Nonlinear Multi-input Multi-output Research Articles

Improved Set-point Tracking Control of an Unmanned Aerodynamic MIMO System Using Hybrid Neural Networks

Artificial neural networks (ANN), an Artificial Intelligence (AI) technique, are both bio-inspired and nature-inspired models that mimic the operations of the human brain and the central nervous system that is capable of learning. This paper is based on a system that optimizes the performance of an uncertain unmanned nonlinear Multi-Input Multi-Output (MIMO) aerodynamic plant called Twin Rotor MIMO System (TRMS). The pitch and yaw angles which are challenging to control and optimize in practice, are being used as the input to the Nonlinear Auto-Regressive with eXogenous (NARX) model, and eventually trained. The training features use the Matlab Deep Learning Toolbox. The NARX structure has its core in the neural networks’ architecture. Data is collected from the TRMS testbed which is used to train the network. ANN as a Hybrid intelligent control strategy of ANN in combination with Pattern Search and Genetic Algorithm, is then utilized to optimize the parameters of the neural networks. At the end it was validated, tested and the optimized system run in simulation and compared with other intelligent and conventional controllers, with the proposed controller outperforming them, giving a very fast tracking control, stable and optimal performance that satisfactorily met all our design requirements.

Higher Order Sliding Mode Control of MIMO Induction Motors: A New Adaptive Approach

In this paper the objective is to force the outputs of nonlinear nonaffine multi-input multi-output (MIMO) systems to track those of a linear system with the desired properties. The approach is based on designing higher order sliding mode controller (HOSMC) with the definition of a new proportional-integral (PI) sliding surface. To this end, a linear state feedback with an adaptive switching gain (ASG) is applied to the nonlinear MIMO systems. Therefore, the switching gain can increase or decrease based on the system conditions. Then, the chattering is completely removed using a combination of HOSMC and ASG. Moreover, the proposed procedure is independent from the upper bound of the matched uncertainty, which is in the direction of system inputs. The finite time convergence to the sliding surface is also proved, which provides an invariance property in finite time. Note that invariance is the most important property of SMC. Finally, the general model of MIMO induction motors (IM) is used to address and to verify the proposed controller.

Adaptive Containment Control for Heterogeneous MIMO Nonlinear Multiagent Systems With Unknown Direction Actuator Faults

In this article, a novel output-feedback adaptive containment control scheme is proposed for a class of heterogeneous multi-agent systems, where the agents are nonlinear multi-input multi-output (MIMO) systems whose relative degrees are allowed to be different. Unlike existing results, we only require the leading principal minors of agents' control gain matrices (CGMs) to be nonzero and take into account unknown direction actuator faults, which relaxes the restrictions on CGMs and enhances system reliability. The difficulties jointly caused by the unknown CGMs, unknown parameters, and unknown jumps introduced by the actuator faults are successfully overcome by a novel recursive contradiction argument based on some Nussbaum functions and a matrix similarity transformation. Moreover, an event-triggering mechanism is introduced to avoid continuous communication among agents and reduce the communication burden. It is shown that all closed-loop signals are globally uniformly bounded and the containment errors converge to a residual set that can be made arbitrarily small. Simulation results illustrate the effectiveness of the proposed scheme.

Improved Model-Free Adaptive Control for MIMO Nonlinear Systems With Event-Triggered Transmission Scheme and Quantization.

In this article, an improved model-free adaptive control (iMFAC) is proposed for discrete-time multi-input multioutput (MIMO) nonlinear systems with an event-triggered transmission scheme and quantization (ETQ). First, an event-triggered scheme is designed, and the structure of the uniform quantizer with an encoding-decoding mechanism is given. With the concept of partial form dynamic linearization based on event-triggered and quantization (PFDL-ETQ), a linearized data model of the MIMO nonlinear system is constructed. Then, an improved model-free adaptive controller with the ETQ process is designed. By this design, the update of the pseudo partitioned Jacobean matrix (PPJM) estimates and control inputs occurs only when the trigger conditions are met, which reduces the network transmission burden and saves the computing resources. Theoretical analysis shows that the proposed iMFAC with the ETQ process can achieve a bounded convergence of tracking error. Finally, a numerical simulation and a biaxial gantry motor contour tracking control system simulation are given to illustrate the feasibility of the proposed iMFAC method with the ETQ process.

Data-Driven Bipartite Formation for a Class of Nonlinear MIMO Multiagent Systems.

