Unknown Multi-input Multi-output Research Articles

Development of a Universal Adaptive Control Algorithm for an Unknown MIMO System Using Recursive Least Squares and Parameter Self-Tuning

Development of a Universal Adaptive Control Algorithm for an Unknown MIMO System Using Recursive Least Squares and Parameter Self-Tuning

General fuzzy adaptive fault-tolerant control based on Nussbaum-type function with additive and multiplicative sensor and state-dependent actuator faults

The present paper devotes to propose a general active fault-tolerant control (GAFTC) for a class of unknown multi-input multi-output (MIMO) nonlinear systems that are subject to simultaneous additive and multiplicative sensor and nonaffine nonlinear state-dependent actuator faults, exogenous disturbances and multiple unknown control directions. By combining fuzzy logic systems and back-stepping technique, an adaptive control unit along with a robust control unit are developed. In the proposed approach, the unknown dynamics along with sensor and non-affine nonlinear state-dependent actuator faults are approximated to avoid developing fault detection and isolation unit. Furthermore, the difficulty caused by the unknown control gain directions is solved by using the Nussbaum-type function. The adaptation mechanism is proposed to overcome fuzzy approximation errors and exogenous disturbances, and the Butterworth low-pass filter is adopted to get rid of the algebraic loop appearing in the actuator faults approximation. The stability of the closed-loop system is proved by Lyapunov method where all the signals involved in the resulting closed-loop system are shown to be bounded, and the tracking errors converge asymptotically to the origin. Quadrotor attitude dynamics stabilization is proposed in the simulation study to test the accuracy and the effectiveness of the proposed control scheme.

Exponentially Stable Adaptive Control of MIMO Systems with Unknown Control Matrix

The scope of this research is a problem of direct model reference adaptive control of linear time-invariant multi-input multi-output (MIMO) plants without any a priori knowledge about system matrices. To handle it, a new method is proposed, which includes three main stages. Firstly, using the well-known DREM procedure, the plant parametrization is made to obtain the linear regressions, in which the plant matrices and state initial conditions are the unknown parameters. Secondly, such regressions are substituted into the known equations for the controller parameters calculation. Thirdly, the controller parameters are identified using the novel adaptive law with the exponential rate of convergence. To the best of the authors’ knowledge, such a method is the first one to provide the following features simultaneously: 1) it is applicable for the unknown MIMO systems (e.g. without any information about state or control allocation matrices, the sign of the latter, etc.); 2) it guarantees the exponential convergence of both the parameter and tracking errors under the mild requirement of the regressor finite excitation; 3) it ensures element-wise monotonicity of the transient curves of the control law parameters matrices. The results of the conducted experiments with the model of a rubber and ailerons control of a small passenger aircraft corroborate all theoretical results.

Inverse-model-based iterative learning control for unknown MIMO nonlinear system with neural network

This paper provides an inverse-model-based iterative learning control (ILC) for the unknown multi-input multi-output (MIMO) nonlinear system with neural network (NN), where a novel gradient adaptive law is used to update the NN weights both hidden and output layers such a faster convergence can be achieved. First, a three-layer NN structure is introduced to observe the MIMO nonlinear system with input–output data, and a new gradient algorithm is proposed to update the unknown parameters of both hidden and output layers. Then, the input dynamic can be obtained with the NN observer, and the inversion-model-based control is designed. Moreover, the ideal inversion control can be obtained based on the reference signal, and the inverse ILC is designed. The stability of the NN observer and the convergence of the inverse-model-based control are analyzed. Finally, a SCARA manipulator MIMO model is simulated to illustrate the correctness of the proposed methods.

Adaptive Neural Partial State Tracking Control for Full-State-Constrained Uncertain Singularly Perturbed Nonlinear Systems and Its Applications to Electric Circuit

This paper is concerned with the adaptive neural network (NN) partial tracking control problem for a class of completely unknown multi-input multi-output (MIMO) singularly perturbed nonlinear systems possessing time-varying asymmetric state constraints. To satisfy the constraints, we utilize the state-depended transformation technique to convert the original state-constrained system to an equivalent unconstrained one, then the state constraint problem can be solved by ensuring its stability. Partial state tracking can be achieved without the violation of state constraints. The adaptive tracking controllers are designed by using singular perturbation theory and the adaptive control method, in which NNs are used to approximate unknown nonlinear functions. The ill-conditioned numerical problems lurking in the controller design process are averted and the closed-loop system stability can be guaranteed by introducing an appropriate Lyapunov function with singular perturbation parameter. Finally, a practical example is given to demonstrate the effectiveness of our proposed adaptive NN tracking control scheme.

