Class Of MIMO Nonlinear Systems Research Articles

Generalised observers for a class of non-linear systems

A general class of MIMO non-linear systems with unknown inputs is considered with a view to observer synthesis. The particularity of this class of systems lies in the fact that the expression of the outputs depends on the unknown inputs. Different situations are considered, and in each case, a non-linear observer, synthesised under appropriate hypotheses, is proposed to jointly estimate all state variables together with the unknown inputs. Simulation results are given in order to highlight the performances of the proposed observers.

Fuzzy approximate disturbance decoupling of MIMO nonlinear systems by backstepping approach

The concept of fuzzy approximate disturbance decoupling is introduced for a class of MIMO nonlinear systems with unknown nonlinearities. Based on the backstepping technique, a direct adaptive fuzzy almost disturbance decoupling control scheme is proposed. The proposed fuzzy controllers guarantee internal uniform ultimate boundedness of the closed-loop adaptive systems and render a bounded approximate L 2 gain from the disturbance input to the output. The main characteristics of the proposed algorithm is that the adaptive fuzzy controllers have a simple structure, and less adaptive parameters than the existing results. At last, the developed design scheme is applied to control a two continuous stirred tank reactor process. The simulation results illustrate the effectiveness of the method proposed in this paper.

Mixed Feedforward/Feedback Based Adaptive Fuzzy Control for a Class of MIMO Nonlinear Systems

This paper proposes a mixed feedforward/feedback (FFB) based adaptive fuzzy controller design for a class of multiple-input-multiple-output (MIMO) uncertain nonlinear systems. By integrating both feedforward and feedback compensation, we introduce the FFB-based fuzzy controller composed of a feedforward fuzzy compensator and a robust error-feedback compensator. To achieve a forward compensation of uncertainties, the feedforward fuzzy compensator takes the desired commands as premise variables of fuzzy rules and adaptively adjusts the consequent part from an error measure. Meanwhile, the feedback controller part is constructed based on Hinfin control techniques and nonlinear damping design. Then, the attenuation of both disturbances and estimated fuzzy parametric errors is guaranteed from a linear matrix inequality (LMI)-based gain design. The main advantages are: i) a simpler architecture for implementation is provided; and ii) the typical boundedness of assumption on fuzzy universal approximation errors is not required. Finally, an inverted pendulum system and a two-link robot are taken as application examples to show the expected performance

Decentralized model reference adaptive sliding mode control based on fuzzy model

Abstract A new design scheme of decentralized model reference adaptive sliding mode controller for a class of MIMO nonlinear systems with the high-order interconnections is proposed. The design is based on the universal approximation capability of the Takagi — Seguno (T-S) fuzzy systems. Motivated by the principle of certainty equivalentcontrol, a decentralized adaptive controller is designed to achieve the tracking objective without computation of the T-S fuzz ymodel. The approach does not require the upper bound of the uncertainty term to be known through some adaptive estimation. By theoretical analysis, the closed-loop fuzzy control system is proven to be globally stable in the sense that all signalsinvolved are bounded, with tracking errors converging to zero. Simulation results demonstrate the effectiveness of the approach.

Virtual Grouping based adaptive actuator failure compensation for MIMO nonlinear systems

A new control design technique called virtual grouping is presented to handle actuator redundancy and failures for multiple-input-mutliple-output (MIMO) systems, enlarging the set of compensable actuator failures. An adaptive compensation scheme is thus developed for a class of nonlinear MIMO systems to ensure closed-loop signal boundedness and asymptotic output tracking despite unknown actuator failures. Simulation results are given to show the effectiveness of the adaptive design.

Robust MIMO water level control in interconnected twin-tanks using second order sliding mode control

A novel second order sliding mode control algorithm is presented for a class of MIMO nonlinear systems in input–output (I–O) form. The algorithm produces a dynamic control and does not require the derivative of the sliding variable, thus eliminating the requirement to design observers or peak detectors. The algorithm has been applied for robust control of liquid level in interconnected twin-tanks. The controller is implemented on a laboratory rig and the results presented validate the proposed theory. The implementation results show robustness to parameter variations such as tank area, the admittance coefficients of various pipes, leakage in the tanks and uncertainty in the pump dynamics. In order to contextualise the results obtained with second-order sliding mode control, the results obtained using a classical PI controller are also presented.

Disturbance attenuation and rejection for systems with nonlinearity via DOBC approach

In this paper the disturbance attenuation and rejection problem is investigated for a class of MIMO nonlinear systems in the disturbance-observer-based control (DOBC) framework. The unknown external disturbances are supposed to be generated by an exogenous system, where some classic assumptions on disturbances can be removed. Two kinds of nonlinear dynamics in the plants are considered, respectively, which correspond to the known and unknown functions. Design schemes are presented for both the full-order and reduced-order disturbance observers via LMI-based algorithms. For the plants with known nonlinearity, it is shown that the full-order observer can be constructed by augmenting the estimation of disturbances into the full-state estimation, and the reduced-order ones can be designed by using of the separation principle. For the uncertain nonlinearity, the problem can be reduced to a robust observer design problem. By integrating the disturbance observers with conventional control laws, the disturbances can be rejected and the desired dynamic performances can be guaranteed. If the disturbance also has perturbations, it is shown that the proposed approaches are infeasible and further research is required in the future. Finally, simulations for a flight control system is given to demonstrate the effectiveness of the results. Copyright © 2005 John Wiley & Sons, Ltd.