The bipartite formation control for the nonlinear discrete-time multiagent systems with signed digraph is considered in this article, in which the dynamics of the agents are completely unknown and multi-input multi-output (MIMO). First, the unknown nonlinear dynamic is converted into the compact-form dynamic linearization (CFDL) data model with a pseudo-Jacobian matrix (PJM). Based on the structurally balanced signed graph, a distance-based formation term is constructed and a bipartite formation model-free adaptive control (MFAC) protocol is designed. By employing the measured input and output data of the agents, the theoretical analysis is developed to prove the bounded-input bounded-output stability and the asymptotic convergence of the formation tracking error. Finally, the effectiveness of the proposed protocol is verified by two numerical examples.

Prescribed-Time Tracking Control of MIMO Nonlinear Systems With Nonvanishing Uncertainties

It is highly desirable yet challenging to achieve zero-error tracking within a given short time period for uncertain multi-input multi-output (MIMO) nonlinear systems. Previous results are primarily state-regulation oriented and are valid only for single-input single-output (SISO) linear systems or nonlinear systems in normal-form. This note presents a tracking control solution for high-order MIMO nonlinear systems in strict-feedback-like form. The proposed control is able to achieve precise tracking within the prescribed time irrespective of initial conditions in the presence of mismatched uncertainties and non-vanishing disturbances.

An improved model-free adaptive control for nonlinear systems: An LMI approach

This paper proposes two model-free adaptive control (MFAC) schemes by using the linear matrix inequality (LMI) approach for the single-input single-output (SISO) and multi-input multi-output nonlinear (MIMO) systems, respectively. For each control scheme, with the aid of the dynamic linearization technique, the nonlinear system is transformed into an equivalent linear data model. In such a transformation, the nonlinear characteristic of systems is compressed into a time-varying parameter. Then, with the help of the introduction of the observer method, the tracking control problem can be converted into an optimization problem and the controller parameters can be obtained by using the LMI technique. This conversion cannot only reduce the complexity of the stability analysis but also find the appropriate controller parameters, especially for the MIMO case. Finally, three examples with comparisons are provided to illustrate the validity of the devised MFAC schemes.

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.

Ball Balancing on 3-RRS Parallel Manipulator Using PD and LQR Control

Ball and plate system (BPS) is known as a nonlinear multi-input multi-output (MIMO) system that has been usually used to investigate and develop control algorithms. In this paper the study deals with a 3-RRS parallel manipulator which has a metal ball, three DC motors with linkage mechanism to a fixed base that can be a resistive touch screen . The moving base has two rotational movements, it can be rotated around the x-axis and y-axis and translated along the z-axis. The main purpose of this study is obtaining dynamics equations of motions and designing PD and LQR controllers. Through simulation and experiment, both control algorithms are proved to work well on this model.

KLMS algorithm in Vector-Valued RKHS for online nonlinear MIMO systems identification

This paper proposes an extension of the KLMS algorithm to the Vector-Valued Reproducing Kernel Hilbert Space (VV-RKHS), enabling the use of the operator-valued kernel (OV-kernel) in the online identification of multi-input multi-output (MIMO) nonlinear systems. The yielded multivariate kernel model offers more design flexibility and involves fewer parameters than other vector-valued KLMS algorithms present in the literature. Conditions ensuring the convergence of the proposed OV-KLMS algorithm are given. Experiments on a multivariate chaotic attractor as well as numerical simulations are carried out and show the effectiveness of the proposed algorithm

Filter-Based Event-Triggered Adaptive Fuzzy Control for Discrete-Time MIMO Nonlinear Systems With Unknown Control Gains

In this article, an event-triggered output feedback adaptive fuzzy control scheme is developed for a class of uncertain discrete-time multiinput–multioutput (MIMO) nonlinear systems with immeasurable states and unknown control gains. Due to the existence of unmeasured states, a set of fuzzy filters are designed, then a filter-based event-triggered adaptive fuzzy control scheme is developed for discrete-time MIMO nonlinear systems. To solve the problem of state estimation caused by the coupling of control input and unknown control gains, a fuzzy filters-based state observer is developed by combining filter states. And then, a parameterized state observer is constructed to effectively estimate immeasurable state signals by the combination of the fuzzy filter states and the gradient-based fuzzy parameter updating law. Based on filter states and estimation states, an event-based adaptive fuzzy control scheme is proposed by novel intermediate errors and backstepping. To overcome the causal problem caused by the low-triangular structure, the variable substitution and a predictor are, respectively, employed to forecast the future state and reference signals. A series of stability analyses illustrates that the proposed scheme achieves immeasurable state estimations, guarantees the ultimately uniformly boundedness of the closed-loop system, and obtains the good tracking performance, while reducing communication occupancy. Finally, simulation studies on a numerical and a practical example are conducted to demonstrate the effectiveness of the proposed scheme.

