Second-order SM approach to SISO time-delay system output tracking

A fully linearizable single-input-single-output relative-degree n system with an output time delay is considered in this paper. Using the approach of Pade approximation, system center approach, and second-order sliding-mode (SM) control, we have obtained good output tracking results. The Smith predictor is used to compensate the difference between the actual delayed output and its approximation. A second-order supertwisting SM observer observes the disturbance in the plant. A nonlinear example is studied to show the effect of this methodology

Time Complexity of Decentralized Fixed-Mode Verification

Given an interconnected system, this note is concerned with the time complexity of verifying whether an unrepeated mode of the system is a decentralized fixed mode (DFM). It is shown that checking the decentralized fixedness of any distinct mode is tantamount to testing the strong connectivity of a digraph formed based on the system. It is subsequently proved that the time complexity of this decision problem using the proposed approach is the same as the complexity of matrix multiplication. This work concludes that the identification of distinct DFMs (by means of a deterministic algorithm, rather than a randomized one) is computationally very easy, although the existing algorithms for solving this problem would wrongly imply that it is cumbersome. This note provides not only a complexity analysis, but also an efficient algorithm for tackling the underlying problem

Sequential processing and performance optimization in nonlinear state estimation

We propose a framework for designing observers for noisy nonlinear systems with global convergence properties and performing robustness and noise sensitivity. Our state observer is the result of the combination of a state norm estimator with a bank of Kalman-type lters, parametrized by the state norm estimator. The state estimate is sequentially processed through the bank of lters. In general, existing nonlinear state observers are responsible for estimation errors which are sensitive to model uncertainties and measurement noise, depending on the initial state conditions. Each Kalman-type lter of the bank contributes to improve the estimation error performances to a certain degree in terms of sensitivity with respect to noise and initial state conditions. A sequential processing algorithm for performance optimization is given and simulations show the eectiveness of these sequential lters

Observer design for systems with an energy-preserving non-linearity

Observer design is considered for a class of non-linear systems whose non-linear part is energy preserving. A strategy to construct convergent observers for this class of non-linear system is presented. The approach has the advantage that it is possible, via convex programming, to prove whether the constructed observer converges, in contrast to several existing approaches to observer design for non-linear systems. Finally, the developed methods are applied to the Lorenz attractor and to a low order model for shear fluid flow

Finite time observers: application to secure communication

International audienceIn this paper, control theory is used to formalize finite time chaos synchronization as a nonlinear finite time observer design issue. This paper introduces a finite time observer for nonlinear systems that can be put into a linear canonical form up to output injection. The finite time convergence relies on the homogeneity properties of nonlinear systems. The observer is then applied to the problem of secure data transmission based on finite time chaos synchronization and the two-channel transmission method

Design and frequency analysis of continuous finite-time-convergent differentiator

In this paper, a continuous finite-time-convergent differentiator is presented based on a strong Lyapunov function. The continuous differentiator can reduce chattering phenomenon sufficiently than normal sliding mode differentiator, and the outputs of signal tracking and derivative estimation are all smooth. Frequency analysis is applied to compare the continuous differentiator with sliding mode differentiator. The beauties of the continuous finite-time-convergent differentiator include its simplicity, restraining noises sufficiently, and avoiding the chattering phenomenon