Multiple-input Multiple-output Nonlinear Systems Research Articles

Robust sliding-mode observer for unbounded state nonlinear systems

Designing a full-state observer for nonlinear systems has always been accompanied by challenges and restrictive constraints. Mainly, applying a state observer in nonlinear systems with non-minimum phase characteristics is more challenging when the limiting constraints are not satisfied due to diverging internal dynamics. In this paper, a robust sliding-mode observer approach has been successfully employed to estimate the states of nonlinear systems with unbounded and diverging dynamics. The design principles of this observer are based on applying a classifying algorithm in single-input single-output and multiple-input multiple-output nonlinear systems. It is noteworthy that this observer is highly robust against disturbance, uncertainty and measurement noise, and its conditions are less conservative compared to previous nonlinear sliding-mode observers. One novel feature of the proposed observer is that while the system's state gets unbounded and diverged in fault-occurring scenarios or critical circumstances, this observer retains accuracy. The efficiency of the proposed observer is verified in the simulation results for two nonlinear industrial systems, including a hydro-turbine power generation plant and a continuous stirred tank reactor.

Performance recovery of a discrete-time MIMO nonlinear system using a fast observer

This paper presents a multi-rate digital control scheme for a class of nonlinear systems where the controller and observer are both designed in discrete time and where the plant has zero dynamics and is multiple input, multiple output (MIMO). The fast observer is a discrete time analogue to the high gain observer, which can achieve quick estimation of states. Performance recovery is achieved with the fast observer and control saturation.

Resilient Neural Control Based on Event-Triggered Extended State Observers and the Application in Unmanned Aerial Vehicles

In the real world, many systems can be written as multiple-input multiple-output (MIMO) systems, such as unmanned aerial vehicles (UAVs), unmanned vehicles, etc. Therefore, this is a problem for the generality of the research method, and this paper aimming at the control problem of MIMO nonlinear systems with system uncertainties and external disturbances, a resilient control approach is proposed based on the event-triggered extended state observer (ETESO) with neural networks (NNs) in this paper. Firstly, the constraint problem of the tracking error is transformed into an unconstrained problem based on the performance function, then the NNs are employed to approximate the uncertainties, and the ETESO with NNs is designed to estimate the combination of the approximation error and the external disturbance. Secondly, the perturbation of the controller gain is described by an external system, which is estimated by a fault observer. To avoid the problem of the differential explosion, the resilient controller is designed by the backstepping control method based on the command filter. Through the Lyapunov stability analysis, all signals of the entire system are uniformly ultimate bounded. Finally, the flight control experiment is shown to demonstrate the feasibility of the control scheme.

Nonsingular Practical Fixed-Time Adaptive Output Feedback Control of MIMO Nonlinear Systems.

This article studies the nonsingular fixed-time control problem of multiple-input multiple-output (MIMO) nonlinear systems with unmeasured states for the first time. A state observer is designed to solve the problem that system states cannot be measured. Due to the existence of the unknown system nonlinear dynamics, neural networks (NNs) are introduced to approximate them. Then, through the combination of adaptive backstepping recursive technology and adding power integration technology, a nonsingular fixed-time adaptive output feedback control algorithm is proposed, which introduces a filter to avoid the complicated derivation process of the virtual control function. According to the fixed-time Lyapunov stability theory, the practical fixed-time stability of the closed-loop system is proven, which means that all signals of the closed-loop system remain bounded in a fixed time under the proposed algorithm. Finally, the effectiveness of the proposed algorithm is verified by the numerical simulation and practical simulation.

