Modeling and forecasting of stock markets under a system adaptation framework

This paper adopts the concept of dynamic feedback systems to model the behavior of financial markets,or more specifically,the stock market from a dynamic system point of view.Based on a feedback adaptation scheme,the authors model the movement of a stock market index within a framework that is composed of an internal dynamic model and an adaptive filter.The output-error model is adopted as the internal model whereas the adaptive filter is a time-varying state space model with instrumental variables.Its input-output behavior,and internal as well as external forces are then identified.Special attention has also been paid to the recent financial crisis by examining the movement of Dow Jones Industrial Average(DJIA) as an example to illustrate the advantage of the proposed framework.Supported by time-varying causality tests,five influential factors from economic and sentiment aspects are introduced as the input of this framework.Testing results show that the proposed framework has a much better prediction performance than the existing methods,especially in complicated economic situations.An application of this framework is also presented with focuses on forecasting the turning periods of the market trend.Realizing that a market trend is about to change when the external force begins to exhibit clear patterns in its frequency responses,the authors develop a set of rules to recognize this kind of clear patterns.These rules work well for stock indexes from US, China and Singapore.     

IMPROVED ROBUST H-INFINITY ESTIMATION FOR UNCERTAIN CONTINUOUS-TIME SYSTEMS

The design of full-order robust estimators is investigated for continuous-time polytopic uncertain systems. The main purpose is to obtain a stable linear estimator such that the estimation error system remains robustly stable with a prescribed H∞ attenuation level. Firstly, a simple alternative proof is given for an improved LMI representation of H∞ performance proposed recently. Based on the performance criterion which keeps the Lyapunov matrix out of the product of the system dynamic matrices, a sufficient condition for the existence of the robust estimator is provided in terms of linear matrix inequalities. It is shown that the proposed design strategy allows the use of parameterdependent Lyapunov functions and hence it is less conservative than the earlier results. A numerical example is employed to illustrate the feasibility and advantage of the proposed design.     

EXISTENCE AND ANALYTICAL APPROXIMATIONS OF LIMIT CYCLES IN A THREE-DIMENSIONAL NONLINEAR AUTONOMOUS FEEDBACK CONTROL SYSTEM

This paper is concerned with the existence and the analytical approximations of limit cycles in a three-dimensional nonlinear autonomous feedback control system. Based on three-dimensional Hopf bifurcation theorem, the existence of limit cycles is first proved. Then the homotopy analysis method （HAM） is applied to obtain the analytical approximations of the limit cycle and its frequency. In deriving the higher-order approximations, the authors utilized the idea of a perturbation procedure proposed for limit cycles＇ approximation in van der Pol equation. By comparing with the numerical integration solutions, it is shown that the accuracy of the analytical results obtained in this paper is very high, even when the amplitude of the limit cycle is large.     

ROBUST CONSENSUS FOR MULTI-AGENT SYSTEMS OVER UNBALANCED DIRECTED NETWORKS

In this paper, a distributed consensus protocol is proposed for discrete-time single-integer multi-agent systems with measurement noises under general fixed directed topologies, The time-varying control gains satisfying the stochastic approximation conditions are introduced to attenuate noises, thus the closed-loop multi-agent system is intrinsically a linear time-varying stochastic difference system. Then the mean square consensus convergence analysis is developed based on the Lyapunov technique, and the construction of the Lyapunov function especially does not require the typical balanced network topology condition assumed for the existence of quadratic Lyapunov function. Thus, the proposed consensus protocol can be applicable to more general networked multi-agent systems, particularly when the bidirectional and/or balanced information exchanges between agents are not required. Under the proposed protocol, it is proved that the state of each agent converges in mean square to a common random variable whose mathematical expectation is the weighted average of agents＇ initial state values; meanwhile, the random variable＇s variance is bounded.     

Linear generalized synchronization of chaotic systems with uncertain parameters

A more general form of projective synchronization, so called linear generalized synchronization （LGS） is proposed, which includes the generalized projective synchronization （GPS） and the hybrid projective synchronization （HPS） as its special cases, Based on the adaptive technique and Lyapunov stability theory, a general method for achieving the LGS between two chaotic or hyperehaotic systems with uncertain parameters in any scaling matrix is presented. Some numerical simulations are provided to show the effectiveness and feasibility of the proposed synchronization method.     

