Multi-input Multi-output Uncertain Systems Research Articles

Adaptive quantized finite-time fault-tolerant control for uncertain multi-input multi-output systems and its application

The article proposes a novel state-feedback control method for a multiple-input multiple-output (MIMO) nonlinear system with actuator faults and input quantization. The innovation of the design approach lies in the utilization of fuzzy logic systems (FLSs) to approximate the uncertain intermediate virtual control laws, thereby achieving a simplified virtual control design form. Additionally, finite-time control is employed to enhance the system’s response speed. Different from the existing literatures, the adaptive control scheme of partial loss fault gain is integrated with input quantization, which completes the unknown gain estimation and avoids the assumption condition of unknown control gain. The theoretical analysis combined with Lyapunov stability analysis shows that the tracking error can converge regardless of whether the system experiences a fault, while the closed-loop signal remains stably bounded for a finite time. Finally, the simulation results of the quadrotor unmanned aerial vehicle (UAV) attitude system indicate that this control scheme is effective.

Active disturbance rejection decoupling control for nonlinear MIMO uncertain systems with application to path following of self-driving bus

This paper focuses on the control problem for a general class of multi-input multi-output (MIMO) uncertain systems with unknown coupling dynamics, uncertain control input gain matrix and external disturbances. The active disturbance rejection decoupling control is proposed to force the closed-loop systems to achieve desired performance despite these uncertainties. In particular, the general extended state observer corresponding the relative degree vector of considered system is constructed to timely estimate the total disturbance vector. The tuning laws for our controller to handle the uncertainty of control input gain matrix are quantitatively presented. Also, it is proven that the tracking error between the state vector and its ideal trajectory in the entire transient process can be small enough by tuning ESO’s bandwidths. Moreover, the necessary and sufficient condition for closed-loop system’s tracking error and estimation error to converge to zero is given. The proposed method is applied to the path following of self-driving bus (SDB), where the lateral error subsystem and the velocity subsystem are severely coupled with each other. Both unknown road-tire friction and steering wheel friction need to be handled. The experiment results on SDB demonstrate that the desired performance can be achieved despite both external disturbance and nonlinear uncertainties.

Multivariable Robust Proportional-Integral-Derivative Control for Linear Quadratic Compensation of a Class of Norm-Bounded Uncertain Systems

AbstractThis paper is concerned with designing multi-input multi-output (MIMO) proportional-integral-derivative (PID) control having filtered derivative terms to achieve optimal linear quadratic performance for a class of linear uncertain MIMO systems with norm-bounded time-varying uncertainties. A necessary and sufficient condition for existence of the PID controller is obtained in terms of rank constrained linear matrix inequalities (LMIs). Using an existing penalty-function-based approximation for matrix rank minimization, an algorithm is proposed to solve these rank constrained LMIs and find PID gains. A suitable numerical example is considered to show the efficacy of the proposed approach in ensuring robust performance as compared to the existing ones. The proposed algorithm is also tested on several benchmark examples and found to be computationally much more efficient than some well-known methods.

Asymptotic Tracking Control for Uncertain MIMO Systems: A Biologically Inspired ESN Approach.

In this study, a biologically inspired echo state network (ESN)-based method is established for the asymptotic tracking control of a class of uncertain multi-input multi-output (MIMO) systems. By mimicking the characters of real biological systems, a diversified multiclustered echo state network (DMCESN) is proposed in this work and then it is applied to deal with the modeling uncertainties and coupling nonlinearities in the control systems. Different from the most existing neural network (NN)-based control methods that only ensure the uniform ultimate boundedness result, the proposed method can allow the tracking error to achieve asymptotic convergence through rigorous theoretical analysis. The effectiveness of the proposed method is also confirmed by numerical simulation by comparing with multilayer feedforward network-based control scheme and traditional ESN-based control, admitting better tracking performance of the proposed control.

Performance analysis of typical linear augmented observers for a class of MIMO systems with nonlinear uncertainty

To estimate the states and the uncertainties for multi-input–multi-output (MIMO) systems is significant in control engineering. The paper investigates the estimating performance of a widely-used linear augmented observer (LAO) by quantitatively analyzing the biased term of estimation error, which generalizes the previous studies. Then the necessary and sufficient condition for unbiased estimation of LAO is thoroughly discussed. More importantly, by investigating the observability of MIMO uncertain systems, the paper proves that the estimation of LAO is unbiased if and only if the states and the uncertainties of MIMO uncertain systems are observable. The presented theoretical analysis can help practitioners evaluate the feasibility of estimating the specific uncertainties via LAO in practical systems. Finally, even if the estimation of LAO is biased, the design procedure of extended state observer is presented, which offers the unbiased estimation of total disturbance and the derivatives of output.

