Observer-based robust predictive control of singular systems with time-delay and parameter uncertainties

The problem of observer-based robust predictive control is studied for the singular systems with norm-bounded uncertainties and time-delay, and the design method of robust predictive observer-based controller is proposed. By constructing the Lyapunov function with the error terms, the infinite time domain ＂min-max＂ optimization problems are converted into convex optimization problems solving by the linear matrix inequality （LMI）, and the sufficient conditions for the existence of this control are derived. It is proved that the robust stability of the closed-loop singular systems can be guaranteed by the initial feasible solutions of the optimization problems, and the regular and the impulse-free of the singular systems are also guaranteed. A simulation example illustrates the efficiency of this method.

Consensus of second-order nonlinear multi-agent systems via sliding mode observer and controller

This paper investigates the consensus problem of second-order nonlinear multi-agent systems (MASs) via the sliding mode control (SMC) approach. The velocity of each agent is assumed to be unmeasurable. A second-order sliding mode observer is designed to estimate the velocity. Then a distributed discontinuous control law based on first-order SMC is presented to solve the consensus problem. Moreover, to overcome the chatting problem, two controllers based on the boundary layer method and the super-twisting algorithm respectively are presented. It is shown that the MASs will achieve consensus under some given conditions. Some examples are provided to demonstrate the effectiveness of the proposed control laws.

Adaptive Fuzzy Observer Backstepping Control for a Class of Uncertain Nonlinear Systems with Unknown Time-delay

In this paper, a new adaptive fuzzy backstepping control approach is developed for a class of nonlinear systems with unknown time-delay and unmeasured states. Using fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy state observer is designed for estimating the unmeasured states. On the basis of the state observer and applying the backstepping technique, an adaptive fuzzy observer control approach is developed. The main features of the proposed adaptive fuzzy control approach not only guarantees that all the signals of the closed-loop system are semiglobally uniformly ultimately bounded, but also contain less adaptation parameters to be updated on-line. Finally, simulation results are provided to show the effectiveness of the proposed approach.

Robust H_∞ Controller Design for Uncertain Neutral Systems via Dynamic Observer Based Output Feedback

In this paper, the dynamic observer-based controller design for a class of neutral systems with H∞ control is considered. An observer-based output feedback is derived for systems with polytopic parameter uncertainties. This controller assures delay-dependent stabilization and H∞ norm bound attenuation from the disturbance input to the controlled output. Numerical examples are provided for illustration and comparison of the proposed conditions.

Feedforward and feedback optimal control for linear time-varying systems with persistent disturbances

The optimal control problem for linear time-varying systems affected by external persistent disturbances with known dynamic characteristics but unknown initial conditions is consider and a design procedure of a feedforward and feedbaek optimal controller is presented. The condition of existence and uniqueness of the control law is given. The disturbanee observer is proposed to make the feedforward control law realizable physically. Simulation results demonstrate that the feedforward and feedbaek optimal control law is more effective and robust than the elassical state feedbaek control law with respect to external disturbanees.

Reduced-Order Observer-Based Leader-Following Formation Control for Discrete-Time Linear Multi-Agent Systems

Formation control of discrete-time linear multi-agent systems using directed switching topology is considered in this work via a reduced-order observer, in which a formation control protocol is proposed under the assumption that each directed communication topology has a directed spanning tree. By utilizing the relative outputs of neighboring agents, a reduced-order observer is designed for each following agent. A multi-step control algorithm is established based on the Lyapunov method and the modified discrete-time algebraic Riccati equation. A sufficient condition is given to ensure that the discrete-time linear multi-agent system can achieve the expected leader-following formation.Finally, numerical examples are provided so as to demonstrate the effectiveness of the obtained results.

Exact Controllability and Exact Observability of Descriptor Infinite Dimensional Systems

Necessary and sufficient conditions for the exact controllability and exact observability of a descriptor infinite dimensional system are obtained in the sense of distributional solution.These general results are used to examine the exact controllability and exact observability of the Dzektser equation in the theory of seepage and the exact controllability of wave equation.

Controllability and observability of networked control systems with time-varying delays

The controllability and observability of networked control systems are studied. Aiming at the networked control system with time-varying delay, the sufficient and necessary conditions for complete controllability and complete observability of the system are presented, respectively. Because of Markov characteristic of the network-induced delay, in terms of stochastic theory, a sufficient and necessary condition for completely mean value controllability of networked control systems is obtained. Further, the conditions that the controllability and observability of networked control systems are equivalent to the initial time-invariant system are given. Controllability and observability realization indexes are also discussed, respectively. The numerical example demonstrates the effectiveness of the proposed theory.