Synthetic Lyapunov stabilization technique for designing actuation-constrained multi-input multi-output control systems

The main objective of this paper is to present a non-predictive method in the design of nonlinear multi-input multi-output (MIMO) control systems with the presence of constraints that are determinant in practical conditions, namely, the frequency bandwidth limitation of the actuation system and saturation boundaries in control commands. If these constraints are applied in the non-predictive control design problem, it is not possible to simultaneously satisfy Lyapunov stability and actuation constraints, analytically. Instead of model-predictive-based algorithms, which in most cases are computationally expensive, this paper proposes an algorithm based on synthetic Lyapunov stability. In this technique, by defining an intelligent filter applied to the system desired trajectories, defining intelligent proximity coefficients in decoupled inequalities resulting from Lyapunov stability, and determining the admissible boundaries of control commands, a space of regulatory parameters is generated. By appropriately adjusting these parameters based on statistical analysis conducted on the overall dynamics of the system, the Lyapunov stability is guaranteed, and the mentioned control constraints are not violated. In summary, the proposed control algorithm includes the formulation of discrete-time dynamics of sliding functions, the presentation of the procedure of defining and adjusting the control algorithm parameters with the proposed synthetic stability criterion, and the calculation of control inputs based on constraints imposed on the problem. Finally, the algorithm is applied to a cart moving in the X-Y plane, including two rigid cooperative arms that are carrying a load. The most important features of synthetic Lyapunov stability compared to the model predictive-based method are its small computational load and its acceptable performance in satisfying both the Lyapunov stability conditions and determinant control constraints in more realistic situations.

Adaptive Fuzzy Tracking Control of Switched MIMO Nonlinear Systems With Full State Constraints and Unknown Control Directions

In this brief, an adaptive fuzzy tracking control method is proposed for switched multi-input multi-output (MIMO) nonlinear systems with time-varying full state constrains (TFSCs) and unknown control directions. First, the fuzzy logic systems are utilized to approximate unknown dynamic functions. A tangent barrier Lyapunov function (BLF-Tan) is used to solve the problem of TFSCs, and the unknown control directions problem is addressed by applying Nussbaum-type function. Then, an adaptive tracking controller is constructed by the backstepping technique. Under the designed control scheme, all the systems signals are derived to be bounded, and the tracking error of the systems is converged to a neighborhood near zero. Finally, the simulation example illustrates the control design programme is reasonable and effective.

Hybrid GA-MANFIS Model for Organizational Competencies and Performance in Construction

The majority of competency and performance modeling methods available in the literature are deterministic conceptual, statistical, and/or regression models that cannot capture the subjective uncertainty, complex, and nonlinear relationships inherent in construction, which makes accurate prediction difficult. Past studies utilized neuro-fuzzy system (NFS) models, such as adaptive neuro-fuzzy inference system (ANFIS), that combine the learning power of artificial neural networks and functionality of fuzzy systems to develop accurate predictive models. ANFIS is robust, fast, and effective in solving complex problems for a range of real-world construction engineering and management (CEM) applications. NFS models such as ANFIS have some limitations in handling multiple outputs common in construction industry problems, such as being prone to early convergence due to local minima entrapment. To address these limitations, this paper proposes a hybrid NFS combining the evolutionary optimization technique of a genetic algorithm (GA) with a multi-output adaptive neuro-fuzzy inference system (MANFIS) that can handle multi-input multi-output (MIMO) problems for CEM applications. The proposed modeling approach is demonstrated using a case study that showed good results in predicting multiple organizational performance metrics using organizational competencies. The contributions of this paper are threefold: It (1) proposes a novel methodology of integrating different computing techniques for developing a GA-based multi-output adaptive neuro-fuzzy inference system (GA-MANFIS) model that can handle complex and nonlinear MIMO problems inherent in construction processes and practices; (2) relates organizational competencies to performance and predicts multiple organizational performance metrics; and (3) provides a GA-based feature selection approach that reduces data dimensionality, enabling identification of organizational competencies that significantly influence organizational performance. By uniquely integrating these techniques, this model enables construction organizations to evaluate their competencies and predict multiple organizational performance metrics simultaneously, and researchers can adapt it for a variety of construction contexts.

A decoupler assisted optimised controller design for the greenhouse system

This paper presents the novelty of the feedback feed-forward linearisation integrated with the optimised PID controller for the greenhouse system (GHS). The GHS is a group of multi-input multi-output (MIMO) systems with highly coupled, disturbed, and nonlinear dynamics. Using the proposed novel approach, initially, the nonlinear MIMO system is decoupled into two independent linearised single-input single-output (SISO) systems (i.e., temperature loop and humidity loop). After the decoupling, the separated loops are regulated by the genetic algorithm-based optimised PID controllers. The extensive simulation study is carried out for the stabilising and the tracking control for both the loops of the GHS in the presence of various initial conditions, and various load disturbances (e.g., canopy temperature, external temperature, external humidity, and solar radiation). Finally, the performance robustness of the proposed control structure is compared with the linear quadratic regulator (LQR) controller, conventional PID controller, and the Ziegler-Nichols tuned PID controller under diversified scenarios.

