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The paper deals with the problems of state estimation for nonlinear dynamical control system described by differential equations with unknown but bounded initial condition. The nonlinear function in the right-hand part of a differential system is assumed to be of quadratic type with respect to the state variable. Basing on the well-known results of ellipsoidal calculus developed for linear uncertain systems we present the modified state estimation approaches which use the special structure of the dynamical system.

The modular-hierarchical modeling subdivides a system into dynamic describing atomic, and structure describing coupled systems. Due to the usally static structure of coupled systems, it can sometimes be hard to realize a component-oriented mapping of real system elements in model components. Hence, several approaches to model structural changes are developed, which are roughly classified in the paper.

The relevance of the differential flatness property in the context of sliding mode controller design is explored for the case of linear and nonlinear SISO and MIMO systems. We also explore, for linear systems, the possibilities of extending the idea of Generalized PI control, based on state reconstructors, to the problem of sliding surface asymptotic synthesis requiring no state measurements, or asymptotic observer design. An experimental example is presented, dealing with the sliding mode control of an electro-mechanical system, where there is no need for mechanical sensors.

Analogously to the formulation of the so-called classical servomechanism problem, the problem of tracking a reference signal while rejecting the effect of a disturbance signal by means of the VSS technique is studied by formulating the sliding mode servomechanism problem for which conditions for the existence of a solution for in general case and for a classes of nonlinear system presented in the Regular Form or in the Nonlinear Block Controllable Form are derived. The effectiveness of the proposed method is demonstrated by the application to the Pendubot system.

In this paper, we investigate a new identification algorithm grounded on the Variable Structure theory in order to study parameter and state identification for uncertain nonlinear systems in continuous time. On the one hand, we use a specific observer to estimate unknown states of the studied nonlinear system, based on the Variable Structure theory. On the other hand, the well-known chattering property and the invariance properties, characteristic of the Variable Structure theory, make possible the design of the parameter sliding identifier without the use of the additional persisting excitation condition usually required for the input in order to guarantee the parameter convergence. Stability of the state observer, parameter identifiability of the plant and asymptotic convergence of estimated parameters to their nominal values are studied. Finally, we propose some simulations on a pendulum in order to point out the validity of the methodology even if the input u is not persistently exciting. These numerical simulations highlight the robustness of the state and parameter identification with respect to significant parameter uncertainties thanks to the use of the Variable Structure theory.

A class of T-S fuzzy models with parameter perturbations, input and external disturbances is studied in this paper. Both the case of matched uncertainties and the case of mismatched uncertain- ties are investigated using variable structure control technique and LMI method. Firstly, we study the problem of stabilization of T-S fuzzy systems by using a variable structure controller. Secondly, for the given reference model, we design another variable structure controller such that the system output tracks the reference system output in a finite time interval. Finally, the simulation example is employed to illustrate the validity and effectiveness of the proposed method.

A method investigating a Gaussian radial-basis-function neural network (GRBFNN) with sliding mode control (SMC) for missile electrohydraulic servo mechanism is presented. Since the dynamics of the system are highly nonlinear and have large extent of model uncertainties, such as big changes in parameters and external disturbance, firstly, SMC is introduced. Since the accurate equivalent control is difficult to reach, a Gaussian radial basis function neural network is utilized. By adjusting the weight on-line, a neural-network-based SMC is developed to estimate the equivalent control of SMC control system. Then the switching control is appended to guarantee the stability of the proposed controller, and a set of fuzzy control rules are used to attenuate chattering phenomenon of the switching control. We apply the control method to the missile electro-hydraulic servo mechanism. Simulation results verify the validity of the proposed approach.

Compact representation of knowledge having strong internal interactions has become possible with the developments in neurocomputing and neural information processing. The field of neural networks has offered various solutions for complex problems, however, the problems associated with the learning performance has constituted a major drawback in terms of the realization performance and computational requirements. This paper discusses the use of variable structure systems theory in learning process. The objective is to incorporate the robustness of the approach into the training dynamics, and to ensure the stability in the adjustable parameter space. The results discussed demonstrate the fulfillment of the design specifications and display how the strength of a robust control scheme could be an integral part of a learning system. This paper discusses how Gaussian radial basis function neural networks could be utilized to drive a mechatronic system’s behavior into a predefined sliding regime, and it is seen that the results are promising.

