Lyapunov Schemes Research Articles

Adaptive observer‐based control for fractional‐order chaotic MEMS system

AbstractThis paper proposes an adaptive observer‐based scheme to control fractional‐order chaotic micro‐electro‐mechanical‐systems (MEMS). The fractional‐order model of a system exhibits the dynamic behaviour of a physical system more accurately than a similar integer‐order one. An observer‐based control considering the unknown parameters is presented for a fractional‐order chaotic micro‐electro‐mechanical‐system. To handle the existence of the unknown parameters, the control law consists of both estimated parameters and also estimated states that have been designed. First, a fractional‐order observer is designed to estimate the state variables. The asymptotic convergence to zero of the estimation state error is proved using the Lyapunov scheme. After that, with the designed observer as a foundation, adaptive control is expanded for the closed‐loop system to ensure its asymptotic stability. An evaluation of the proposed method shows its efficacy via simulations for two case studies.

Analytical simulation of nanoparticle-embedded blood flow control with magnetic field influence through spectra homotopy analysis method

Nanoparticles-based infusion strategies are presently being employed for a range of clinical interventions either for in vivo or in vitro applications while imposition of magnetic field is also identified as an important technique for fluid manipulation during nanoparticles-based propulsion. The impact of magnetic field to control of the transport of nanoparticles-based blood flow is demonstrated numerically over an elaborate variant of transport mechanisms. Mathematical formulations were undertaken and stability analysis of the mathematical problem was a scrutinized by generation of eigen values using the Lyapunov scheme. The numerical solution based on Chebysehev pseudo-spectra and spectra homotopy analysis method (SHAM) was implemented to handle the combination on nonlinear ordinary differential equations derived from the transport models. We observed that far-field of the stagnation point, nanoparticles specie dispersion increased with higher thermal diffusivity, while the decrease in concentration profile around the vicinity of stagnation point depicts clustering of nanoparticles-embedded blood flow. The observations revealed that higher magnitude of thermophoretic parameters constitute significantly to increase in momentum as well as energy fields during transport of nanoparticles-containing blood flow under magnetic field influence. These findings showed the potentials of magnetic-field for control of suspended particles in transport medium which could be harnessed to manipulate transport of nanoparticles-containing fluids in microfluidic platforms with intricate configurations.

Designing a self-constructing fuzzy neural network controller for damping power system oscillations

This study presents a self-constructing fuzzy neural network (SCFNN) based static synchronous series control (SSSC) to mitigate the inter-area oscillations in interconnected power systems. The proposed intelligent system includes an on-line trained fuzzy neural network (FNN) controller with adaptive learning rates (ALRs) and self-constructing mechanism. The Lyapunov scheme is employed to obtain the adaptive learning rates. Therefore, convergence of the suggested controller can be ensured. The proposed approach is such that, at first, originally, no neurons exist in the structure of FNN. In fact, they are automatically created and if it is required, they will be created. Therefore, the total time for training algorithm is significantly reduced and the speed of controller is considerably increased. In addition, the Prony technique is utilized to guesstimate the damping ratio of oscillations. The results confirm the usefulness of the suggested controller.

Adaptive sliding mode control for non-linear discrete-time systems with mismatched uncertainty

This paper is concerned with an adaptive Sliding Mode Control (SMC) for non-linear discrete-time systems with mismatched uncertainty. The proposed adaptive SMC is composed of the equivalent and the switching controls, and it is constructed on the basis of the information from the proposed estimator to take the estimates for the state and uncertainty. It is assumed that some of the state variables can be measured and the uncertainty in the discrete-time systems is parameterised linearly in the unknown constant terms. The estimates for the state and the uncertainty are taken by applying the proposed weighted least squares method. It is verified based on the Lyapunov scheme according to which the estimation errors converge to zero as time increases, and the trajectory of the system response is stable as the sliding surface is suitably selected. The effectiveness of the proposed adaptive SMC is illustrated by the simulation experiment in a simple numerical example.

A New Iterative Method for Solving Large-Scale Lyapunov Matrix Equations

In this paper we propose a new projection method to solve large-scale continuous-time Lyapunov matrix equations. The new approach projects the problem onto a much smaller approximation space, generated as a combination of Krylov subspaces in A and $A^{-1}$. The reduced problem is then solved by means of a direct Lyapunov scheme based on matrix factorizations. The reported numerical results show the competitiveness of the new method, compared to a state-of-the-art approach based on the factorized alternating direction implicit iteration.

Systematization of approaches to adaptive boundary stabilization of PDEs

AbstractWhile adaptive control of finite dimensional systems is an advanced field that has produced adaptive control methods for a very general class of LTI systems, adaptive control techniques have been developed for only a few of the classes of PDEs for which non‐adaptive controllers exist. We present a catalog of approaches for the design of adaptive controllers for PDEs controlled from a boundary and containing unknown destabilizing parameters affecting the interior of the domain. We differentiate between two major classes of schemes: Lyapunov schemes and certainty equivalence schemes. Within the certainty equivalence class, two types of identifier designs are pursued: passivity‐based and swapping designs. Each of those designs is applicable to two types of parametrizations: the plant model in its original form (which we refer to as the ‘u‐model’) and a transformed model to which a backstepping transformation has been applied (which we refer to as the ‘w‐model’). Hence, a large number of control algorithms result from combining different design tools—Lyapunov schemes, w‐passive schemes, u‐swapping schemes, etc.Our method builds upon the explicitly parametrized control formulae that we introduced in our earlier work on non‐adaptive backstepping control for PDEs. These formulae allow us to develop tunable controllers that avoid solving Riccati or Bezout equations at each time step.This paper is primarily a tutorial. Its purpose is to provide structure that helps the future reader of five other papers currently under review which contain the detailed proofs for the designs presented here. Additionally, the paper can serve as an entry point for a non‐expert reader interested in an introduction to adaptive boundary control of PDEs. For this reason, our presentation proceeds through a series of examples, which are generalized in the companion papers. Copyright © 2006 John Wiley & Sons, Ltd.

Comparative studies of model reference adaptive control systems

A brief but up-to-date survey on existing methods of designing a class of model reference adaptive control systems is given in this paper. A comparison of the merits of the various design rules is also made with particular attention to the M.I.T. rule and the Lyapunov synthesis technique. Subsequently a systematic performance comparison of the various designs, with deterministic as well as stochastic inputs, is presented using the computer simulation studies of two simple gain adjustment schemes. From the dimensionless characteristic graphs obtained the Lyapunov schemes are found to exhibit superior performance over other designs. These graphs also uncover the strange adaptive response of those designs based on gradient methods in that the performance index may increase or decrease with increasing system gain parameters.