Robust bounded control for uncertain flight dynamics using disturbance observer

The robust bounded flight control scheme is developed for the uncertain longitudinal flight dynamics of the fighter with control input saturation invoking the backstepping technique. To enhance the disturbance rejection ability of the robust flight control for fighters, the sliding mode disturbance observer is designed to estimate the compounded disturbance including the unknown external disturbance and the effect of the control input saturation. Based on the backstepping technique and the compounded disturbance estimated output, the robust bounded flight control scheme is proposed for the fighter with the unknown external disturbance and the control input saturation. The closed-loop system stability under the developed robust bounded flight control scheme is rigorously proved using the Lyapunov method and the uniformly asymptotical convergences of all closed-loop signals are guaranteed. Finally, simulation results are presented to show the effectiveness of the proposed robust bounded flight control scheme for the uncertain longitudinal flight dynamics of the fighter.     

Adaptive fuzzy controller for a class of strict-feedback nonaffine nonlinear systems

A robust adaptive fuzzy control scheme is presented for a class of strict-feedback nonaffine nonlinear systems with modeling uncertainties and external disturbances by using a backstepping approach.Fuzzy logic systems are employed to approximate the unknown parts of the desired virtual controls,and the approximation errors of fuzzy systems are only required to be norm-bounded.The function tanh(·) is introduced to avoid problems associated with sgn(·).The tracking error is guaranteed to be uniformly ultimately bounded with the aid of an additional adaptive compensation term.Chua’s circuit system and R o¨ssler system are presented to illustrate the feasibility and effectiveness of the proposed control technique.     

Stability of stochastic switched epidemic systems with discrete or distributed time delay

Stochastic switched epidemic systems with a discrete or distributed time delay are constructed and investigated. By the Lyapunov method and lto＇s differential rule, the existence and uniqueness of global positive solution of each system is proved. And stability conditions of the disease-free equilibrium of the systems are obtained. Numerical simulations are presented to illustrate the results.     

Enhanced two-loop model predictive control design for linear uncertain systems

Model predictive controllers(MPC)with the two-loop scheme are successful approaches practically and can be classified into two main categories,tube-based MPC and MPCbased reference governors(RG).In this paper,an enhanced twoloop MPC design is proposed for a pre-stabilized system with the bounded uncertainty subject to the input and state constraints.The proposed method offers less conservatism than the tube-based MPC methods by enlarging the restricted input constraint.Contrary to the MPC-based RGs,the investigated method improves tracking performance of the pre-stabilized system while satisfying the constraints.Additionally,the robust global asymptotic stability of the closed-loop system is guaranteed in a novel procedure with terminal constraint relaxation.Simulation of the proposed method on a servo system shows its effectiveness in comparison to the others.     

FBFN-based adaptive repetitive control of nonlinearly parameterized systems

An adaptive repetitive control scheme is presented for a class of nonlinearly parameterized systems based on the fuzzy basis function network （FBFN）. The parameters of the fuzzy rules are tuned with adaptive schemes. To attenuate chattering effectively, the discontinuous control term is approximated by an adaptive PI control structure. The bound of the discontinuous control term is assumed to be unknown and estimated by an adaptive mechanism. Based on the Lyapunov stability theory, an adaptive repetitive control law is proposed to guarantee the closed-loop stability and the tracking performance. By means of FBFNs, which avoid the nonlinear parameterization from entering into the adaptive repetitive control, the controller singularity problem is solved. The proposed approach does not require an exact structure of the system dynamics, and the proposed controller is utilized to control a model of permanent-magnet linear synchronous motor subject to significant disturbances and parameter uncertainties. The simulation results demonstrate the effectiveness of the proposed method.     

Anti-synchronization of Chaotic Neural Networks with Time Delay

In the paper, the anti-synchronization problem of the general delayed chaotic neural networks is investigated. For the master and slave systems, we obtain a control law to achieve the state anti-synchronization of two identical chaotic neural networks. By using the Halanay inequality lemma and Lyapunov stability method, we derive a delay indepen- dent sufficient exponential anti-synchronization condition relative to the parameters of the systems and controller gain matrix. The condition is easily verified in practice. Finally, the theoretical results are applied to two delayed chaotic neural networks, and numerical simulations are given to demonstrate the performance of the proposed scheme throughout some examples.     

Trajectory linearization control of an aerospace vehicle based on RBF neural network

An enhanced trajectory linearization control （TLC） structure based on radial basis function neural network （RBFNN） and its application on an aerospace vehicle （ASV） flight control system are presensted. The influence of unknown disturbances and uncertainties is reduced by RBFNN thanks to its approaching ability, and a robustifying itera is used to overcome the approximate error of RBFNN. The parameters adaptive adjusting laws are designed on the Lyapunov theory. The uniform ultimate boundedness of all signals of the composite closed-loop system is proved based on Lyapunov theory. Finally, the flight control system of an ASV is designed based on the proposed method. Simulation results demonstrate the effectiveness and robustness of the designed approach.     

