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Adaptive control of uncertain nonholonomic systems in finite time

Jiankui Wang, Guoshan Zhang, Hongyi Li (2009)


In this paper, the finite-time stabilization problem of chained form systems with parametric uncertainties is investigated. A novel switching control strategy is proposed for adaptive finite-time control design with the help of Lyapunov-based method and time-rescaling technique. With the proposed control law, the uncertain closed-loop system under consideration is finite-time stable within a given settling time. An illustrative example is also given to show the effectiveness of the proposed controller....

An observability problem for a class of uncertain-parameter linear dynamic systems

Krzysztof Oprzędkiewicz (2005)

International Journal of Applied Mathematics and Computer Science

An observability problem for a class of linear, uncertain-parameter, time-invariant dynamic SISO systems is discussed. The class of systems under consideration is described by a finite dimensional state-space equation with an interval diagonal state matrix, known control and output matrices and a two-dimensional uncertain parameter space. For the system considered a simple geometric interpretation of the system spectrum can be given. The geometric interpretation of the system spectrum is the base...

Control of constrained nonlinear uncertain discrete-time systems via robust controllable sets: a modal interval analysis approach

Jian Wan, Josep Vehí, Ningsu Luo, Pau Herrero (2009)

ESAIM: Control, Optimisation and Calculus of Variations

A general framework for computing robust controllable sets of constrained nonlinear uncertain discrete-time systems as well as controlling such complex systems based on the computed robust controllable sets is introduced in this paper. The addressed one-step control approach turns out to be a robust model predictive control scheme with feasible unit control horizon and contractive constraint. The solver of 1-dimensional quantified set inversion in modal interval analysis is extended to 2-dimensional...

Control of distributed delay systems with uncertainties: a generalized Popov theory approach

Dan Ivanescu, Silviu-Iulian Niculescu, Jean-Michel Dion, Luc Dugard (2001)


The paper deals with the generalized Popov theory applied to uncertain systems with distributed time delay. Sufficient conditions for stabilizing this class of delayed systems as well as for γ -attenuation achievement are given in terms of algebraic properties of a Popov system via a Liapunov–Krasovskii functional. The considered approach is new in the context of distributed linear time-delay systems and gives some interesting interpretations of H memoryless control problems in terms of Popov triplets...

Delay-dependent robust stability conditions and decay estimates for systems with input delays

Kostas Hrissagis, Olga I. Kosmidou (1998)


The robust stabilization of uncertain systems with delays in the manipulated variables is considered in this paper. Sufficient conditions are derived that guarantee closed-loop stability under state-feedback control in the presence of nonlinear and/or time-varying perturbations. The stability conditions are given in terms of scalar inequalities and do not require the solution of Lyapunov or Riccati equations. Instead, induced norms and matrix measures are used to yield some easy to test robust stability...

Derivation of physically motivated constraints for efficient interval simulations applied to the analysis of uncertain dynamical systems

Mareile Freihold, Eberhard P. Hofer (2009)

International Journal of Applied Mathematics and Computer Science

Interval arithmetic techniques such as VALENCIA-IVP allow calculating guaranteed enclosures of all reachable states of continuous-time dynamical systems with bounded uncertainties of both initial conditions and system parameters. Considering the fact that, in naive implementations of interval algorithms, overestimation might lead to unnecessarily conservative results, suitable consistency tests are essential to obtain the tightest possible enclosures. In this contribution, a general framework for...

Design of reaching phase for variable structure controller based on Householder transformation

Goshaidas Ray, Sitansu Dey, T. K. Bhattacharyya (2005)


The paper presents control signals generation methods, preventing the excitation of residual vibration in slightly damped oscillational systems. It is focused on the feedforward methods, as most of the vibrations in examined processes are induced by the control, while the influence of disturbances is mostly negligible. Application of these methods involves ensuring of the insensitivity to natural frequency change, which can be reached in classical approach only by considerable increase of transient...

Estimation of the output deviation norm for uncertain, discrete-time nonlinear systems in a state dependent form

Przemysław Orłowski (2007)

International Journal of Applied Mathematics and Computer Science

Numerical evaluation of the optimal nonlinear robust control requires estimating the impact of parameter uncertainties on the system output. The main goal of the paper is to propose a method for estimating the norm of an output trajectory deviation from the nominal trajectory for nonlinear uncertain, discrete-time systems. The measure of the deviation allows us to evaluate the robustness of any designed controller. The first part of the paper concerns uncertainty modelling for nonlinear systems...

Fault diagnosis and fault tolerant control using set-membership approaches: Application to real case studies

Vicenç Puig (2010)

International Journal of Applied Mathematics and Computer Science

This paper reviews the use of set-membership methods in fault diagnosis (FD) and fault tolerant control (FTC). Setmembership methods use a deterministic unknown-but-bounded description of noise and parametric uncertainty (interval models). These methods aims at checking the consistency between observed and predicted behaviour by using simple sets to approximate the exact set of possible behaviour (in the parameter or the state space). When an inconsistency is detected between the measured and predicted...

Forecast horizon and planning horizon paths in time-indexed network

Stanisław Bylka (2006)

Banach Center Publications

The problem of existence of a forecast (or planning) horizon has been considered in many special models, more or less precisely. We specify and investigate this problem for families of cheapest paths in networks with weakly ordered nodes. In a discrete network, the standard forward algorithm finds the subnetwork generated by optimal paths. The proposed forward procedure reduces subnetworks such that the forecast horizon remains unchanged. Based on the final subnetwork, we have an answer to the forecast...

Forecasting return products in an integrated forward/reverse supply chain utilizing an ANFIS

D. Thresh Kumar, Hamed Soleimani, Govindan Kannan (2014)

International Journal of Applied Mathematics and Computer Science

Interests in Closed-Loop Supply Chain (CLSC) issues are growing day by day within the academia, companies, and customers. Many papers discuss profitability or cost reduction impacts of remanufacturing, but a very important point is almost missing. Indeed, there is no guarantee about the amounts of return products even if we know a lot about demands of first products. This uncertainty is due to reasons such as companies' capabilities in collecting End-of-Life (EOL) products, customers' interests...

Fuzzy diagnostic reasoning that takes into account the uncertainty of the relation between faults and symptoms

Jan Kościelny, Michał Syfert (2006)

International Journal of Applied Mathematics and Computer Science

Knowledge about the relation between faults and the observed symptoms is necessary for fault isolation. Such a relation can be expressed in various forms, including binary diagnostic matrices or information systems. The paper presents the use of fuzzy logic for diagnostic reasoning. This method enables us to take into account various kinds of uncertainties connected with diagnostic reasoning, including the uncertainty of the faults-symptoms relation. The presented methods allow us to determine the...

How humans fly

Alain Ajami, Jean-Paul Gauthier, Thibault Maillot, Ulysse Serres (2013)

ESAIM: Control, Optimisation and Calculus of Variations

This paper is devoted to the general problem of reconstructing the cost from the observation of trajectories, in a problem of optimal control. It is motivated by the following applied problem, concerning HALE drones: one would like them to decide by themselves for their trajectories, and to behave at least as a good human pilot. This applied question is very similar to the problem of determining what is minimized in human locomotion. These starting points are the reasons for the particular classes...

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