Adaptive Variable Structure Control of MIMO Nonlinear Systems with Time-varying Delays and Unknown Dead-zones

In this paper, adaptive variable structure neural control is presented for a class of uncertain multi-input multi-output （MIMO） nonlinear systems with state time-varying delays and unknown nonlinear dead-zones. The unknown time-varying delay uncer- tainties are compensated for using appropriate Lyapunov-Krasovskii functionals in the design. The approach removes the assumption of linear function outside the deadband without necessarily constructing a dead-zone inverse as an added contribution. By utilizing the integral-type Lyapunov function and introducing an adaptive compensation term for the upper bound of the residual and optimal approximation error as well as the dead-zone disturbance, the closed-loop control system is proved to be semi-globally uniformly ultimately bounded. In addition, a modified adaptive control algorithm is given in order to avoid the high-frequency chattering phenomenon. Simulation results demonstrate the effectiveness of the approach.

Variable structure control with sliding mode prediction for discrete-time nonlinear systems

A new variable structure control algorithm based on sliding mode prediction for a class of discrete-time nonlinear systems is presented. By employing a special model to predict future sliding mode value, and combining feedback correction and receding horizon optimization methods which are extensively applied on predictive control strategy, a discrete-time variable structure control law is constructed. The closed-loop systems are proved to have robustness to uncertainties with unspecified boundaries. Numerical simulation and pendulum experiment results illustrate that the closed-loop systems possess desired performance, such as strong robustness, fast convergence and chattering elimination.

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.

Stabilization of nonlinear systems based on robust control Lyapunov function

This paper deals with the robust stabilization problem for a class of nonlinear systems with structural uncertainty. Based on robust control Lyapunov function, a sufficient and necessary condition for a function to be a robust control Lyapunov function is given. From this condition, simply sufficient condition for the robust stabilization （robust practical stabilization） is deduced. Moreover, if the equilibrium of the closed-loop system is unique, the existence of such a robust control Lyapunnv function will also imply robustly globally asymptotical stabilization. Then a continuous state feedback law can be constructed explicitly. The simulation shows the effectiveness of the method.

ROBUST STABILIZATING FOR A OLASS OF UNOERTAIN NONLINEAR INTEROONNECTED SYSTEMS USING VARIABLE STRUCTURE CONTROL

The robust stabilizating control problem for a class of uncertain nonlinear large-scale systems is discussed. Based on the theory of both input/output (I/O) linearization and decentralized variable structure control (VSC),two-level and decentralized variable structure control laws for this kind of systems are presented respectively,which achieve asymptotically stabilization despite the uncertainties and disturbances. At last,sirnulation of the disturbed two-pendulum system is given to illustrate the feasibility of proposed technique.

Control Lyapunov Stabilization of Nonlinear Systems with Structural Uncertainty

This paper deals with global stabilization problem for the nonlinear systems with structural uncertainty. Based on control Lyapunov function, a sufficient and necessary condition for the globally and asymptotically stabilizing the equailibrium of the closed system is given. Moreovery, an almost smooth state feedback control law is constructed. The simulation shows the effectiveness of the method.

Design of Variable Structure Control by Using the L_2 Gain Method

The robust stabilization problem for a family of nonlinear plants with mismatch uncertainties is addressed, and a solution is presented based on variable structure control theory and H∞ control theory. A kind of boundary layer is built near the ideal switch surface which can eliminate chattering in the switch surface. The proposed control method with L2 gain can guarantee exponential stability of a system state with no parameter uncertainty and exter- nal disturbance, while it can guarantee state ultimate boundness if parameter uncertainty and external disturbance exist. In the proposed design method, stability of the closed-loop system is analyzed by adopting the Lyapurtov func- tion approach. Finally the numerical simulation results show that the proposed smooth variable structure controller has good pelformance without chattering in the switch surface.

Adaptive Sliding Mode Control for MIMO Nonlinear Systems Based on Fuzzy Logic Scheme

In this study an indirect adaptive sliding mode control (SMC) based on a fuzzy logic scheme is proposed to strengthen the tracking control performance of a general class of multi-input multi-output (MIMO) nonlinear uncertain systems. Combining reaching law approach and fuzzy universal approximation theorem, the proposed design procedure combines the advantages of fuzzy logic control, adaptive control and sliding mode control. The stability of the control systems is proved in the sense of the Lyapunov second stability theorem. Two simulation studies are presented to demonstrate the effectiveness of our new hybrid control algorithm.

The variable structure controller design for a class of nonlinear uncertain systems based on robust observer

The variable structure controller is designed for a class of nonlinear uncertain time-delay system by using robust observer, and incorporating H-infinity control technique, the controller can guarantee the H-infinity performance of sliding mode dynamics and satisfy the reaching condition, which also does not require uncertainties to satisfy matching condition and linear boundary condition. The simulation example is given to illustrate the method.

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.

Stability Criteria for Large－Scale Linear Systems with Structured Uncertainties

The robust stability analysis for large scale linear systems with structured time varying uncertainties is investigated in this paper.By using the scalar Lyapunov functions and the properties of M matrix and nonnegative matrix,stability robustness measures are proposed.The robust stability criteria obtained are applied to derive an algebric criterion which is expressed directly in terms of plant parameters and is shown to be less conservative than the existing ones.A numerical example is given to demonstrate the stability criteria obtained and to compare them with the previous ones.