Recursive d-step-ahead predictive control of MIMO nonlinear systems with input time-delay via multi-dimensional Taylor network extended from PID

In this paper, a recursive d-step-ahead predictive control scheme based on multi-dimensional Taylor network (MTN) is proposed for the real-time tracking control of multiple-input multiple-output (MIMO) nonlinear systems with input time-delay. The MTN predictive model is designed using a recursive approach to compensate the influence of time-delay, and an extended Kalman filter (EKF) is applied as its learning algorithm. An MTN controller is developed based on a proportional–integral–derivative (PID) controller where the closed-loop errors between the reference input and the system output are set as the MTN controller’s inputs. Then, a back propagation (BP) algorithm, designed to update its weights according to errors caused by system uncertainty, is used as a learning algorithm for the MTN controller. Meanwhile, the convergence of the MTN predictive model and the stability of the closed-loop system are evaluated. Two numerical examples and a practical example – continuous stirred tank reactor (CSTR) process are presented to verify the superiority of the proposed scheme. The experimental results and the computational complexity analysis show that the proposed scheme is effective, promising its desirable robustness, anti-disturbance, tracking and real-time performance.

Unifying performance specifications in tracking control of MIMO nonlinear systems with actuation faults

Guaranteeing prescribed performance is critical to maintaining system efficiency and reliability. The state-of-the-art approaches achieve different performance specifications with different control structures and settings. In this paper, we propose a novel control methodology to uniformly address the prescribed performance problem for uncertain multiple-input multiple-output (MIMO) nonlinear systems in the presence of actuator faults. By constructing a non-monotonic function transformation and an asymmetric barrier function, we recast the underlying problem into one that only needs for simple selection of certain design parameters. With such a treatment, different performance behaviors can be achieved under a single (unified) control framework without the requirement for alternating the control structure, making the design more user-friendly and implementation less demanding. Furthermore, by embedding the available information on the state-dependent diagonal matrix into the filtered-error-like design procedure, the obstacle of ensuring the controllability of the closed-loop system, caused by the actuator faults and performance behaviors, is circumvented. Both theoretical analysis and numerical simulation demonstrate the effectiveness and benefits of the proposed method.

PI Stabilizing Control of Nonaffine MIMO Systems by Additive-State-Decomposition Dynamic Inversion Design

This paper addresses the stabilizing control issue for a class of non-affine MIMO (Multiple Input Multiple Output) nonlinear systems subject to time-varying disturbance using an additive-state-decomposition dynamic inversion control scheme. First, the original system is transformed into a minimum phase system through a proposed output redefinition method. Then, the transformed minimum-phase system is further additively decomposed into a primary subsystem and a secondary subsystem. Next, the dynamic inversion control scheme solves the non-affine control problem. Stability analysis shows that the proposed control method guarantees all closed-loop system signals being semi-globally uniformly ultimately bounded. Finally, a simulation and an attitude control experiment of a quadcopter show the effectiveness of the proposed control method.

Nonsingular Fixed-Time Control of Nonstrict Feedback MIMO Nonlinear System With Asymptotically Convergent Tracking Error

In this paper, the research on fixed-time tracking control problem of multiple-input multiple-output (MIMO) nonlinear systems with non-strict feedback control structure is carried out. By means of the fuzzy logic systems (FLSs), the unknown system nonlinear dynamics are identified, and the “algebraic loop problem” is solved. Then, through the combination of adaptive back-stepping recursive technology and adding power integration technology, a non-singular fixed-time adaptive tracking control scheme is presented. Under the action of the presented control scheme, the system can track the specified reference signal within a fixed time independent of the initial state of the system, and the tracking control error can converge to zero asymptotically. Next, on the basis of the fixed-time Lyapunov stability theory, the practical fixed-time stability of the closed-loop system is theoretically demonstrated. Finally, two simulations verify the validity and practicability of the proposed control scheme.