Two-sided linear matrix inequality solution of affine input matrix for feasible discrete finite-time sliding mode control of uncertain nonlinear mechanical machines

In this article, a new control method is proposed based on finite-time discrete sliding mode control for uncertain multi-input multi-output systems which are affine to their inputs considering uncertain input multipliers in the case where signs of input gains remain constant over uncertainty spaces. In addition, a method for solving a set of convex control inequalities is introduced. The proposed control strategy is based on merging data obtained from investigation of common candidate Lyapunov functions assigned to various subsystems and their subsequent decoupling based on matrix elementary row operations. Initially, separate sliding functions corresponding to a single degree of freedom are assigned to each subsystem in the overall multi-input multi-output system, which results in obtaining a convex inequality corresponding to input bounds. Stacking the data obtained from various subsystems, the product of the uncertain input gain matrix in input vector is obtained as the middle term in a set of convex inequalities. Subsequently, the convex inequality is solved according to a set of matrix elementary row operations transforming the corresponding input matrix to row echelon form such that the bounds of each input are clearly expressed. Then, based on assigning input bounds proximity factors to each lower bound–upper bound duo, appropriate control inputs are generated. Chattering effects are eliminated as no switching term is included in construction of the control model. Effectiveness of the proposed method is demonstrated using numerical simulations. The implementation of control algorithm using microprocessors is also illustrated, indicating the feasibility of digital application.

Fractional order MIMO controllers for robust performance of airplane longitudinal motion

This paper presents fractional order multi-input multi-output (MIMO) controllers for the robust performance of airplane longitudinal motion. A novel necessary and sufficient criterion is offered by using the value set concept to analyze the robust performance of fractional order MIMO uncertain systems based on the location of the characteristic equation roots. The criterion is applicable to all linear time-invariant systems of commensurate and incommensurate orders with complex coefficients. The obtained results are applied to an uncertain linear model of a business airplane to improve the robust performance of its longitudinal motion by decentralized MIMO output feedback and MIMO state feedback controllers. Numerical simulations are conducted to confirm the effectiveness of the presented criterion and controllers.

Adaptive Fault‐Tolerant Control of Uncertain MIMO Systems with Reduced Requirement on Desired Trajectory Under Unknown Control Direction

AbstractThis paper aims at investigating the tracking control problem for a class of multi‐input multi‐output (MIMO) nonlinear systems with non‐square control gain matrix subject to unknown control direction and uncertain desired trajectory. By using the artificial neural network (NN) reconstructs the target trajectory with actual disguised trajectory, we are able to design a practical and stable tracking control scheme without the need for the unavailable desired trajectory. Nussbaum‐type function is incorporated in the control law to handle the unknown control direction. The remarkable feature of the proposed scheme is that it is robust against modeling uncertainties and tolerant to actuation faults, yet guarantees that the closed‐loop system is stable in the sense of ultimately uniformly bounded (UUB). The effectiveness of the proposed control schemes are illustrated through simulation results.

New results on robust stability analysis and synthesis for MIMO uncertain systems

This paper provides theoretical preliminary results and develops a first methodology, that allows one to efficiently estimate the maximum time constant of a dynamic matrix of an uncertain system with rational multi-affine structure with respect to parameters, and a second one to find a majorant system of a multi-input multi-output (MIMO) system with rational multi-affine structure with respect to parameters. The developed methodologies are used to estimate the evolution of an uncertain linear time-invariant (LTI) system with additional bounded nonlinearities and/or additional bounded input signals. Moreover, the above results are also used to design a robust controller for an uncertain MIMO system with unmeasurable states and subject to a rate-bounded disturbance in order to track a rate-bounded reference signal. The obtained theoretical results are illustrated by three examples. The first two examples deal with the analysis of a LTI system with bounded disturbances and measurement noise, and additional bounded and not bounded nonlinearities, respectively; in the second example a new control law with saturation is also designed. In the last example, a robust controller for an uncertain electro-mechanical system with unmeasurable state is designed to track a rate-bounded reference signal in the presence of a disturbance with bounded derivative.

Adaptive backstepping control for a class of MIMO uncertain underactuated systems with input constraints

This paper presents a backstepping methodology-based semi generic adaptive controller scheme for a class of multi-input multi-output (MIMO) uncertain underactuated systems in presence of actuator constraints. To develop a feasible controller scheme for multi-input multi-output underactuated systems, (n – p + 1) dimensions of the n dimensional configuration space are stabilised by using one dimension of the input space. This control term is developed by applying hierarchical methodology whereas as remaining p – 1 input dimensions are assigned as dedicated control terms to solve the control problem of remaining dimensions of the configuration space. Backstepping technique is used to develop the classical control terms whereas wavelet networks are used to approximate the uncertain dynamics as well as the nonlinear effects of actuator saturation. The proposed scheme, thus, relaxes the constraint of completely and accurately known system dynamics as well as the requirement of measuring the clipped portion of the control effort. A robust control term is used to attenuate the approximation error to a prescribed level. Uniform ultimate boundedness (UUB) stability of the closed loop system is verified in the Lyapunov sense. Simulation results illustrate the effectiveness of theoretical development.

