Multi-input Multi-output Nonlinear Systems Research Articles

Sufficient Conditions for Global Integral Action via Incremental Forwarding for Input-Affine Nonlinear Systems

In this article, we study the problem of constant output regulation for a class of input-affine multi-input multi-output nonlinear systems, which do not necessarily admit a normal form. We allow the references and the disturbances to be arbitrarily large and the initial conditions of the system to range in the full-state space. We cast the problem in the contraction framework, and we rely on the common approach of extending the system with an integral action processing the regulation error. We then present sufficient conditions for the design of a state-feedback control law able to make the resulting closed-loop system incrementally stable, uniformly with respect to the references and the disturbances. Such a property ensures uniqueness and attractiveness of an equilibrium on which output regulation is obtained. To this end, we develop an incremental version of the forwarding (mod <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\lbrace L_gV\rbrace$</tex-math></inline-formula> ) approach. Finally, we provide a set of sufficient conditions for the design of a pure (small-gain) integral-feedback control. The proposed approach is also specialized for two classes of systems that are linear systems having a Lipschitz nonlinearity and a class of minimum-phase systems whose zero dynamics are incrementally stable.

Observer-Based Event-Triggered Adaptive Fuzzy Control for Fractional-Order Time-Varying Delayed MIMO Systems Against Actuator Faults

This article presents the observer-based event-triggered adaptive hybrid fuzzy dynamic surface control strategy for a category of uncertain nonstrict-feedback fractional-order nonlinear multi-input multi-output systems, including unknown time-varying delays and actuator faults. First, an adaptive hybrid fuzzy state observer and a serial-parallel estimation system are constructed to estimate the unmeasured system states and incorporate them into the control design scheme, respectively, where some appropriate fuzzy logic systems are introduced to approximate the unknown nonlinear functions. According to the dynamic surface control technique, the designed adaptive fuzzy control approach can surmount the deficiency of “complexity explosion.” Then, an observer-based adaptive event-triggered control algorithm is developed by constructing the Lyapunov–Krasovskii functionals and estimating the compounded disturbances. Furthermore, it is proved that under the drive of the reference signals, all the signals in the closed-loop system are semiglobally uniformly ultimately bounded and Zeno behavior can be successfully excluded. Finally, an example with numerical simulations is utilized to exhibit the applicability of the obtained observer-based event-triggered adaptive fuzzy control approach.

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.

Special issue on PID control in the information age: Theoretical advances and applications

Special issue on PID control in the information age: Theoretical advances and applications

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

Prescribed Performance Fuzzy Adaptive Output Feedback Control for Nonlinear MIMO Systems in a Finite Time

This article studies the fuzzy adaptive output feedback control design problem for nonstrict feedback multi-input–multi-output nonlinear systems with full-states prescribed performance in finite time. Fuzzy logic systems are introduced to solve the problem of unknown nonlinear dynamics. And on this basis, a fuzzy-based state observer is designed to observe the unmeasurable state. Further, by combining the adaptive back-stepping control algorithm and the nonlinear filters, a novel dynamic surface control (DSC) method is proposed, which not only solves the computational complexity explosion problem inherent in the back-stepping control algorithm, but also improves the control performance, in contrast to the traditional DSC methods with linear filters. Besides, to further improve the tracking performance under the structure of full-states prescribed performance, a new Lyapunov function is designed considering the transform error constraint. Based on the Lyapunov theory, the stability of the closed-loop system is analyzed to ensure that all signals of the closed-loop system are semiglobal practical finite-time stability. Finally, to elaborate on the feasibility and effectiveness of the proposed control method, a simulation example is provided.

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.

Fast finite‐time adaptive neural fault‐tolerant tracking control for multi‐input multi‐output systems with full‐state constraints

SummaryThis article investigates the problem of fast finite‐time adaptive neural fault‐tolerant tracking control for multi‐input multi‐output (MIMO) nonlinear systems with full‐state constraints and actuator faults. The radial basis function neural networks are introduced to deal with unknown nonlinear functions. In addition, an additive transformation and one‐to‐one mapping method are employed to deal with the control problem of MIMO nonlinear systems with full‐state constraints. Based on the fast finite‐time stability theory and adaptive backstepping technique, which guarantees all the closed‐loop system signals are bounded, the tracking error eventually converges to a small neighborhood of the origin in a fast finite‐time and full‐state constraints are not violated. Finally, simulation results demonstrate the feasibility of the proposed control scheme.

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.