Global stabilization control for multiple input multiple output nonlinear systems with unknown function vector

AbstractIn this article, a control algorithm is proposed to solve the global stabilization control problem of multiple input multiple output (MIMO) nonlinear systems with unknown function vectors (UFVs). Firstly, a Lemma dealing with UFVs is proposed. Then, combined with the backstepping method, the controller is designed such that all signals of the closed‐loop system are globally stable. Compared with the approximation method, the algorithm in this article solves the global stabilization control problem. Compared with the assumptions of UFVs, the algorithm in this article reduces the conservatism problem. At the same time, the algorithm in this article also solves the “explosion of terms” problem of backstepping. Compared with the methods to solve this problem: dynamic surface control (DSC) and direct fuzzy control, the algorithm in this article can make all signals of the closed‐loop system converge to the origin. Finally, the algorithm is applied to the model of spacecraft with modified Rodrigues parameters, and the simulation results show the effectiveness of this algorithm.

Decoupling Control of Outer Rotor Coreless Bearingless Permanent Magnet Synchronous Motor Based on Least Squares Support Vector Machine Generalized Inverse Optimized by Improved Genetic Algorithm

In the decoupling control process of the outer rotor coreless bearingless permanent magnet synchronous motor using a least squares support vector machine, the kernel width <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">σ</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and the penalty factor <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">γ</i> of the least squares support vector machine are difficult to tune, resulting in high kernel space complexity and low fitting accuracy. A new improved genetic algorithm is used to optimize the above parameters. First, the generalized inverse system model of the original nonlinear multiple-input multiple-output system is fitted online with the optimized least squares support vector machine, and the generalized inverse system model is connected in series with the original system to form a pseudolinear system. Then, a linear closed-loop controller is used for control. Simulations and experiments show that the robustness and wide applicability of the original system are guaranteed. The dynamic and static performances of the system are improved, verifying the effectiveness of the scheme.

Design and Analysis of a Space Dynamic Test Platform

This paper describes a kind of laboratory simulation test platform. The dynamic coupling model of the simulation test platform has been obtained by using the Newton-Euler equation. According to the inverse-system, the equation can be decoupled, and the decoupling analysis and calculation of the system are performed through the decoupling theorem. As a result, the coupled nonlinear Multiple-Input Multiple-Output system is converted to two linear decoupled Single-Input Single-Output subsystems. The establishment of the mathematical model can provide reference for the design of the controller in the simulation test platform. In order to verify the error of the rotation accuracy of the simulated test platform developed, a reasonable experimental scheme was developed for testing.

Robust multimodel control for uncertain nonlinear MIMO systems based on ARX-Laguerre multimodel and LSDP approach

In this paper, we propose a new alternative for the robust control of nonlinear MIMO (multiple-input multiple-output) systems based on the multimodel approach and LSDP (Loop-Shaping Design Procedure)approach in the discrete case. First, the multimodel approach is exploited by representing each linear sub-model in the form of the recent linear MIMO ARX (Auto-Regressive with eXogenous inputs) -Laguerre model which guarantees a significant parameters number reduction compared with the MIMO ARX model. Thus, the resulting multivariable multimodel, entitled MIMO ARX-Laguerre multimodel, ensures a reduction of the parametric complexity with a simple recursive vector representation. However, this reduction is conditioned by an optimal choice of the pole characterising each Laguerre base. To deal with this, we propose the identification, using the genetic algorithm, of the Laguerre poles as well as the weighting function parameters of the MIMO ARX-Laguerre multimodel. This latter allows to generate a set of linear MIMO ARX-Laguerre sub-models which are exploited to propose a robust multimodel control for uncertain nonlinear MIMO systems. In fact, for each identified sub-model, we combine the LSDP approach and the RGA (Relative Gain Array) theory to develop a local robust controller. Then, a multivariable roust multimodel control algorithm is developed where the overall control strategy by multimodel approach amounts to incorporating the same weighting functions used in the considered multivariable multimodel in order to interpolate the control laws calculated from each local robust controller. The optimisation of Laguerre poles and weighting functions parameters as well as the proposed multivariable robust multimodel control algorithm are validated on the experimental prototype Quanser Aero system.