Prescribed Performance Neuroadaptive Fault-Tolerant Compensation for MIMO Nonlinear Systems Under Extreme Actuator Failures

This article investigates the issue of neuroadaptive tracking control for a family of unknown multi-input multi-output (MIMO) nonlinear uncertain systems subject to extreme actuation failures. Different from most existing methods that are built upon partial loss of actuation effectiveness, here, in this article, we explicitly consider the situation that some actuators at some particular channel completely fail to work, an issue that has not been well addressed. By integrating the neural network approximation technique with two error transformations, a neuroadaptive fault-tolerant control strategy is developed with two attractive features: 1) it is capable of coping with the scenario that some of the actuators suffer from extreme actuation faults without the need for fault detection and diagnosis (FDD)/fault detection and isolation (FDI) or actuator switching and 2) the tracking error is forced to converge to a prescribed residual (symmetric or asymmetric) boundary at a preassignable decay mode within a prechosen finite settling time despite actuator failures and external disturbances. Numerical simulation studies confirm the effectiveness and benefits of the presented control approach.

Model-Free Adaptive Control for Unknown MIMO Nonaffine Nonlinear Discrete-Time Systems With Experimental Validation.

In this article, a model-free adaptive control (MFAC) algorithm based on full form dynamic linearization (FFDL) data model is presented for a class of unknown multi-input multi-output (MIMO) nonaffine nonlinear discrete-time learning systems. A virtual equivalent data model in the input-output sense to the considered plant is established first by using the FFDL technology. Then, using the obtained data model, a data-driven MFAC algorithm is designed merely using the inputs and outputs data of the closed-loop learning system. The theoretical analysis of the monotonic convergence of the tracking error dynamics, the bounded-input bounded-output (BIBO) stability, and the internal stability of the closed-loop learning system is rigorously proved by the contraction mapping principle. The effectiveness of the proposed control algorithm is verified by a simulation and a quad-rotor aircraft experimental system.

Robust adaptive fault-tolerant control of nonlinear uncertain systems tracking uncertain target trajectory

The problem of enabling nonlinear uncertain dynamic systems to track a moving target with uncertain trajectory is of theoretical and practical importance. The underlying problem becomes further complicated if there involve unexpected actuation failures. In this paper, a robust adaptive fault-tolerant tracking control approach is proposed for unknown multi-input multi-output (MIMO) nonlinear systems without a priori precise knowledge of the desired target trajectory. To account for the impact of the uncertain desired trajectory, a mathematical model based on the extended Kalman filter (EKF) for reconstructing desired trajectory is proposed, which is then integrated into the development of tracking control algorithms to cope with modelling uncertainties and actuation faults. The matrix decomposition technique and the concept of deep-rooted information are used to facilitate the control design and stability analysis. The effectiveness of the proposed method is verified via computer simulation.

Tracking Control for a Class of Unknown Nonsquare MIMO Nonaffine Systems: A Deep-Rooted Information Based Robust Adaptive Approach

The tracking control problem of multi-input multi-output (MIMO) nonaffine dynamic systems is studied in this note. A globally uniformly ultimately bounded (GUUB) stable tracking control solution for non-square MIMO nonaffine systems with unknown dynamics and disturbances is established. Different from most existing methods, the proposed control design is based on the readily computable deep-rooted information on the system and does not involve linearization or approximation; and the resultant control algorithms are simple in structure, inexpensive in computation, user-friendly in design, and undemanding in implementation. Both theoretical analysis and numerical simulation verify the effectiveness and benefits of the proposed method.

Predictor-Based Adaptive Output Feedback Control: Application to Functional Electrical Stimulation of a Human Arm Model

