditions are obtained for a discrete-time nonlinear dynamical system to be equivalent to the so-called feedforward form.     

A linear algebraic framework for dynamic feedback linearization

To any accessible nonlinear system we associate a so-called infinitesimal Brunovsky form. This gives an algebraic criterion for strong accessibility as well as a generalization of Kronecker controllability indices. An output function which defines a right-invertible system without zero dynamics is shown to exist if and only if the basis of the Brunovsky form can be transformed into a system of exact differential forms. This is equivalent to the system being differentially flat and hence constitutes a necessary and sufficient condition for dynamic feedback linearizability     

Synthesis of product-driven coordination controllers for a class of discrete-event manufacturing systems

A synthesis approach is proposed for discrete-event coordination architectures applied to a class of automated manufacturing systems (AMS) in which a clear separation is established between equipment control activities and product manufacturing procedures. Manufacturing procedures are modeled by regular languages constructed with a class of control commands named imperative. Equipment controllers are synthesized as a standard discrete-event supervisors dealing only with operational and safety issues of equipment groupings. The control of equipment modules is carried out following the imperative control commands sequences. Conditions are established to guarantee that the manufacturing procedure of a given product can be achieved using the synthesized supervisors in a particular AMS. Therefore, equipment controllers are not needed to be modified to consider the manufacturing of different products, whilst the construction of achievable manufacturing procedures becomes an “ad hoc” simple process using a reduced set of procedural blocks. The approach is illustrated with an experimental AMS.     

Constructive nonsmooth stabilization of triangular systems

The problem of local asymptotic continuous feedback stabilization of single-input nonlinear systems is considered here. The aim is to explicitly construct a continuous asymptotically stabilizing feedback for a class of nonlinear systems that is known to be continuous feedback asymptotically stabilizable, but for which the known results do not provide an effective method to compute the stabilizer. Computer simulations are included to show practical applicability of our approach.     

Global approximate output tracking for nonlinear systems

Addresses the global output tracking problem for nonlinear systems with singular points. For nonlinear systems which satisfy a suitable observability condition, the authors identify a class of smooth output trajectories which the system can track using continuous open-loop controls. This class includes all output trajectories generated by smooth state feedback. They then study the problem of approximate output tracking using discontinuous time-varying feedback controllers. Given a smooth output trajectory for which exact tracking is possible, the authors construct a discontinuous feedback controller which achieves robust tracking of the desired output trajectory in the face of perturbations. Finally, it is shown that their results can be applied to the control of a chain system, and some numerical results are presented to illustrate the performance of their controller     

Emulation of n−trailer Systems through Differentially Driven Multi-Agent Systems: Continuous- and Discrete- Time Approaches

This paper proposes the emulation of a physical standard or generalized n?trailer through the decentralized control of a multi-agent system composed of several differentially driven mobile robots. The key point is to solve a time-varying version of the well known formation tracking or marching problem. The problem is solved both in discrete- and continuous-time cases. Four different control laws are proposed which require different variables to be available for feedback or feedforward, depending on the specifications of the experimental platform. The performance of the proposed control laws is illustrated through real-time experiments. It is shown that the discrete-time control law exhibits a performance comparable to that of the continuous-time control law with a sampling period 20 times larger than the one used in the continuous-time experiment.     

Linearization of discrete-time systems by exogenous dynamic feedback

It is shown that a discrete-time system may be linearizable by exogenous dynamic feedback, even if it cannot be linearized by endogenous feedback. This property is completely unexpected and constitutes a fundamental difference with respect to the continuous-time case. The notion of exogenous linearizing output is introduced. It is shown that existence of an exogenous linearizing output is a sufficient condition for dynamic linearizability. Necessary and sufficient conditions for the existence of an exogenous linearizing output are provided. The results of the paper are obtained using transformal operator matrices. The properties of such operators are studied. The theory is applied to the exact discrete-time model of a mobile robot, showing that the above-mentioned property concerns not only academic examples, but also physical systems.