Augmented Lyapunov functional approach for stability of neutral systems with mixed delays

This paper is concerned with the neutral‐delay‐dependent and discrete‐delay‐dependent stability for uncertain neutral systems with mixed delays and norm‐bounded uncertainties. Through constructing a new augmented Lyapunov‐Krasovskii functional and proving its positive definiteness, introducing some slack matrices and using integral inequality, the improved delay‐dependent stability criteria are derived in terms of linear matrix inequalities. Numerical examples are given to illustrate the significant improvement on the conservatism of the delay bound over some existing results. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Isochoric specific heat of sulfur hexafluoride at the critical point: Laboratory results and outline of a spacelab experiment for the d1-mission in 1985

The specific heat at constant volume c_v shows a weak singularity at the critical point. Renormalization group techniques have been applied, predicting a universal critical behavior which has to be experimentally confirmed for different systems. In this paper an experiment is presented to measure the specific heat of SF₆ along the critical isochore (_c=0.737 g·cm^–3), applying a continuous heating method. The results cover a temperature span of –1.5×10^–2< <1.70×10^–2 [=(T–T _c)/T _c] and were strongly affected by gravity effects that emerge in the sample of 1-mm hydrostatic height near the critical point. Using regression analysis, data were fitted with functions of the form c _v/R=A × ¦¦^– + B for the one-phase state and c _v/R=A × ¦¦^– + B for the twophase state. Within their error bounds the critical values (==0.098, A/A=1.83) represent the measurements for the temperature span 3.5×10^{–5< ¦¦<2.0×10 –3}, in good agreement with theoretical predictions. In order to exclude density profiles in the specimen, which are unavoidable in terrestrial experiments due to the high compressibility of fluids at the critical point and the gravity force, a space-qualified scanning ratio calorimeter has been constructed, which will permit long-term c_v measurements under microgravity (-g) conditions. The experiment will be part of the German Spacelab mission in October 1985. The significant features of the apparatus are briefly sketched.Paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

Stabilization of Rössler chaotic dynamical system using fuzzy logic control algorithm

This paper proposes a fuzzy logic control algorithm (FLCA) to stabilize the Rössler chaotic dynamical system. The fuzzy logic control system is based on a Takagi-Sugeno-Kang inference engine and the stability analysis in the sense of Lyapunov is carried out using Lyapunov’s direct method. The new FLCA is formulated to offer sufficient inequality stability conditions. The asymptotic complexity of our algorithm is analyzed and proved to be lower in comparison with that of linear matrix inequality-based FLCAs. A set of simulation results illustrates the effectiveness of the proposed FLCA.     

Non-existence of finite-time stable equilibria in fractional-order nonlinear systems

We note that in the literature it is often taken for granted that for fractional-order system without delays, whenever the system trajectory reaches the equilibrium, it will stay there. In fact, this is the well-known phenomenon of finite-time stability. However, in this paper, we will prove that for fractional-order nonlinear system described by Caputo’s or Riemann–Liouville’s definition, any equilibrium cannot be finite-time stable as long as the continuous solution corresponding to the initial value problem globally exists. In addition, some examples of stability analysis are revisited and linear Lyapunov function is used to prove the asymptotic stability of positive fractional-order nonlinear systems.     

Locally optimal controllers and globally inverse optimal controllers

In this paper we consider the problem of global asymptotic stabilization with prescribed local behavior. We show that this problem can be formulated in terms of control Lyapunov functions. Moreover, we show that if the local control law has been synthesized employing an LQ approach, then the associated Lyapunov function can be seen as the value function of an optimal problem with some specific local properties. We illustrate these results on two specific classes of systems: backstepping and feedforward systems. Finally, we show how this framework can be employed when considering the orbital transfer problem.     

A new calculation method of feedback controller gain for bilinear paper-making process with disturbance

This paper presents a new method to calculate the feedback control gain for a class of multivariable bilinear system, and also applied this method on the control of two sections of paper-making process with disturbance. The robust H∞ control problem is to design a state feedback controller such that the robust stability and a prescribed H∞ performance of the resulting closed-loop system are ensured. The controller turns out to be robust with respect to the disturbance in the plant. Utilizing the Schur complement and some variable transformations, the stability conditions of the multivariable bilinear systems are formulated in terms of Lyapunov function via the form of linear matrix inequality (LMI). The gain of controller will be calculated via LMI. Finally, the application examples of a headbox section and a dryer section of paper-making process are used to illustrate the applicability of the proposed method.     

Data-driven asymptotic stabilization for discrete-time nonlinear systems

In this paper, we propose a data-driven feedback controller design method based on Lyapunov approach, which can guarantee the asymptotic stability of the closed-loop and enlarge the estimate of domain of attraction (DOA) for the closed-loop. First, sufficient conditions for a feedback controller asymptotically stabilizing the discrete-time nonlinear plant are proposed. That is, if a feedback controller belongs to an open set consisting of pairs of control input and state, whose elements can make the difference of a control Lyapunov function (CLF) to be negative-definite, then the controller asymptotically stabilizes the plant. Then, for a given CLF candidate, an algorithm, to estimate the open set only using data, is proposed. With the estimate, it is checked whether the candidate is or is not a CLF. If it is, a feedback controller is designed just using data, which satisfies sufficient conditions mentioned above. Finally, the estimate of DOA for closed-loop is enlarged by finding an appropriate CLF from a CLF candidate set based on data. Because the controller is designed directly from data, complexity in building the model and modeling error are avoided.     

Adaptive tracking control of an autonomous underwater vehicle

This paper presents the trajectory tracking control of an autonomous underwater vehicle(AUV). To cope with parametric uncertainties owing to the hydrodynamic effect, an adaptive control law is developed for the AUV to track the desired trajectory. This desired state-dependent regressor matrix-based controller provides consistent results under hydrodynamic parametric uncertainties.Stability of the developed controller is verified using the Lyapunov s direct method. Numerical simulations are carried out to study the efficacy of the proposed adaptive controller.     

A sum of squares approach to backstepping controller synthesis for piecewise affine and polynomial systems

This paper develops a backstepping controller synthesis methodology for piecewise polynomial (PWP) systems in strict form. The main contribution of the paper is to formulate sufficient conditions for controller design for PWP systems in strict form as a sum of squares feasibility problem under the assumption that an initial control Lyapunov function exists to start the iterative backstepping procedure. This problem can then be translated into a convex SDP problem and solved by available software packages. The controller synthesis problem for PWP systems in strict feedback form is divided into two cases. The first case consists of the construction of a sum of squares polynomial control Lyapunov function for PWP systems with discontinuous vector fields. The second case addresses the construction of a PWP control Lyapunov function for PWP systems with continuous vector fields. One major advantage of the proposed method is the fact that it can handle systems with discontinuous vector fields and sliding modes. The new synthesis method is applied to several numerical examples. One of these examples offers the first convex optimization solution to piecewise affine (PWA) control of a benchmark circuit system addressed before in the literature using non‐convex PWA control solutions. Copyright © 2013 John Wiley & Sons, Ltd.