A simulation study to control the motion of a human arm using muscle excitations as inputs is presented to validate a recently developed adaptive output feedback controller for a class of unknown multi-input multi-output (MIMO) systems. The main contribution of this paper is to extend the results of Nguyen and Leonessa (2014, “Adaptive Predictor-Based Output Feedback Control for a Class of Unknown MIMO Linear Systems,” ASME Paper No. DSCC2014-6214; 2014, “Adaptive Predictor-Based Output Feedback Control for a Class of Unknown MIMO Linear Systems: Experimental Results,” ASME Paper No. DSCC2014-6217; and 2015, “Adaptive Predictor-Based Output Feedback Control for a Class of Unknown MIMO Systems: Experimental Results,” American Control Conference, pp. 3515–3521) by combining a recently developed fast adaptation technique and a new controller structure to derive a simple approach for a class of high relative degree uncertain systems. Specifically, the presented control approach relies on three components: a predictor, a reference model, and a controller. The predictor is designed to predict the systems output for any admissible control input. A full state feedback control law is then derived to control the predictor output to approach the reference system. The control law avoids the recursive step-by-step design of backstepping and remains simple regardless of the system relative degree. Ultimately, the control objective of driving the actual system output to track the desired trajectory is achieved by showing that the system output, the predictor output, and the reference system trajectories all converge to each other. Thelen and Millard musculotendon models (Thelen, D. G., 2003, “Adjustment of Muscle Mechanics Model Parameters to Simulate Dynamic Contractions in Older Adults,” ASME J. Biomech. Eng., 125(1), pp. 70–77; Millard, M, Uchida, T, Seth, A, and Delp, Scott L., 2013, “Flexing Computational Muscle: Modeling and Simulation of Musculotendon Dynamics,” ASME J. Biomech. Eng., 135(2), p. 021005) are used to validate the proposed controller fast tracking performance and robustness.

Extended dynamic fuzzy logic system for a class of MIMO nonlinear systems and its application to robotic manipulators

SUMMARYThis paper presents an indirect adaptive fuzzy control scheme for a class of unknown multi-input multi-output (MIMO) nonlinear systems with external disturbances. Within this scheme, the dynamic fuzzy logic system (DFLS) is employed to identify the unknown nonlinear MIMO systems. The control law and parameter adaptation laws of DFLS are derived based on the Lyapunov synthesis approach. The control law is robustified in H∞ sense to attenuate external disturbance, model uncertainties, and fuzzy approximation errors. It is shown that under appropriate assumptions it guarantees the boundness of all signals in the closed-loop system and the asymptotic convergence to zero of tracking errors. An extensive simulation on the tracking control of a two-link rigid robotic manipulator verifies the effectiveness of the proposed algorithms.

A novel neural internal model control for multi-input multi-output nonlinear discrete-time processes

An internal model-based neural network control is proposed for unknown non-affine discrete-time multi-input multi-output (MIMO) processes in nonlinear state space form under model mismatch and disturbances. Based on the neural state-space model built for an unknown nonlinear MIMO state space process, an approximate internal model and approximate decoupling controllers are derived simultaneously. Thus, the learning of the inverse process dynamics is not required. A neural network model-based extended Kalman observer is used to estimate the states of a nonlinear process as not all states are accessible. The proposed neural internal model control can work for open-loop unstable processes with its closed-loop stability derived analytically. The application to a distributed thermal process shows the effectiveness of the proposed approach for suppressing nonlinear coupling and external disturbances and its feasibility for the control of unknown non-affine nonlinear discrete-time MIMO state space processes.

Multichannel system identification and deconvolution: performance bounds

We consider the problem of estimating the parameters of an unknown multi-input multi-output (MIMO) linear system and the related problem of deconvolving and recovering its inputs. Only the system outputs are assumed to be observable. The system inputs are assumed to be non-Gaussian. We derive simple closed-form asymptotic expressions for the Cramer-Rao lower bound (CRLB) for the system parameters, as well as lower bounds on the signal reconstruction performance. These show that the identification/deconvolution performance depend on the accuracy with which the location (mean) and the scale (standard deviation) parameters of the input probability density functions can be identified from observation of the input signals.

Design of G-interactor and its application to direct multivariable adaptive control

In the design of multi-input multi-output (MIMO) adaptive control systems an interactor plays an important role. The derivation of the interactor requires system parameter values unless the interactor is in diagonal form. This is a considerable restriction when the interactor is applied to the adaptive control system design. In MIMO adaptive control many parameters must be estimated to achieve good tracking. Over-parametrization causes many problems, e.g. bad tracking performance and long calculation time of control input. A design of interactor, called a G-interactor, for unknown MIMO plants is given. It is applied to MIMO adaptive control systems. The G-interactor requires minimum information on the plant, such as the relative degree of each element of the plant transfer matrix. For this design a canonical form, called the G-canonical form, of a matrix A is investigated. The canonical form is also used to eliminate redundant parameters of MIMO adaptive control systems. Numerical examples show the effect...