Sliding-mode control of retarded nonlinear systems via finite spectrum assignment approach

International audienceIn the present study, a sliding mode control design method based on the finite spectrum assignment procedure is proposed. The finite spectrum assignment for retarded nonlinear systems can transform retarded nonlinear systems into delay-free linear systems via a variable transformation and a feedback, which contain the past values of the state. This method can be considered to be an extension of both the finite spectrum assignment for retarded linear systems with controllability over polynomial rings of the delay operator and the exact linearization for finite dimensional nonlinear systems. The proposed method is to design a sliding surface via the variable transformation used in the finite spectrum assignment and to derive a switching feedback law. The obtained surface contains not only the current values of the state variables but also the past values of the state variables in the original coordinates. The effectiveness of the proposed method is tested by an illustrative example

Управление спектром дифференциально-разностной системы при помощи обратной связи

Для спектрально управляемой линейной автономной системы запаздывающего типа с соизмеримыми запаздываниями строится статическая обратная связь по состоянию, обеспечивающая произвольный конечный спектр замкнутой системы. За счет выбора последнего замкнутая система может быть сделана асимптотически устойчивой. Результаты проиллюстрированы примером

Consensus Over Ergodic Stationary Graph Processes

In this technical note, we provide a necessary and sufficient condition for convergence of consensus algorithms when the underlying graphs of the network are generated by an ergodic and stationary random process. We prove that consensus algorithms converge almost surely, if and only if, the expected graph of the network contains a directed spanning tree. Our results contain the case of independent and identically distributed graph processes as a special case. We also compute the mean and variance of the random consensus value that the algorithm converges to and provide a necessary and sufficient condition for the distribution of the consensus value to be degenerate

A reachability test for systems over polynomial rings using Gröbner bases

Conditions for the reachability of a system over a polynomial ring are well known in the literature. However, the verification of these conditions remained a difficult problem in general. Application of the Gröbner Basis method from constructive commutative algebra makes it possible to carry out this test explicitly. In this paper it is shown how this can be done in an efficient way. In comparison with a very simple and rather straightforward method, the algorithm proposed in this paper has an enormous advantage: it has a good performance for both reachable and non-reachable systems. Moreover, the method can be used to obtain a right- or left-inverse of a general non-square polynomial matrix. Such inverse matrices are often required for the design of feedback compensators. Finally, a modification of the reachability test is given to speed up the computations in the non-reachable case

Implementation and Comparison of H∞ Observers for Time-Delay Systems

abstract: In this thesis, different H∞ observers for time-delay systems are implemented and their performances are compared. Equations that can be used to calculate observer gains are mentioned. Different methods that can be used to implement observers for time-delay systems are illustrated. Various stable and unstable systems are used and H∞ bounds are calculated using these observer designing methods. Delays are assumed to be known constants for all systems. H∞ gains are calculated numerically using disturbance signals and performances of observers are compared. The primary goal of this thesis is to implement the observer for Time Delay Systems designed using SOS and compare its performance with existing H∞ optimal observers. These observers are more general than other observers for time-delay systems as they make corrections to the delayed state as well along with the present state. The observer dynamics can be represented by an ODE coupled with a PDE. Results shown in this thesis show that this type of observers performs better than other H∞ observers. Sub-optimal observer-based state feedback system is also generated and simulated using the SOS observer. The simulation results show that the closed loop system converges very quickly, and the observer can be used to design full state-feedback closed loop system.Dissertation/ThesisMasters Thesis Mechanical Engineering 201

Module structure of constant linear systems and its applications to controllability

AbstractWe shall introduce a new module structure to a large class of continuous-time constant linear systems. This is done as a natural extension of the classical k[z]-module structure of finite-dimensional constant linear systems. This module action is used to investigate the relationship between reachability and controllability of linear systems. After introducing the notion of K-controllability due to Kamen [12], we give the following result in Section 5: If a constant linear system is described by a functional differential equation ẋ = Fx + Gu, where x and G belong to a Banach space X, and if G is K-controllable to zero, then every reachable state is reachable and controllable in bounded time. (The result given in Section 5 is a little more general than this.) We also give a simple example in Section 6 to illustrate this result

Delay identification in time-delay systems using variable structure observers

In this paper we discuss delay estimation in time-delay systems. In the introduction section a short overview is given of some existing estimation techniques as well as identifiability studies. In the following sections we propose several algorithms for the delay identification based on variable structure observers

Algebraic principles as a tool for energy saving

This paper discusses algebraic approaches of control design for a set of Single Input - Single Output (SISO) delayed systems that are further developed and discussed. The first principle utilises a special ring RQM, - a set of RQ-meromorphic functions. The second one is based on a ring of proper and stable rational functions RPS and can be considered as a special case. Controller parameters are derived through the general solution of linear Diophantine equations in the appropriate ring. A final controller can be tuned by the scalar real parameter m0>0. The methodology is illustrated by a comparison with another approach, some analyses of a tuning parameter and example. The simulations are performed in the Matlab environment. Copyright © 2020, AIDIC Servizi S.r.l