Robust adaptive attenuation of unknown periodic disturbances in uncertain multi-input multi-output systems

In high-performance high-accuracy systems, the attenuation of vibrational disturbances is essential. In this paper, we design and analyze a robust output-feedback adaptive control scheme to attenuate noise-corrupted vibrational disturbances with unknown characteristics for multi-input multi-output linear time-invariant systems in the presence of plant unstructured modeling uncertainties. The conditions and the design parameters that contribute to the performance of the closed-loop system are investigated. The main ingredients of the proposed scheme include the use of a compensator to properly shape the singular values of the plant model, a robust adaptive law to handle unmodeled dynamics and output random noise, as well as an over-parametrization in the estimated parameters in order to provide flexibility for performance improvement. Analysis and simulations together with practical design considerations are presented to demonstrate the efficacy of the proposed scheme.

Variable neural adaptive robust control: a switched system approach.

Variable neural adaptive robust control strategies are proposed for the output tracking control of a class of multiinput multioutput uncertain systems. The controllers incorporate a novel variable-structure radial basis function (RBF) network as the self-organizing approximator for unknown system dynamics. It can determine the network structure online dynamically by adding or removing RBFs according to the tracking performance. The structure variation is systematically considered in the stability analysis of the closed-loop system using a switched system approach with the piecewise quadratic Lyapunov function. The performance of the proposed variable neural adaptive robust controllers is illustrated with simulations.

An adaptive fuzzy sliding-mode controller design for walking control with functional electrical stimulation: A computer simulation study

A major challenge to developing neuroprostheses for walking and to widespread acceptance of these walking systems is the design of a robust control strategy that provides satisfactory tracking performance, to be robust against time-varying properties of neuromusculoskeletal dynamics, day-today variations, muscle fatigue, and external disturbances, and to be easy to apply without requiring offline identification during different experiment sessions. The lower extremities of human walking are a highly nonlinear, highly time-varying, multi-actuator, multi-segment with highly inter-segment coupling, and inherently unstable system. Moreover, there always exist severe structured and unstructured uncertainties such as spasticity, muscle fatigue, external disturbances, and unmodeled dynamics. Robust control design for such nonlinear uncertain multi-input multi-output system still remains as an open problem. In this paper we present a novel robust control strategy that is based on combination of adaptive fuzzy control with a new well-defined sliding-mode control (SMC) with strong reachability for control of walking in paraplegic subjects. Based on the universal approximation theorem, fuzzy logic systems are employed to approximate the neuromusculoskeletal dynamics and an adaptive fuzzy controller is designed by using Lyapunov stability theory to compensate for approximation errors. The proposed control strategy has been evaluated on a planar model of bipedal locomotion as a virtual patient. The results indicate that the proposed strategy provides accurate tracking control with fast convergence during different conditions of operation, and could generate control signals to compensate the effects of muscle fatigue, system parameter variations, and external disturbances. Interesting observation is that the controller generates muscle excitation that mimic those observed during normal walking.

A fuzzy adaptive variable-structure control scheme for uncertain chaotic MIMO systems with sector nonlinearities and dead-zones

In this paper, a fuzzy adaptive variable-structure controller is investigated for a class of uncertain multi-input multi-output (MIMO) chaotic systems with both sector nonlinearities and dead-zones. A suitable adaptive fuzzy system is used to reasonably approximate the uncertain functions. A Lyapunov approach is employed to derive the parameter adaptation laws and prove the boundedness of all signals of the closed-loop system as well as the exponential convergence of the closed-loop errors to an adjustable region. The proposed controller can be applied to the systems with or without sector nonlinearities and/or dead-zones in the input. The effectiveness of the proposed fuzzy adaptive controller is illustrated throughout simulation results.

Modeling and control of nonlinear systems using novel fuzzy wavelet networks: The output adaptive control approach

This paper proposes an observer based self-structuring robust adaptive fuzzy wave-net (FWN) controller for a class of nonlinear uncertain multi-input multi-output systems. The control signal is comprised of two parts. The first part arises from an adaptive fuzzy wave-net based controller that approximates the system structural uncertainties. The second part comes from a robust H ∞ based controller that is used to attenuate the effect of function approximation error and disturbance. Moreover, a new self structuring algorithm is proposed to determine the location of basis functions. Simulation results are provided for a two DOF robot to show the effectiveness of the proposed method.