A novel framework to finite-time tracking of nonlinear MIMO systems based on fast terminal sliding-mode method

In this paper, a novel approach is proposed to design a robust finite-time tracking controller for uncertain affine multi-input multi-output (MIMO) systems. In the proposed approach, a fast terminal sliding mode (FTSM) controller is designed, based on the input–output relation of the MIMO nonlinear systems. The main advantage of the proposed method is its capability to handle the internal dynamics of the system. Moreover, in the proposed controller, the state variables of the internal dynamics of the system are not necessary to be measured. To realize the finite-time convergence of the output variables, a set of switching manifolds with a recursive procedure is utilized. Finally, the robust stability and tracking efficiency of the proposed control law are shown through computer simulations.

Synchronization problem for a class of multi-input multi-output systems with terminal sliding mode control based on finite-time disturbance observer: Application to Chameleon chaotic system

This paper studies the synchronization problem of two nonlinear multi-input multi-output (MIMO) systems in finite-time period. For this purpose, a terminal sliding mode controller (TSMC) with a finite-time disturbance observer (FTDO) is employed. Using an FTDO, in a finite time interval, the disturbance parameters precisely can be identified which produce a better transient performance compared to the Lyapunov parameter estimation (LPE) method. Unlike previous literature, the imposed restrictions over external disturbances have been relaxed, i.e., the upper bounds of disturbances and the restrictive condition over the disturbances’ first derivatives have been removed. According to the proposed FTDO, a continuous control input is developed that eliminates chattering in synchronization of nonlinear MIMO master-slave system; as a result, a chattering-free TSMC is attained which makes the synchronization errors converge to the origin in finite-time period. By means of the Lyapunov function (CLF), the stability of the introduced TSMC and the FTDO are proved. Finally, in the simulation section, the efficiency and the accuracy of the proposed approach are revealed by applying the proposed method on a Chameleon master-slave chaotic flow.

Application of a GA-Optimized NNARX controller to nonlinear chemical and biochemical processes

Chemical and biochemical processes generally suffer from extreme nonlinearities with respect to internal states, manipulated variables, and also disturbances. These processes have always received special technical and scientific attention due to their importance as the means of large-scale production of chemicals, pharmaceuticals, and biologically active agents. In this work, a general-purpose genetic algorithm (GA)-optimized neural network (NNARX) controller is introduced, which offers a very simple but efficient design. First, the proof of the controller stability is presented, which indicates that the controller is bounded-input bounded-output (BIBO) stable under simple conditions. Then the controller was tested for setpoint tracking, handling modeling error, and disturbance rejection on two nonlinear processes that is, a continuous fermentation and a continuous pH neutralization process. Compared to a conventional proportional-integral (PI) controller, the results indicated better performance of the controller for setpoint tracking and acceptable action for disturbance rejection. Hence, the GA-optimized NNARX controller can be implemented for a variety of nonlinear multi-input multi-output (MIMO) systems with minimal a-priori information of the process and the controller structure.

Output feedback control with disturbance compensation in nonlinear MIMO systems under measurement noises

A novel output feedback control law with disturbance compensation for nonlinear multi-input multi-output (MIMO) time-invariant systems under measurement noises is proposed. The designed control law, based on the noise and disturbance estimations, ensures the accuracy in steady state depending on the disturbance, only one component of noise vector and its first derivatives. Therefore, the proposed algorithm is efficient under noises with large magnitudes. Sufficient conditions in terms of linear matrix inequalities (LMIs) provide a practical exponential stability of the closed-loop system. The simulations illustrate an efficiency of the proposed method compared with some existing ones.

Fuzzy Observer Constraint Based on Adaptive Control for Uncertain Nonlinear MIMO Systems With Time-Varying State Constraints.

This article presents an adaptive output feedback approach of nonlinear multi-input-multi-output (MIMO) systems with time-varying state constraints and unmeasured states. An adaptive approximator is designed to approximate the unknown nonlinear functions existing in the state-constrained systems with immeasurable states. To deal with the tracking problem of such systems, a state observer with time-varying barrier Lyapunov functions (BLFs) is introduced in the controller design procedure. The backstepping design with time-varying BLFs is utilized to guarantee that all system states remain within the time-varying-constrained interval. The constant constraint is only the special case of the time-varying constraint which is more general in the real systems. The proposed control approach guarantees that all signals in the closed-loop systems are bounded and the tracking errors converge to a bounded compact set, and time-varying full-state constraints are never violated. A simulation example is given to confirm the feasibility of the presented control approach in this article.