Adaptive fuzzy control of a class of MIMO nonlinear systems

This paper presents two indirect adaptive fuzzy control schemes for a class of uncertain continuous-time multi-input multi-output nonlinear dynamic systems. Within these schemes, fuzzy systems are employed to approximate the plant's unknown nonlinear functions and robustifying control terms are used to compensate for approximation errors. By using a regularized matrix inverse, a stable well-defined adaptive controller is firstly investigated. Then, in order to obtain an adaptive controller not depending upon any parameter initialization conditions and to relax the requirement of bounding parameter values, a second adaptive controller is proposed. All parameter adaptive laws and robustifying control terms are derived based on Lyapunov stability analysis so that, under appropriate assumptions, semi-global stability and asymptotic convergence to zero of tracking errors can be guaranteed. Simulations performed on a two-link robot manipulator illustrate the approach and exhibit its performance.

Direct Adaptive Control for a Class of MIMO Nonlinear Systems Using Neural Networks

In this note, direct adaptive neural network (NN) control is studied for a class of multiple-input-multiple-output nonlinear systems based on input-output discrete-time model with unknown interconnections between subsystems. By finding an orthogonal matrix to tune the NN weights, the closed-loop system is proven to be semiglobally uniformly ultimately bounded. The control performance of the closed-loop system is guaranteed by suitably choosing the design parameters.

MULTI-INPUT AND MULTI-OUTPUT NONLINEAR SYSTEMS: INTERCONNECTED CHUA'S CIRCUITS

In this paper, a class of MIMO nonlinear systems are studied. Some frequency domain conditions are established for the property of dichotomy. These kinds of systems can also be viewed as a class of interconnected systems composed of SISO systems through some linear and nonlinear interconnections. A class of nonlinear input and output interconnections are presented. The corresponding condition for testing dichotomy is given. Furthermore, Chua's circuit and interconnected Chua's circuit are studied to illustrate the theoretical results.

Observer design for a class of MIMO nonlinear systems

A simple observer is proposed for a large class of MIMO nonlinear systems which includes many physical models. The main characteristic of the proposed observer lies in the easiness of its implementation and calibration. Indeed, the gain of this observer does not necessitate the resolution of any dynamical system and its expression is given. Moreover, its calibration is achieved through the choice of a single parameter. A simulation example is given in order to illustrate the performance of the proposed observer.

Online adaptive fuzzy neural identification and control of a class of mimo nonlinear systems

This paper presents a robust adaptive fuzzy neural controller (AFNC) suitable for identification and control of a class of uncertain multiple-input-multiple-output (MIMO) nonlinear systems. The proposed controller has the following salient features: 1) self-organizing fuzzy neural structure, i.e., fuzzy control rules can be generated or deleted automatically; 2) online learning ability of uncertain MIMO nonlinear systems; 3) fast learning speed; 4) fast convergence of tracking errors; 5) adaptive control, where structure and parameters of the AFNC can be self-adaptive in the presence of disturbances to maintain high control performance; 6) robust control, where global stability of the system is established using the Lyapunov approach. Simulation studies on an inverted pendulum and a two-link robot manipulator show that the performance of the proposed controller is superior.

State observer for MIMO nonlinear systems

A state observer design for a special class of MIMO nonlinear systems which has a block triangular structure is presented. For this purpose an extension of the existing design for SISO triangular systems to MIMO cases is performed. Since the gain of the proposed observer depends on both the nonlinear and linear parts of the system, it improves the transient performance of the high gain observer. Also, by using a generalised similarity transformation for the error dynamics, it is shown that under a boundedness condition, the proposed observer guarantees the global exponential convergence of the estimation error. Finally, an illustrative example is included to show the validity of the design approach.

Robust adaptive control for a class of mimo nonlinear systems with guaranteed error bounds

The design of stabilizing controllers for multiple-input-multiple-output (MIMO) nonlinear plants with unknown nonlinearities is a challenging problem. The high dimensionality coupled with the inability to identify the nonlinearities online or offline accurately motivates the design of stabilizing controllers based on approximations or on approximate estimates of the plant nonlinearities that are simple enough to be generated in real time. The price paid in such case, could be lack of theoretical guarantees for global stability, and nonzero tracking or regulation error at steady state. In this paper, a nonlinear robust adaptive control algorithm is designed and analyzed for a class of MIMO nonlinear systems with unknown nonlinearities. The proposed control scheme provides a general approach to bypass the stabilizability problem where the estimated plant becomes uncontrollable without any restrictive assumptions. The controller is continuous and guarantees closed-loop semi-global stability and convergence of the tracking error to a small residual set. The size of the tracking error at steady state can be specified a priori and guaranteed by choosing certain design parameters. A procedure for choosing these parameters is presented. The properties of the proposed control algorithm are demonstrated using simulations.