A new learning algorithm for fuzzy system to approximate unknown nonlinear continuous functions is presented. Fast terminal sliding mode combining the finite time convergent property of terminal attractor and exponential convergent property of linear system is introduced into the conventional back-propagation learning algorithm to improve approximation ability. The Lyapunov stability analysis guarantees that the approximation is stable and converges to the unknown function with improved speed. The proposed fuzzy approximator is then applied in the control of an unstable nonlinear system. Simulation results demonstrate that the proposed method is better than conventional method in approximation and tracing control of nonlinear dynamic system.

In this paper, we present a new sliding mode controller for a class of unknown nonlinear discrete-time systems. We make the following two modifications: 1) The neural identifier which is used to estimate the unknown nonlinear system, applies new learning algorithms. The stability and non-zero properties are proved by dead-zone and projection technique. 2) We propose a new sliding surface and give a necessary condition to assure exponential decrease of the sliding surface. The time-varying gain in the sliding mode produces a low-chattering control signal. The closed-loop system with sliding mode controller and neural identifier is proved to be stable by Lyapunov method.

We consider perfect verifiable secret sharing (VSS) in a synchronous network of n processors (players) where a designated player called the dealer wishes to distribute a secret s among the players in a way that no t of them obtain any information, but any t + 1 players obtain full information about the secret. The round complexity of a VSS protocol is defined as the number of rounds performed in the sharing phase. Gennaro, Ishai, Kushilevitz and Rabin showed that three rounds are necessary and sufficient when n > 3t. Sufficiency, however, was only demonstrated by means of an inefficient (i.e., exponential-time) protocol, and the construction of an efficient three-round protocol was left as an open problem. In this paper, we present an efficient three-round protocol for VSS. The solution is based on a three-round solution of so-called weak verifiable secret sharing (WSS), for which we also prove that three rounds is a lower bound. Furthermore, we also demonstrate that one round is sufficient for WSS when n > 4t, and that VSS can be achieved in 1 + e amortized rounds (for any e > 0 ) when n>3t.

This paper address the kinematic variables control problem for the low-speed manoeuvring of a low cost and underactuated underwater vehicle Control of underwater vehicles is not simple, mainly due to the non-linear and coupled character of plant equations, the lack of a precise model of vehicle dynamics and parameters, as well as the appearance of internal and external perturbations The proposed methodology is an approach that makes use of a pioneering algorithm in underwater vehicles, based on the fusion of a robust or sliding mode controller and an adaptive fuzzy system, including the advantages of both systems The main property of this methodology is that it relaxes the required knowledge of vehicle model, reducing the cost of its design.

This paper investigates the chaos synchronization problem of a new 4-scroll chaotic system. Three nonlinear control approaches via state variables are studied, namely nonlinear feedback control, adaptive control and adaptive sliding mode type of control. Based on Lyapunov stability theory, control laws are derived such that the two identical 4-scroll systems are to be synchronized. Some sufficient conditions for the synchronization are obtained analytically in three cases. Numerical simulation results are given to show the effectiveness of the proposed methods.

The proposed controller in this paper, which combines the capability of fuzzy logic with the robustness of sliding mode controller, presents prevailing results with its adaptive architecture and proves to overcome the global stability problem of the control of nonlinear systems. Effectiveness of the controller and the performance comparison are demonstrated with chosen control techniques including PID and PD type self-tuning fuzzy controller on a quarter car model which consists of component-wise nonlinearities.

The novel fuzzy sliding mode control problem is presented for a class of uncertain nonlinear systems. The Takagi-Sugeno (T-S) fuzzy model is employed to represent a class of complex uncertain nonlinear system. A virtual state feedback technology is proposed to design the sliding mode plane. Based on Lyapunov stability theory, sufficient conditions for design of the fuzzy sliding model control are given. Design of the sliding mode controller based on reaching law concept is developed, which to ensure system trajectories from any initial states asymptotically convergent to sliding mode plane. The global asymptotic stability is guaranteed. A numerical example with simulation results is given to illustrate the effectiveness of the proposed method.