New fuzzy wavelet network for modeling and control: The modeling approach

In this paper, a fuzzy wavelet network is proposed to approximate arbitrary nonlinear functions based on the theory of multiresolution analysis (MRA) of wavelet transform and fuzzy concepts. The presented network combines TSK fuzzy models with wavelet transform and ROLS learning algorithm while still preserve the property of linearity in parameters. In order to reduce the number of fuzzy rules, fuzzy clustering is invoked. In the clustering algorithm, those wavelets that are closer to each other in the sense of the Euclidean norm are placed in a group and are used in the consequent part of a fuzzy rule. Antecedent parts of the rules are Gaussian membership functions. Determination of the deviation parameter is performed with the help of gold partition method. Here, mean of each function is derived by averaging center of all wavelets that are related to that particular rule. The overall developed fuzzy wavelet network is called fuzzy wave-net and simulation results show superior performance over previous networks. The present work is complemented by a second part which focuses on the control aspects and to be published in this journal( [17]). This paper proposes an observer based self-structuring robust adaptive fuzzy wave-net (FWN) controller for a class of nonlinear uncertain multi-input multi-output systems.

Almost disturbance decoupling and tracking control for multi-input multi-output non-linear uncertain systems: Application to a half-car active suspension system

This study presents a novel feedback linearization control of non-linear multi-input multi-output uncertain systems for the tracking and almost disturbance decoupling performances. The main contribution of this study is to construct a controller, under appropriate conditions, such that the resulting closed-loop system is valid for any initial condition and bounded tracking signal with the following characteristics: input-to-state stability with respect to disturbance inputs and almost disturbance decoupling. In addition, a new theorem on robust stability is proposed in this study to provide a new criterion for closed-loop stability. A typical case, which cannot be solved by any previous study on the almost disturbance decoupling problem, is proposed in this study to exploit the fact that the tracking and the almost disturbance decoupling performances can be easily achieved by the proposed approach. Finally, the proposed control law is simulated in a half-car active suspension system on which the effectiveness of the design is verified.

Almost disturbance decoupling control of nonlinear MIMO uncertain system and application to half-car active suspension system

This paper studies the tracking and almost disturbance decoupling problem of nonlinear multi-input multi-output uncertain systems based on the feedback linearisation approach. The main contribution of this study is to construct a controller, under appropriate conditions, such that the resulting closed-loop system is valid for any initial condition and bounded tracking signal with the following characteristics: input-to-state stability with respect to disturbance inputs and almost disturbance decoupling, i.e., the influence of disturbances on the L2 norm of the output tracking error can be arbitrarily attenuated by changing some adjustable parameters. One example, which cannot be solved by the first paper on the almost disturbance decoupling problem, is proposed in this paper to exploit the fact that the tracking and the almost disturbance decoupling performances are easily achieved by the proposed approach. In order to demonstrate the practical applicability, the paper has investigated a famous half-car active suspension system.

불감시간을 갖는 Affine 시스템의 안정도 해석과 제어기 설계

The Nyquist robust stability margin is proposed as a measure of robust stability for systems with Affine TFM(Transfer Function Matrix) parametric uncertainty. The parametric uncertainty is modeled through a Affine TFM MIMO (Multi-Input Multi-Output) description with dead-time, and the unstructured uncertainty through a bounded perturbation of Affine polynomials. Gershgorin's theorem and concepts of diagonal dominance and GB(Gershgorin Bands) are extended to include model uncertainty. Multiloop PI/PID controllers can be tuned by using a modified version of the Ziegler-Nichols (ZN) relations. Consequently, this paper provides sufficient conditions for the robustness of Affine TFM MIMO uncertain systems with dead-time based on Rosenbrock's DNA. Simulation examples show the performance and efficiency of the proposed multiloop design method for Affine uncertain systems with dead-time.

Fuzzy sliding mode control with a fuzzy switching function for non-linear uncertain multi-input multi-output systems

This paper presents two approaches for the fuzzy sliding mode control of uncertain and disturbed non-linear multi-input multi-output (MIMO) systems. In the first approach, the control law is deduced from a nominal model of the plant. An adaptive fuzzy system is introduced to substitute the switching control and, hence, to eliminate the chattering phenomenon. In the second approach, two other adaptive fuzzy systems are used to approximate and thereby to overcome the unavailability of the nominal model. The stability and the robustness are proven analytically in both cases, and the adaptation laws of the fuzzy systems are deduced from Lyapunov synthesis. A simulation example of a two-link robot is used for illustration.