Stable direct adaptive fuzzy control for a class of MIMO non-linear systems

Two new schemes of direct adaptive fuzzy controller for a class of multi-input multi-output non-linear systems with unknown constant gains or function gains are proposed in this paper. The design is based on a modified Lyapunov function and the approximation capability of the first type fuzzy system. The approach is able to avoid the requirement of the upper bound of the first-time derivative of the control gain, which is assumed to know a priori in some of the existing adaptive fuzzy/neural network control schemes. In addition, it is also able to avoid the controller singularity problem. By theoretical analysis, the closed-loop fuzzy control system is proven to be globally stable in the sense that all signals involved are bounded, with tracking errors converging to zero. The simulation results verify the effectiveness the proposed controllers and the theoretical discussion.

A hybrid adaptive fuzzy control for a class of nonlinear MIMO systems

A hybrid indirect and direct adaptive fuzzy output tracking control schemes are developed for a class of nonlinear multiple-input-multiple-output (MIMO) systems. This hybrid control system consists of observer and other different control components. Using the state observer, it does not require the system states to be available for measurement. Assisted by observer-based state feedback control component, the adaptive fuzzy system plays a dominant role to maintain the closed-loop stability. Being the auxiliary compensation, H/sup /spl infin// control and sliding mode control are designed to suppress the influence of external disturbance and remove fuzzy approximation error, respectively. Thus, the system performance can be greatly improved. The simulation results demonstrate that the proposed hybrid fuzzy control system can guarantee the system stability and also maintain a good tracking performance.

Adaptive Neural Control of MIMO Nonlinear Systems in Block-triangular Pure-feedback Form

In this paper, an adaptive neural control scheme is proposed for a class of MIMO nonlinear systems in block-triangular pure-feedback form. The MIMO system is composed of interconnected subsystems. Each subsystem is in the pure-feedback form with all the nonlinearities unknown. Firstly, we design for each subsystem an adaptive neural controller by using backstepping methodology. With the help of NN approximation, there is no need to solve the implicit functions for the explicit virtual controls to cancel the unknown functions in backstepping design. Secondly, by exploiting the structure properties of the MIMO system, we conclude the stability of the whole closed-loop MIMO system by stability analysis of all the signals in the closed-loop in a nested iterative manner. Semi-global uniform ultimate boundedness of all the signals in the closed-loop of MIMO nonlinear systems is guaranteed. The outputs of the systems are proven to converge to small neighborhoods of the desired trajectories. The control performance of the closed-loop system is guaranteed by suitably choosing the design parameters.

Disturbance decoupling for a class of nonlinear MIMO systems by static measurement feedback

In this paper, the disturbance decoupling problem for a square-invertible nonlinear system is stated and solved by static feedback of measured variables only, in contrast with standard solutions which assume that the full state is available for feedback. The results are valid for left-invertible systems as well.

Switching structure state and parameter estimator for MIMO non-linear robust control

In this paper the problem of simultaneous robust state and parameter estimation for a class of MIMO non-linear systems under mixed uncertainties (unmodelled dynamics as well as observation noises) it tackled. A switching gain robust 'observer-identifier' is introduced to obtain the corresponding estimates. This is achieved by applying an observer to the so-called nominal extended system, obtained from the original system without any uncertainties and considering the parameters as additional constant states. As it is shown, in general the extended system can lose the global observability property, supposed by valid for the original non-extended system, and a special procedure is needed to provide a good estimation process in this situation. The suggested adaptive observer has the Luenberger type observer structure with switching matrix gain that guarantees a good enough upper bound for the identification error performance index. The Van der Monde generalized transformation is introduced to derive this bound which turns out to be 'tight' (it is equal to zero in the absence of both noises and unmodelled dynamics). The example dealing with an inverted pendulum illustrates the high effectiveness of the suggested approach.

An adaptive H/sup ∞/ tracking control for a class of nonlinear multiple-input multiple-output (MIMO) systems

An adaptive H/sup /spl infin// tracking control equipped with a VSC algorithm is proposed for a class of nonlinear multiple-input-multiple-output (MIMO) systems that are represented by input-output models involving parametric uncertainties, unmodeled perturbations and external disturbances. In order to counteract the effect due to the unmodeled perturbation in the input weighting gain the H/sup /spl infin// tracking control requires to solve a modified algebraic Riccati-like matrix equation. The derived hybrid adaptive-robust tracking control schemes guarantee that all the signals and states are bounded, the tracking error is uniformly and ultimately bounded and an H/sup /spl infin// tracking performance is achieved. Compared with the conventional H/sup /spl infin// tracking control design the developed adaptive-robust H/sup /spl infin// tracking control scheme can be applied to a broader class of nonlinear MIMO systems in the presence of high-degree uncertainties.