Adaptive fuzzy sliding mode control for robotic airship with model uncertainty and external disturbance

An adaptive fuzzy sliding mode control (AFSMC) approach is proposed for a robotic airship.First,the mathematical model of an airship is derived in the form of a nonlinear control system.Second,an AFSMC approach is proposed to design the attitude control system of airship,and the global stability of the closed-loop system is proved by using the Lyapunov stability theorem.Finally,simulation results verify the effectiveness and robustness of the proposed control approach in the presence of model uncertainties and external disturbances.     

Impulsive controller design for nonlinear networked control systems with time delay and packet dropouts

The globally exponential stability of nonlinear impulsive networked control systems(NINCS) with time delay and packet dropouts is investigated.By applying Lyapunov function theory,sufficient conditions on the global exponential stability are derived by introducing a comparison system and estimating the corresponding Cauchy matrix.An impulsive controller is explicitly designed to achieve exponential stability and ensure state converge with a given decay rate for the system.The Lorenz oscillator system is presented as a numerical example to illustrate the theoretical results and effectiveness of the proposed controller design procedure.     

Fixed-Time Controller Design for a Quadrotor UAV with Asymmetric Output Error Constraints

In this article, a fixed-time tracking control strategy is proposed for a quadrotor UAV(QUAV) with external disturbance and asymmetric output error constraints. Firstly, a dynamic model of the QUAV is transformed into a strict feedback system with external disturbance, and it is decoupled into attitude subsystem and position subsystem for simplifying controller design. Secondly,an asymmetric tangent barrier Lyapunov function(ATBLF) is applied to solve the tracking error constraints problem, and ...     

The Dynamics and Control of the Fractional Forms of Some Rational Chaotic Maps

This paper proposes three fractional discrete chaotic systems based on the Rulkov, Chang,and Zeraoulia–Sprott rational maps. The dynamics of the proposed maps are investigated by means of phase plots and bifurcations diagrams. Adaptive stabilization schemes are proposed for each of the three maps and the convergence of the states is established by using the Lyapunov method. Furthermore, a combination synchronization scheme is proposed whereby a combination of the fractional Rulkov and Chang maps is synchronized to the fractional Zeraoulia-Sprott map. Numerical results are used to confirm the findings of the paper.     

Fault detection of switched linear systems with its application to turntable systems

This paper is concerned with the H∞ fault detection for continuous-time linear switched systems with its application to turntable systems.The solvability condition for a desired filter is established based on the proposed sufficient condition.Based on the double channel scheme of the turntable control system,the turntable system can be modeled as a switched system.Finally,by taking the turntable system as a numerical example,the effectiveness of the proposed theory is well validated.     

SOFT CONTROL ON COLLECTIVE BEHAVIOR OF A GROUP OF AUTONOMOUS AGENTS BY A SHILL AGENT

This paper asks a new question： how can we control the collective behavior of self-organized multi-agent systems？ We try to answer the question by proposing a new notion called ＇Soft Control＇ which keeps the local rule of the existing agents in the system. We show the feasibility of soft control by a case study. Consider the simple but typical distributed multi-agent model proposed by Vicsek et al. for flocking of birds： each agent moves with the same speed but with different headings which are updated using a local rule based on the average of its own heading and the headings of its neighbors. Most studies of this model are about the self-organized collective behavior, such as synchronization of headings. We want to intervene in the collective behavior （headings） of the group by soft control. A specified method is to add a special agent, called a ＇Shill＇, which can be controlled by us but is treated as an ordinary agent by other agents. We construct a control law for the shill so that it can synchronize the whole group to an objective heading. This control law is proved to be effective analytically and numerieally. Note that soft control is different from the approach of distributed control. It is a natural way to intervene in the distributed systems. It may bring out many interesting issues and challenges on the control of complex systems.     

Robust reliable guaranteed cost control for nonlinear singular stochastic systems with time delay

To study the design problem of robust reliable guaranteed cost controller for nonlinear singular stochastic systems, the Takagi-Sugeno （T-S） fuzzy model is used to represent a nonlinear singular stochastic system with norm-bounded parameter uncertainties and time delay. Based on the linear matrix inequality （LMI） techniques and stability theory of stochastic differential equations, a stochastic Lyapunov function method is adopted to design a state feedback fuzzy controller. The resulting closed-loop fuzzy system is robustly reliable stochastically stable, and the corresponding quadratic cost function is guaranteed to be no more than a certain upper bound for all admissible uncertainties, as well as different actuator fault cases. A sufficient condition of existence and design method of robust reliable guaranteed cost controller is presented. Finally, a numerical simulation is given to illustrate the effectiveness of the proposed method.