Observer-based Adaptive Optimal Control for Unknown Singularly Perturbed Nonlinear Systems With Input Constraints

This paper introduces an observer-based adaptive optimal control method for unknown singularly perturbed nonlinear systems with input constraints. First, a multi-Time scales dynamic neural network MTSDNN observer with a novel updating law derived from a properly designed Lyapunov function is proposed to estimate the system states. Then, an adaptive learning rule driven by the critic NN weight error is presented for the critic NN, which is used to approximate the optimal cost function. Finally, the optimal control action is calculated by online solving the Hamilton-Jacobi-Bellman HJB equation associated with the MTSDNN observer and critic NN. The stability of the overall closed-loop system consisting of the MTSDNN observer, the critic NN and the optimal control action is proved. The proposed observer-based optimal control approach has an essential advantage that the system dynamics are not needed for implementation, and only the measured input U+002F output data is needed. Moreover, the proposed optimal control design takes the input constraints into consideration and thus can overcome the restriction of actuator saturation. Simulation results are presented to confirm the validity of the investigated approach. © 2014 Chinese Association of Automation.

Stability analysis and controller design for a class of delay systems via observer based on network

This paper focuses on the problem of stability analysis and controller design for a class of delay systems based on networked control systems. By introducing some free matrix variables, some criteria for stability analysis and observer-based control law design can be obtained by the solving of linear matrix inequalities. A numerical example is also offered to prove the effectiveness of the proposed method.

Fault detection for nonlinear networked control systems based on fuzzy observer

Security and reliability must be focused on control sys- tems firstly, and fault detection and diagnosis （FDD） is the main theory and technology. Now, there are many positive results in FDD for linear networked control systems （LNCSs）, but nonlinear networked control systems （NNCSs） are less involved. Based on the T-S fuzzy-modeling theory, NNCSs are modeled and network random time-delays are changed into the unknown bounded uncertain part without changing its structure. Then a fuzzy state observer is designed and an observer-based fault detection approach for an NNCS is presented. The main results are given and the relative theories are proved in detail. Finally, some simulation results are given and demonstrate the proposed method is effective.

An observer based asymptotic trajectory control using a scalar state for chaotic systems

A state-observer based full-state asymptotic trajectory control （OFSTC） method requiring a scalar state is presented to asymptotically drive all the states of chaotic systems to arbitrary desired trajectories. It is no surprise that OFSTC can obtain good tracking performance as desired due to using a state-observer. Significantly OFSTC requires only a scalar state of chaotic systems. A sinusoidal wave and two chaotic variables were taken as illustrative tracking trajectories to validate that using OFSTC can make all the states of a unified chaotic system track the desired trajectories with high tracking accuracy and in a finite time. It is noted that this is the first time that the state-observer of chaotic systems is designed on the basis of Kharitonov＇s Theorem.

Observer-based H-infinity output feedback control with feedback gain and observer gain variations for Delta operator system

Considering that the controller feedback gain and the observer gain are of additive norm-bounded variations, a design method of observer-based H-infinity output feedback controller for uncertain Delta operator systems is proposed in this paper. A sufficient condition of such controllers is presented in linear matrix inequality （LMI） forms. A numerical example is then given to illustrate the effectiveness of this method, that is, the obtained controller guarantees the closed-loop system asymptotically stable and the expected H-infinity performance even if the controller feedback gain and the observer gain are varied.

Fault diagnosis and accommodation for linear parameter-varying in flight control systems

The fault diagnosis and accommodation strategy for a class of linear parameter-varying (LPV) systems were investigated. A fast adaptive fault estimation (FAFE) algorithm for LPV systems module, based on an adaptive observer, proposed to enhance the performance of fault estimation including rapidity and accuracy. Then, the obtained fault estimate was used to construct the fault tolerant control (FTC) law. The design method was formulated as a convex linear matrix inequalities (LMIs) optimization problem. Once the faults are estimated, the fault tolerant controller is implemented as a dynamic output feedback controller. This controller can compensate for the effect of the faults by stabilizing the closed-loop systems. Finally, a helicopter model in a vertical flight with actuator fault was used to the effectiveness of the proposed approach.