Lumped uncertainty alleviation in output channels of MIMO nonlinear systems based on robust disturbance observer‐based control strategy

AbstractDisturbances and uncertainties can produce unsatisfactory responses in many industrial and engineering systems. Besides, the practical systems and processes are multiple‐input multiple‐output (MIMO). Hence, achieving a good control performance with adequate output responses is not simple. Many different methods were provided for control of industrial processes in some references. However, in this paper, the primary goal is to design an appropriate tracking controller for alleviating the destructive effects of uncertainties in output channels of MIMO nonlinear systems. For this purpose, a robust mechanism has been introduced according to the optimal design of centralized extended proportional‐derivative (CEPD) and disturbance observer (DOB). By designing the derivative part based on famous Vandermonde matrix and DOB gain , the robust criterion is obtained to tackle the undesirable factors such as nonlinear functions and uncertainties in error dynamics. The closed‐loop stability is guaranteed by tuning the proportional part under linear matrix inequality. The proposed scheme in this paper can be used for a wide range of MIMO nonlinear systems in practical situations.

Introducing a Novel Model-Free Multivariable Adaptive Neural Network Controller for Square MIMO Systems.

In this study, a novel Multivariable Adaptive Neural Network Controller (MANNC) is developed for coupled model-free n-input n-output systems. The learning algorithm of the proposed controller does not rely on the model of a system and uses only the history of the system inputs and outputs. The system is considered as a ‘black box’ with no pre-knowledge of its internal structure. By online monitoring and possessing the system inputs and outputs, the parameters of the controller are adjusted. Using the accumulated gradient of the system error along with the Lyapunov stability analysis, the weights’ adjustment convergence of the controller can be observed, and an optimal training number of the controller can be selected. The Lyapunov stability of the system is checked during the entire weight training process to enable the controller to handle any possible nonlinearities of the system. The effectiveness of the MANNC in controlling nonlinear square multiple-input multiple-output (MIMO) systems is demonstrated via three simulation studies covering the cases of a time-invariant nonlinear MIMO system, a time-variant nonlinear MIMO system, and a hybrid MIMO system, respectively. In each case, the performance of the MANNC is compared with that of a properly selected existing counterpart. Simulation results demonstrate that the proposed MANNC is capable of controlling various types of square MIMO systems with much improved performance over its existing counterpart. The unique properties of the MANNC will make it a suitable candidate for many industrial applications.

Disturbance-Compensation-Based Multilayer Neuroadaptive Control of MIMO Uncertain Nonlinear Systems

Committed to further enhancing the achievable tracking performance, a novel disturbance-compensation-based composite multilayer neural network adaptive control algorithm is developed for a class of multiple input multiple output nonlinear systems with modeling uncertainties. Specially, an extended state observer is utilized to estimate the exogenous disturbance and meanwhile predict the system state. Moreover, the nonlinear function uncertainties are approximated by the multilayer neural networks. Furthermore, the modeling uncertainties can be compensated in a feedforward manner. Notably, the multilayer neural network weights are updated via the composite adaption laws driven by the output tracking error and the prediction errors of the system state and control input, which brings improved function approximation performance. Finally, the application results demonstrate the efficacy of the integrated intelligent controller.

Adaptive Neural Control of Uncertain MIMO Nonlinear Pure-Feedback Systems via Quantized State Feedback

We present an adaptive quantized state feedback tracking methodology for a class of uncertain multiple-input multiple-output (MIMO) nonlinear block-triangular pure-feedback systems with state quantizers. Uniform quantizers are considered to quantize all measurable state variables for feedback. Compared with the existing tracking approaches of MIMO lower-triangular nonlinear systems, the main contributions of the proposed strategy are developing (1) a quantized-state-feedback-based adaptive tracker in the presence of nonaffine interaction of states and control variables of MIMO systems and (2) an analysis strategy for quantized feedback stability using adaptive compensation terms to derive bounded quantization errors. In addition, the stability of the closed-loop system with quantized state feedback is analyzed based on the Lyapunov stability theorem. Finally, simulation examples, including interconnected inverted pendulums, are presented to validate the effectiveness of the proposed control strategy.