Attitude tracking control for variable structure near space vehicles based on switched nonlinear systems

An adaptive robust attitude tracking control law based on switched nonlinear systems is presented for a variable structure near space vehicle （VSNSV） in the presence of uncertainties and disturbances. The adaptive fuzzy systems are employed for approximating unknown functions in the flight dynamic model and their parameters are updated online. To improve the flight robust performance, robust controllers with adaptive gains are designed to compensate for the approximation errors and thus they have less design conservation. Moreover, a systematic procedure is developed for the synthesis of adaptive fuzzy dynamic surface control （DSC） approach. According to the common Lyapunov function theory, it is proved that all signals of the closed-loop system are uniformly ultimately bounded by the continuous controller. The simulation results demonstrate the effectiveness and robustness of the proposed control scheme.

Decentralized Variable Structure Control of Complex Giant Singular Uncertainty Systems

This paper, at the first time, considers the problem of decentralized variable structure control of complex giant singular uncertainty systems by using the property of diagonally dominant matrix and Frobenius-Person theorem. The splendid selection of switching manifold for each subsystem makes the design relatively straightforward and can be easily realized. An illustrate example is given.

Nonlinear and Variable Structure Excitation Controller for Power System Stability

A new nonlinear variable structure excitation controller is proposed. Its design combines the differential geometry theory and the variable structure controlling theory. The mathematical model in the form of ＂an affme nonlinear system＂ is set up for the control of a large-scale power system. The static and dynamic performances of the nonlinear variable structure controller are simulated. The response of system with the controller proposed is compared to that of the nonlinear optimal controller when the system is subjected to a variety of disturbances. Simulation results show that the nonlinear variable structure excitation controller gives more satisfactorily static and dynamic performance and better robustness.

PREDICTIVE VARIABLE STRUCTURE CONTROL FOR A CLASS OF NONLINEAR SYSTEM

Nonlinear sliding m ode predictive controller is designed for a class of nonlinear system w ith unm odeled dynam ic characteristics and nonlinear term . The m ethod is based on nonlinear opti- m alpredictive control. The variable structure controllaw m inim izes the quadratic index ofa predic- tive sliding m ode, w hich contains thecostfunction ofcontrolpreventing the controleffectfrom satu- ration for in m ostpracticalim plem entation the controlinputs are bounded by physicalconstraints and energy constraints. According to the im m easurable states, the variable structure observer for nonlin- ear system sisadapted. The variablestructure system m ethod isaptto therealization ofobserverw ith variable param eters and uncertainty. The proofshow s thatthe states ofthe observer asym ptotically convergence to the realstates ofthe system although itisofuncertainty and nonlinear term s. Final- ly, the digitalsim ulation results prove the effectiveness ofthe proposed m ethod.

TRACKING VARIABLE STRUCTURE CONTROL LAW WITH APPLICATION TO ELECTRO－HYDRAULIC SERVO SYSTEMS

Combining the characteristics of servo systems , tracking variable structure control law is studied. Two kinds of new variable control law , the generalized exponential approaching vari- able structure control law and the integral variable structure control law are put forward for dis- crete time domain. Taking pump-controlled-motor rotational speed servo system for example , the experiment investigation and digital simulation of integral variable structure control law for dis- crete time domain are performed , the rightness of conclusions are verified.

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.

Robust H_∞ controller design for a class of nonlinear fuzzy time-delay systems

The problem of fuzzy modeling for state and input time-delays systems with a class of nonlinear uncertainties by fuzzy T-S model is addressed.By using the linear matrix inequality（LMI） method, the problem of fuzzy robust H ∞ controller design for the system is studied.Assuming that the nonlinear uncertain functions in the model considered are gain-bounded, a sufficient condition for the robustly asymptotic stability of the closed-loop system is obtained via Lyapunov stability theory.By solving the LMI, a feedback control law which guarantees the robustly asymptotic stability of the closed-loop system is constructed and the effect of the disturbance input on the controlled output is ruduced to a prescribed level.

Robust control of spacecraft variable structures during approach for docking

The robust control of spacecraft during approach for docking is studied by first giving the relative motion equations for trajectory and attitude coupling of two spacecraft and then accomplishing the control design of the tracking vehicle using the feedback linearization method and the variable structure theory. Both theoretical analysis and simulation results indicate the robust controller proposed can guarantee non impact docking of two spacecraft even when the object vehicle is subjected to an external interference.

Variable Structure Control of Catastrophic Course in Airdropping Heavy Cargo

The mathematical model of a transport aircraft would be subjected to a sudden change when heavy cargo is dropped off in airdropping, which exerts serious influences upon the safety of the aircraft. A variable structure controller is specially designed for handling the airdrop process. The nonlinear system is linearized by input-output feedback linearization using differential geometry theories. On this basis, an inner loop system for velocity and attitude tracking control is designed by using the exponentially approaching rule of the variable structure theory. The whole flight control system is integrated with the outer loop flight altitude control. Digital simulation evidences the applicability of the system to potentially catastrophic course in airdropping heavy cargo and provides robustness against system parameter perturbation.