An LMI approach to robust H-infinity control for uncertain singular time-delay systems

The problem of robust H-infinity control for a class of uncertain singular time-delay systems is studied in this paper. A new approach is proposed to describe the relationship between slow and fast subsystems of singular time- delay systems, based on which, a sufficient condition is presented for a singular time-delay system to be regular, impulse free and stable with an H-infinity performance. The robust H-infinity control problem is solved and an explicit expression of the desired state-feedback control law is also given. The obtained results are formulated in terms of strict linear matrix inequalities （LMIs） involving no decomposition of system matrices. A numerical example is given to show the effectiveness of the proposed method.

Observer-based robust H-infinity control for uncertain switched systems

The problem of observer-based robust H-infinity control is addressed for a class of linear discrete-time switched systems with time-varying norm-bounded uncertainties by using switched Lyapunov function method. None of the individual subsystems is assumed to be robustly H-infinity solvable. A novel switched Lypunov function matrix with diagonal-block form is devised to overcome the difficulties in designing switching laws. For robust H-infinity stability analysis, two linear-matrix-inequality-based sufficient conditions are derived by only using the smallest region function strategy if some parameters are preselected. Then, the robust H-infinity control synthesis is studied using a switching state feedback and an observer-based switching dynamical output feedback. All the switching laws are simultaneously constructively designed. Finally, a simulation example is given to illustrate the validity of the results.

H-infinity control for cascade minimum-phase switched nonlinear systems

This paper is concerned with the H-infinity control problem for a class of cascade switched nonlinear systems. Each switched system in this class is composed of a zero-mput asymptotically stable nonlinear part, which is also a switched system, and a linearizable part which is controllable. Conditions under which the H-infinity control problem is solvable under arbitrary switching law and under some designed switching law are derived respectively. The nonlinear state feedback and switching law are designed. We exploit the structural characteristics of the switched nonlinear systems to construct common Lyapunov functions for arbitrary switching and to find a single Lyapunov function for designed switching law. The proposed methods do not rely on the solutions of Hamilton-Jacobi inequalities.

Robust adaptive dynamic surface control for nonlinear uncertain systems

We propose a new method for robust adaptive backstepping control of nonlinear systems with parametric uncertainties and disturbances in the strict feedback form. The method is called dynamic surface control. Traditional backstepping algorithms require repeated differentiations of the modelled nonlinearities. The addition of n first order low pass filters allows the algorithm to be implemented without differentiating any model nonlinearities, thus ending the complexity arising due to the 'explosion of terms' that makes other methods difficult to implement in practice. The combined robust adaptive backstepping/first order filter system is proved to be semiglobally asymptotically stable for sufficiently fast filters by a singular perturbation approach. The simulation results demonstrate the feasibility and effectiveness of the controller designed by the method.

Adaptive Robust Servo Control for Vertical Electric Stabilization System of Tank and Experimental Validation

A tracking stability control problem for the vertical electric stabilization system of moving tank based on adaptive robust servo control is addressed.This paper mainly focuses on two types of possibly fast timevarying but bounded uncertainty within the vertical electric stabilization system:model parameter uncertainty and uncertain nonlinearity.First,the vertical electric stabilization system is constructed as an uncertain nonlinear dynamic system that can reflect the practical mechanics transfer process of the system.Second,the dynamical equation in the form of state space is established by designing the angular tracking error.Third,the comprehensive parameter of system uncertainty is designed to estimate the most conservative effects of uncertainty.Finally,an adaptive robust servo control which can effectively handle the combined effects of complex nonlinearity and uncertainty is proposed.The feasibility of the proposed control strategy under the practical physical condition is validated through the tests on the experimental platform.This paper pioneers the introduction of the internal nonlinearity and uncertainty of the vertical electric stabilization system into the settlement of the tracking stability control problem,and validates the advanced servo control strategy through experiment for the first time.

Adaptive Robust Control for a Class of Uncertain MIMO Non-affine Nonlinear Systems

In this paper, the adaptive robust tracking control scheme is proposed for a class of multi-input and multi-output (MIMO) non-affine systems with uncertain structure and parameters, unknown control direction and unknown external disturbance based on backstepping technique. The MIMO non-affine system is first transformed into a time-varying system with strict feedback structure using the mean value theorem, and then the bounded time-varying parameters are estimated by adaptive algorithms with projection. To handle the possible 'controller singularity' problem caused by unknown control direction, a Nussbaum function is employed, and the dynamic surface control (DSC) method is applied to solve the problem of 'explosion of complexity' in backstepping control. It is proved that the proposed control scheme can guarantee that all signals of the closed-loop system are bounded through Lyapunov stability theorem and decoupled backstepping method. Simulation results are presented to illustrate the effectiveness of the proposed control scheme. © 2014 Chinese Association of Automation.