Adaptive fuzzy command filtering control for nonlinear MIMO systems with full state constraints and unknown control direction

In this paper, the command-filter-based adaptive control strategy is proposed for a class of unknown nonlinear multiple input multiple output (MIMO) systems with full state constraints and unknown control direction, whose unknown nonlinear function is approximated by the fuzzy logic system (FLS). First, the fuzzy logic system (FLS) act as the universal approximator of the unknown nonlinear function and the command-filtered backstepping control method is utilized to handle the difficulty induced by the explosion of differentiation, as well as the compensating signals are designed to make up for the command filter error. Besides, the appropriate barrier Lyapunov function and the Nussbaum-type functions are employed to deal with the constraints violation and the unknown direction control gains, respectively. It is proved that the practical tracking performance of the system can be achieved with the designed protocols and all signals in the closed-loop system are semiglobal uniformly ultimately bounded. Finally, the simulation example is performed to verify the effectiveness of the proposed control strategy.

Learning low-dimensional separable decompositions of MIMO non-linear systems

We present a new internal structure exploration method developed for the multiple-input multiple-output (MIMO) dynamical systems with finite memory and almost arbitrary non-linear characteristic. The proposed Double Separation Algorithm applies distance correlation screening for pre-selection of those system inputs that contribute to the consecutive outputs and, based on the first-stage inference outcomes, estimates projection coefficients sensitive to the existence of additive system sub-characteristics. In effect, the proposed approach allows for effective exploration of the internal system structure. A numerical experiment on an MIMO nonlinear finite impulse response (NFIR) system illustrates the ability of the proposed approach to indicate which of the system inputs contribute to which of the system outputs. The experiment also illustrates the ability of the approach to detect which of the nonlinear sub-characteristics, recovered in the first stage of the approach, can be separated into a sum of lower-dimensional sub-characteristics.

Approximation-Based Quantized State Feedback Tracking of Uncertain Input-Saturated MIMO Nonlinear Systems with Application to 2-DOF Helicopter

This paper addresses an approximation-based quantized state feedback tracking problem of multiple-input multiple-output (MIMO) nonlinear systems with quantized input saturation. A uniform quantizer is adopted to quantize state variables and control inputs of MIMO nonlinear systems. The primary features in the current development are that (i) an adaptive neural network tracker using quantized states is developed for MIMO nonlinear systems and (ii) a compensation mechanism of quantized input saturation is designed by constructing an auxiliary system. An adaptive neural tracker design with the compensation of quantized input saturation is developed by deriving an augmented error surface using quantized states. It is shown that closed-loop stability analysis and tracking error convergence are conducted based on Lyapunov theory. Finally, we give simulation and experimental results of the 2-degrees-of-freedom (2-DOF) helicopter system for verifying to the validity of the proposed methodology where the tracking performance of pitch and yaw angles is measured with the mean squared errors of 0.1044 and 0.0435 for simulation results, and those of 0.0656 and 0.0523 for experimental results.

Control design for a class of multivariable nonlinear system with uncertain control direction: A laser cladding case study

In this work, the design of a controller for a multiple-input multiple-output (MIMO) nonlinear system with uncertain control direction is proposed. A formal Lyapunov stability analysis is presented for the design of the MIMO controller by considering the system with and without parametric uncertainties. The design is applied to an additive manufacturing technology known as Laser Cladding (LC). The proposed MIMO controller is composed of a feedback linearization term (aimed at canceling the known nominal dynamics) and a sliding mode term with the boundary layer technique (aimed at compensating the system uncertainties). The proposed control scheme was tested via simulations by considering tracks of two different powder feedstock, Ti6Al4V and IN718. Simulation results confirm that the control objective is achieved under parametric uncertainties, including variations up to 40% of the convection coefficient. Moreover, the control law is easy to implement and the control signal has a continuous behavior precluding any high-frequency oscillation (chattering effect).