Controllability, Observability and Stability for a Class of Fractional-Order Linear Time-Invariant Control Systems

The definitions of controllability, observability and stability were presented for fractional-order linear systems. Using the Cayley-Hamilton theorem and Mittag-Leffler function in two parameters, the sufficient and necessary conditions of controllability and observability for such systems were derived. In terms of Lyapunov’s stability theory, using the theorems of Mittage-Leffler function in two parameters this paper directly derived the sufficient and necessary condition of stability for such systems. The results obtained are useful for the analysis and synthesis of fractional-order linear control systems.

Adaptive Learning with Large Variability of Teaching Signals for Neural Networks and Its Application to Motion Control of an Industrial Robot

Recently, various control methods represented by proportional-integral-derivative （PID） control are used for robotic control. To cope with the requirements for high response and precision, advanced feedforward controllers such as gravity compensator, Coriolis/centrifugal force compensator and friction compensators have been built in the controller. Generally, it causes heavy computational load when calculating the compensating value within a short sampling period. In this paper, integrated recurrent neural networks are applied as a feedforward controller for PUMA560 manipulator. The feedforward controller works instead of gravity and Coriolis/centrifugal force compensators. In the learning process of the neural network by using back propagation algorithm, the learning coefficient and gain of sigmoid function are tuned intuitively and empirically according to teaching signals. The tuning is complicated because it is being conducted by trial and error. Especially, when the scale of teaching signal is large, the problem becomes crucial. To cope with the problem which concerns the learning performance, a simple and adaptive learning technique for large scale teaching signals is proposed. The learning techniques and control effectiveness are evaluated through simulations using the dynamic model of PUMA560 manipulator.

Observer-Based Nonlinear Feedback Controls for Heartbeat ECG Tracking Systems

The analysis and design of observed-based nonlinear control of a heartbeat tracking system is investigated in this paper. Two of Zeeman’s heartbeat models are investigated and modified by adding the control input as a pacemaker, thereby creating the control-affine nonlinear system models that capture the general heartbeat behavior of the human heart. The control objective is to force the output of the heartbeat models to track and generate a synthetic electrocardiogram (ECG) signal based on the actual patient reference data, obtained from the William Beaumont Hospitals, Michigan, and the PhysioNet database. The formulations of the proposed heartbeat tracking control systems consist of two phases: analysis and synthesis. In the analysis phase, nonlinear controls based on input-output feedback linearization are considered. This approach simplifies the difficult task of developing nonlinear controls. In the synthesis phase, observer-based controls are employed, where the unmeasured state variables are estimated for practical implementations. These observer-based nonlinear feedback control schemes may be used as a control strategy in electronic pacemakers. In addition, they could be used in a software-based approach to generate a synthetic ECG signal to assess the effectiveness of diagnostic ECG signal processing devices.

Function Observer Based Event-triggered Control for Linear Systems with Guaranteed L_∞-Gain

This paper is devoted to event-triggered control design for linear systems based on function observer. More specifically, the main purpose is to design event-triggered mechanisms that trigger transmissions when the difference between the current value of the system and its previously transmitted value which includes the plant output or the function observer output exceeds an additional threshold. For such an eventtriggered mechanism, we derive conditions in terms of matrix inequality to guarantee the stability as well as longer inter-event time. We propose two approaches to investigate the closed-loop model, namely, reformulating the event-triggered control system as a hybrid system and interpreting the event-induced error as exogenous disturbance. Furthermore, the minimum inter-event time is guaranteed to be strictly positive. An example is presented to illustrate the feasibility and efficiency of the theoretic results. © 2014 Chinese Association of Automation.

Observer-based adaptive control of uncertain time-delay switched systems with stuck actuator faults

This paper concerns the observer-based adaptive control problem of uncertain time-delay switched systems with stuck actuator faults. Under the case where the original controller cannot stabilize the faulty system, multiple adaptive controllers are designed and a suitable switching logic is incorporated to ensure the closed-loop system stability and state tracking. New delay-independent sufficient conditions for asymptotic stability are obtained in terms of linear matrix inequalities based on piecewise Lyapunov stability theory. On the other hand, adaptive laws for on-line updating of some of the controller parameters are also designed to compensate the effect of stuck failures. Finally, simulation results for reference [1] model show that the design is feasible and efficient.