Global robust optimal sliding mode control for uncertain affine nonlinear systems

The problem of robustifying linear quadratic regulators （LQRs） for a class of uncertain affine nonlinear systems is considered. First, the exact linearization technique is used to transform an uncertain nonlinear system into a linear one and an optimal LQR is designed for the corresponding nominal system. Then, based on the integral sliding mode, a design approach to robustifying the optimal regulator is studied. As a result, the system exhibits global robustness to uncertainties and the ideal sliding mode dynamics is the same as that of the optimal LQR for the nominal system. A global robust optimal sliding mode control （GROSMC） is realized. Finally, a numerical simulation is demonstrated to show the effectiveness and superiority of the proposed algorithm compared with the conventional optimal LQR.

Robust adaptive fuzzy tracking control for a class of strict-feedback nonlinear systems based on backstepping technique

In this paper, the robust adaptive fuzzy tracking control problem is discussed for a class of perturbed strict-feedback nonlinear systems. The fuzzy logic systems in Mamdani type are used to approximate unknown nonlinear functions. A design scheme of the robust adaptive fuzzy controller is proposed by use of the backstepping technique. The proposed controller guarantees semi-global uniform ultimate boundedness of all the signals in the derived closed-loop system and achieves the good tracking performance. The possible controller singularity problem which may occur in some existing adaptive control schemes with feedback linearization techniques can be avoided. In addition, the number of the on-line adaptive parameters is not more than the order of the designed system. Finally, two simulation examples are used to demonstrate the effectiveness of the proposed control scheme.

Robust fault detection for a class of nonlinear network control system with communication delay

To investigate a class of nonlinear network control system, a robust fault diagnosis method is presented based on the robust state observer. To access the objective that the designed robust filter is maximally tolerant to disturbances and sensitive to fault, the robustness and stability properties of the fault diagnosis scheme are established rigorously. Using the residual vector, a fault tolerant controller is established in order to guarantee the stability of the closed-loop system, and the controller law can be obtained by solving a set of linear matrix inequalities. Then, some relevant sufficient conditions for the existence of a solution are given by applying Lyapunov stability theory. Finally, a simulation example is performed to show the effectiveness of the proposed approach.

Robust Control for Uncertain Nonlinear Feedback Systems Using Operator-based Right Coprime Factorization

The robust control issue for uncertain nonlinear system is discussed by using the method of right coprime factorization. As it is difficult to obtain the inverse of the right factor due to the high nonlinearity, the proving of the Bezout identity becomes troublesome. Therefore, two sufficient conditions are derived to manage this problem with the nonlinear feedback system as well as that with the uncertain nonlinear feedback system under the definition of Lipschitz norm. A simulation of temperature control is given to demonstrate the validity of the proposed method.

Robust adaptive fuzzy control for a class of perturbed pure-feedback nonlinear systems

A new design scheme of direct adaptive fuzzy controller for a class of perturbed pure-feedback nonlinear systems is proposed. The design is based on backstepping and the approximation capability of the first type fuzzy systems. A continuous robust term is adopted to minify the influence of modeling errors or disturbances. By introducing the modified integral-type Lyapunov function, the approach is able to avoid the requirement of the upper bound of the first time derivation of the high frequency control gain. Through theoretical analysis, the closed-loop control system is proven to be semi-globally uniformly ultimately bounded, with tracking error converging to a residual set.

Robust Fuzzy Tracking Control for Nonlinear Networked Control Systems with Integral Quadratic Constraints

This paper investigates the robust tracking control problcm for a class of nonlinear networked control systems （NCSs） using the Takagi-Sugeno （T-S） fuzzy model approach. Based on a time-varying delay system transformed from the NCSs, an augmented Lyapunov function containing more useful information is constructed. A less conservative sufficient condition is established such that the closed-loop systems stability and time-domain integral quadratic constraints （IQCs） are satisfied while both time-varying network- induced delays and packet losses are taken into account. The fuzzy tracking controllers design scheme is derived in terms of linear matrix inequalities （LMIs） and parallel distributed compensation （PDC）. Furthermore, robust stabilization criterion for nonlinear NCSs is given as an extension of the tracking control result. Finally, numerical simulations are provided to illustrate the effectiveness and merits of the proposed method.

μ ANALYSIS AND μ SYNTHESIS FOR NONLINEAR ROBUST CONTROL SYSTEMS

A μ analysis and μ synthesis method for nonlinear robust control systems was presented. The nonlinear robust contrl problem using μ method was described. By means of the nonlinear state feedback and state coordinates transformation, many uncertain nonlinear systems can be transformed as a linear fractional transformation (LFT) on the generalized plant and the uncertainty. Based on the LFT, a linear robust controller can be obtained by the DK iteration and then a corresponding nonlinear robust control law is constructed. An example was given in the paper.