Intelligent Command Filter Design for Strict Feedback Unmodeled Dynamic MIMO Systems With Applications to Energy Systems

This study presents a command filtered control scheme for multi-input multi-output (MIMO) strict feedback nonlinear unmodeled dynamical systems with its applications to power systems. To deal with dynamic uncertainties, a dynamic signal is introduced, together with radial basis function neural networks (RBFNNs) to overcome the influences of the dynamic uncertainties. Command filters (CFs) are used to prevent the explosion of complexity, where the compensating signals can eliminate the effect of filter errors. Compared with single-input single-output strict feedback nonlinear systems, the method proposed in this study has more suitability. In the end, the simulation experiments are carried out by applying the developed algorithm to power systems, where the simulation results verify the efficacy of the approach proposed.

Online Detection of Model-Plant Mismatch in Closed-Loop Systems With Gaussian Processes

In model-based strategies, such as real-time optimization (RTO) and model predictive control (MPC), the process model plays an important role. However, model-plant mismatch is inevitable because of various uncertainties in the real application. Therefore, it is highly desirable to detect the mismatch online with measurements of the closed-loop system. This article proposes a mismatch detection approach based on a Gaussian process (GP) model, which is integrated with RTO and MPC to improve economic performance. The GP model is obtained by training a dataset, including parameters and measurements. An ideal system with no model-plant mismatch is designed to compare to the real control system having mismatch. The outputs error of the two systems is used to build a feedback mechanism to adjust the estimation. The re-estimated parameters are used to update the model RTO and MPC. The proposed approach is nonintrusive and can be used in multiinput–multioutput nonlinear systems. Based on the benchmark model of a continuous-stirred tank reactor, a detailed 4-in-4-out nonlinear model of the Fischer esterification reaction is provided to demonstrate the performance of the proposed approach. The result shows that the relative biases of estimates decrease from 5 to 1%, and the economic profit increase by 1.5%

Phase-Unsynchronized Power Decoupling Control of MMC Based on Feedback Linearization

The traditional power decoupling control of modular multilevel converter (MMC) is based on the phase synchronization achieved by the phase-locked loop (PLL), and MMC intricate inner dynamics are ignored, which jeopardizes the system stability and power decoupling. To improve the performance, a nonlinear phase-unsynchronized power decoupling control for MMC is proposed without PLL. At first, the MMC model as a nonlinear multi-input multi-output system is developed. The developed model illustrates that the MMC power coupling is caused by the ac current as well as the MMC capacitor voltages. Then, through the input–output linearization method, the proposed method decouples the MMC output powers without the phase synchronization. Involving integral control, the dynamics of MMC output powers are designed as second-order systems so that the control parameters can be easily determined based on the required transient performance. To verify the accuracy and correctness of the developed model, a comparison of MMC dynamics with the proposed control is conducted between the numerical solution in MATLAB and the EMT simulation in PSCAD/EMTDC. Moreover, seven cases in the EMT simulations and four cases in the experimental results demonstrate the desired phase asynchronization and power decoupling performance of the proposed method compared with the conventional <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$dq$</tex-math></inline-formula> control. At last, the system zero dynamic stability is investigated and the influences of MMC control parameters, ac-side voltage, dc-side voltage and equilibrium points are analyzed to evaluate the stability performance of the proposed method.

Sampled-data-based uncertainty compensation control for a class of continuous-time nonlinear MIMO systems

This paper proposes a sampled-data-based uncertainty compensation control strategy for a class of continuous-time multi-input multi-output nonlinear systems with strong coupling uncertainties. Unlike observer-based uncertainty compensation control methods, this paper utilizes the true value of the total disturbance at an instant in the previous sampling interval rather than its observed value in the last sampling time to compensate for the total disturbance. The total disturbance considered in this paper is composed of the unmodeled nonlinear coupling dynamics and external disturbance. The continuous-time systems and the sampled-data feedback control make up a hybrid closed-loop control system, which, together with the strongly coupled nonlinear uncertainties of the system, brings a significant hurdle to verifying the stability and convergence of the closed-loop control system. A new eigenvalue-and-series-based analysis method is proposed to overcome this hurdle. It is proved that when the tracking target is a bounded function, the tracking error can be arbitrarily small when the sampling period is small enough. Furthermore, when the tracking target is a constant and the nonlinear term is time-invariant, the tracking error converges to zero as time tends to infinity. Numerical results on the attitude control for a 2-DOF UAV validate the effectiveness and merits of the proposed method.

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.