H-infinity control for networked control systems (NCS) with time-varying delays

This paper discusses H-infinity state feedback control for a networked control system with time-varying delays. Based on the flee-weighing matrix method, a dehy-dependent stability criterion satisfying a prescribed H-infinity norm bound is presented for an NCS with unknown, time-varying and bounded delays. And then, the criterion is transformed into sufficient conditions based on linear matrix inequalities for H-infinity control. The conditions thus obtained are also used to design an H-infinity state feedback controller. This design method is further extended to solve the design problem of robust H-infinity state feedback control. A numerical example demonstrates the validity of the method.

Operator-Based Robust Nonlinear Free Vibration Control of a Flexible Plate With Unknown Input Nonlinearity

In this paper,a robust nonlinear free vibration control design using an operator based robust right coprime factorization approach is considered for a flexible plate with unknown input nonlinearity.With considering the effect of unknown input nonlinearity from the piezoelectric actuator,operator based controllers are designed to guarantee the robust stability of the nonlinear free vibration control system.Simultaneously,for ensuring the desired tracking performance and reducing the effect of unknown input nonlinearity,operator based tracking compensator and estimation structure are given,respectively.Finally,both simulation and experimental results are shown to verify the effectiveness of the proposed control scheme.

Operator-Based Robust Nonlinear Control for SISO and MIMO Nonlinear Systems With PI Hysteresis

In this paper, operator based robust nonlinear control for single-input single-output(SISO) and multi-input multi-output(MIMO) nonlinear uncertain systems preceded by generalized Prandtl-Ishlinskii(PI) hysteresis is considered respectively. In detail, by using operator based robust right coprime factorization approach, the control system design structures including feedforward and feedback controllers for both SISO and MIMO nonlinear uncertain systems are given, respectively.In which, the controller design includes the information of PI hysteresis and its inverse, and some sufficient conditions for the controllers in both SISO and MIMO systems should be satisfied are also derived respectively. Based on the proposed conditions, influence from hysteresis is rejected, the systems are robustly stable and output tracking performance can be realized.Finally, the effectiveness of the proposed method is confirmed by numerical simulations.

Robust Tracking Control of Uncertain MIMO Nonlinear Systems with Application to UAVs

In this paper, we consider the robust adaptive tracking control of uncertain multi-input and multi-output (MIMO) nonlinear systems with input saturation and unknown external disturbance. The nonlinear disturbance observer (NDO) is employed to tackle the system uncertainty as well as the external disturbance. To handle the input saturation, an auxiliary system is constructed as a saturation compensator. By using the backstepping technique and the dynamic surface method, a robust adaptive tracking control scheme is developed. The closed-loop system is proved to be uniformly ultimately bounded thorough Lyapunov stability analysis. Simulation results with application to an unmanned aerial vehicle (UAV) demonstrate the effectiveness of the proposed robust control scheme. © 2014 Chinese Association of Automation.

Robust Optimization-Based Iterative Learning Control for Nonlinear Systems With Nonrepetitive Uncertainties

This paper aims to solve the robust iterative learning control(ILC)problems for nonlinear time-varying systems in the presence of nonrepetitive uncertainties.A new optimization-based method is proposed to design and analyze adaptive ILC,for which robust convergence analysis via a contraction mapping approach is realized by leveraging properties of substochastic matrices.It is shown that robust tracking tasks can be realized for optimization-based adaptive ILC,where the boundedness of system trajectories and estimated parameters can be ensured,regardless of unknown time-varying nonlinearities and nonrepetitive uncertainties.Two simulation tests,especially implemented for an injection molding process,demonstrate the effectiveness of our robust optimization-based ILC results.

Event-triggered robust guaranteed cost control for two-dimensional nonlinear discrete-time systems

An event-triggered scheme is proposed to solve the problems of robust guaranteed cost control for a class of two-dimensional(2-D)discrete-time systems.Firstly,an eventtriggered scheme is proposed for 2-D discrete-time systems with parameter uncertainties and sector nonlinearities.Then,according to the Lyapunov functional method,the sufficient conditions for the existence of event-triggered robust guaranteed cost controller for 2-D discrete-time systems with parameter uncertainties and sector nonlinearities are given.Furthermore,based on the sufficient conditions and the linear matrix inequality(LMI)technique,the problem of designing event-triggered robust guaranteed cost controller is transformed into a feasible solution problem of LMI.Finally,a numerical example is given to demonstrate that,under the proposed event-triggered robust guaranteed cost control,the closed-loop system is asymptotically stable and fewer communication resources are occupied.

Robust Output Feedback Control for Fractional Order Nonlinear Systems with Time-varying Delays

Robust controller design problem is investigated for a class of fractional order nonlinear systems with time varying delays. Firstly, a reduced-order observer is designed. Then, an output feedback controller is designed. Both the designed observer and controller are independent of time delays. By choosing appropriate Lyapunov functions, we prove the designed controller can render the fractional order system asymptotically stable. A simulation example is given to verify the effectiveness of the proposed approach. © 2014 Chinese Association of Automation.