Nonlinear optimal control for Maglev platform roll motion

The stable manifold method is applied to construct a nonlinear real-time feedback optimal control system for the roll motion and vertical position of a certain maglev platform. The chosen platform uses combined electromagnetic suspensions consisting of permanent magnets and upper and lower electromagnets. Within the given technical gaps between the platform and guideway, the magnetic forces provide highly nonlinear effects. This makes this object a multi-input multi-output (MIMO) nonlinear control system. The stable manifold method is applied to construct an optimal nonlinear stabilizing controller. The benefit of the nonlinear control in comparison with a linear regulator is illustrated on an ensemble of perturbed motions caused by a set of initial deviations covering the necessary engineering stabilization range.

Distributed deep reinforcement learning-based coordination performance optimization method for proton exchange membrane fuel cell system

A proton exchange membrane fuel cell (PEMFC) is a multi-input multi-output nonlinear complicated system, the output power and operating efficiency of which are affected by various operating variables. To achieve coordinated control of multiple operating variables and thus improve the stability, performance, and efficiency of the PEMFC power system, a data-driven power coordination management method is proposed. Furthermore, a metaverse-based multiagent double delay deep deterministic policy gradient (MET-MADDPG) algorithm is also presented. The design of this algorithm is structured on the concept of the metaverse in that it employs different metaverses during pre-learning and combines imitation learning and curriculum learning to enable agents in different combinations to be fully trained in different environments to improve coordination strategy robustness. In this algorithm, the hydrogen controller, air controller, water pump controller and radiator controller are regarded as four agents; the objective of the training is to enable agents with their different goals to coordinate. The effectiveness of the proposed algorithm is demonstrated in a series of experiments in which it is compared with existing algorithms.

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.

Robust multi-input multi-output adaptive fuzzy terminal sliding mode control of deep brain stimulation in Parkinson\u2019s disease: a simulation study

Deep brain stimulation (DBS) has become an effective therapeutic solution for Parkinson’s disease (PD). Adaptive closed-loop DBS can be used to minimize stimulation-induced side effects by automatically determining the stimulation parameters based on the PD dynamics. In this paper, by modeling the interaction between the neurons in populations of the thalamic, the network-level modulation of thalamic is represented in a standard canonical form as a multi-input multi-output (MIMO) nonlinear first-order system with uncertainty and external disturbances. A class of fast and robust MIMO adaptive fuzzy terminal sliding mode control (AFTSMC) has been presented for control of membrane potential of thalamic neuron populations through continuous adaptive DBS current applied to the thalamus. A fuzzy logic system (FLS) is used to estimate the unknown nonlinear dynamics of the model, and the weights of FLS are adjusted online to guarantee the convergence of FLS parameters to optimal values. The simulation results show that the proposed AFTSMC not only significantly produces lower tracking errors in comparison with the classical adaptive fuzzy sliding mode control (AFSMC), but also makes more robust and reliable outputs. The results suggest that the proposed AFTSMC provides a more robust and smooth control input which is highly desirable for hardware design and implementation.

A new adaptive identification framework for nonlinear multi-input multi-output systems under colored noise

In this paper, an adaptive identification scheme is proposed for nonlinear multi-input multi-output systems with colored noise based on a novel parameter update law. With the help of the hierarchical principle, the identification model is decomposed into three sub-models in which the computational burden is reduced. For each sub-model, the identification algorithm is proposed to estimate the sub-model parameters. In the process of the identification algorithm design, considering the system information corrupted by the noise, an adaptive filter gain is exploited to extract helpful identification data, in which a filter is designed using the system data instead of the independent design. Based on several auxiliary filtered variables, the estimation error data are obtained, and a new parameter adaptive law with a variable learning gain is proposed according to the estimation error data. Compared with the classic parameter update law, the parameter estimation update is derived based on the estimation error information instead of other error information, such as prediction error information. Under the persistent excitation condition, all the estimated parameters converge to the true parameters. an example is used and two experiments are conducted to test the outstanding identification performance of the proposed algorithm in terms of convergence rate and identification accuracy.

A Multi-Spectral Approach to Fuzzy Quantum Modelling of Nonlinear Systems

In this work, we explore multi-input multi-output (MIMO) nonlinear control systems design by generalizing concepts from radio link analysis. We demonstrate practical applications of multidimensional sampling and reconstruction to reducing computational overhead in nonlinear systems analysis. Using multi-spectral analysis, we show that (de)fuzzification in control systems and (de)modulation in communication systems are analogous. Finally, we explore the values of fuzzy submodels as quantum mechanics objects for stability analysis and feedback controller synthesis of nonlinear mechanical systems. The effectiveness of the proposed approach is confirmed by simulating the attitude model a telecommunications satellite.