Bounded-input Bounded-output Research Articles

Robust data-driven model-free adaptive control to uncertainties and disturbances for NARMAX systems

This paper introduces an enhancement to the model-free adaptive control (MFAC) method based on a new control input cost function for full-form dynamic linearization (FFDL) for NARMAX systems. The new control cost function includes the one-step-ahead tracking error, OER, and output error integral. The main feature of the approach is that it has a high ability to overcome disturbances in the control input and measured noise in the output. Analytical and extensive simulations have demonstrated that the novel control law exhibits superior response and robustness in comparison to the prototype MFAC. Moreover, it guarantees stability and convergence of the tracking error by enforcing bounded-input bounded-output (BIBO) criteria. In addition, 20 Monte Carlo simulations were conducted to test the initial conditions and random control parameters, and the results demonstrated that the proposed control outperformed the prototype MFAC.

An analytical criterion for stability testing of delayed Bode’s transfer function with unity feedback

The unity feedback where delayed Bode’s transfer function is placed in forward path is used as reference transfer function in controller design for fractional time delay systems. In this study, bounded input-bounded output stability of this reference transfer function is investigated. This investigation is based on a theorem for fractional order time delay systems using Hassard’s techniques. Sufficient and necessary conditions are obtained for testing the stability of this reference transfer function. Moreover, an explicit formula is given for calculating the number of unstable roots in case of instability. The illustrative examples show that this stability criterion works efficiently.

Observer‐based controller design for blood glucose regulation for type 1 diabetic patients with disturbance estimation: A backstepping approach

AbstractIn this paper, an observer‐based nonlinear controller is proposed to regulate blood glucose concentration (BGC) in type 1 diabetes mellitus (T1DM). The considered virtual patient model is the extended Bergmann minimal model, which is augmented by a meal disturbance and adapted to represent the insulin–glucose homeostasis of T1DM. The backstepping (BS) technique is used to design a closed‐loop feedback controller. The proposed controller does not need to measure insulin, plasma concentrations, and external disturbances while improving control performance and robustness against uncertainty. Insulin concentrations and plasma levels are estimated using state observers and disturbance using a disturbance estimator. These estimations are used as feedback to the controller. The asymptotic stability of the observer‐based controller is proved using the Lyapunov theorem. Furthermore, it is proven that the system is bounded input–bounded output (BIBO) stable in the presence of uncertainties caused by uncertain parameters and external disturbances. For real situations, we consider only the BGC available for measurement, and in addition, inter‐ and intra‐patient variability of system parameters is considered. The results confirm that the proposed controller can asymptotically regulate BGC through appropriate injection of insulin under meal disturbance and of variations in system parameters.

On the Relative Stability of Linear Time Invariant Systems

In this paper, state space representation based approach to relative stability of Linear Time Invariant (LTI) systems is discussed. Specifically, given a bound on the output, relative Bounded Input-Bounded Output (BIBO) stability of LTI systems is discussed. The bound on dominant pole is first determined using input-output description of LTI system. Using state space representation of homogeneous (no external input) LTI system, the components of state vector are upper bound. The results are applied to Continuous Time Markov Chains (i.e. homogeneous stochastic linear systems). Finally, using state space representation of arbitrary (with external input) Linear Time Invariant systems, the location of dominant pole is bounded. Using the upper bound, the location of line (parallel to imaginary-axis jω and to the left of it) is utilized for determining relative stability.

Distributed Event-Triggered Iterative Learning Control for Multiple High-Speed Trains With Switching Topologies: A Data-Driven Approach

This paper studies the distributed data-driven event-triggered model free adaptive iterative learning control (ETMFAILC) of multiple high-speed trains (MHSTs) under iteration-varying topologies, which breaks away from the dependence on the train dynamics. Firstly, the nonlinear MHSTs with unknown dynamics are converted into a linear model. Then, combining the proposed event-based triggering condition and the linear model, the ETMFAILC scheme under the fixed topology is designed. Next, theoretical analysis proves the bounded input bounded output (BIBO) stability of MHSTs. Finally, the study is extended to the switching topologies and the validity of the ETMFAILC is verified by a numerical example.

Active Suspension Robust Preview Control by Considering Actuator Delay

Active suspension systems (ASSs) are crucial for realizing the improvement demand of ride comfort in autonomous vehicles (AVs). This paper presents a novel integrated robust preview control (PC) algorithm to further improve the ride comfort by effectively handling actuator delay. An augmented ASS model is first established to consider actuator delay. Then, to obtain the time-domain feedforward disturbance, updating the local spatial road dataset from sensing systems by low-pass filtering and introducing speed for conversion. A predictive control framework that utilizes preview road disturbances is developed to achieve better ride comfort. And assuming parameterized disturbances, it is transformed into a consistent quadratic programming (QP) problem for real-time application in ASS. Furthermore, an innovative design of combined observer provides accurate and robust observations under multiple uncertainties, with which the algorithm can effectively compensate for actuator delay under different road conditions. Finally, the bounded-input bounded-output (BIBO) stability of the algorithm is well demonstrated. Simulation and bench test results indicate that the proposed algorithm can not only significantly improve road holding and ride comfort, but also realize a robust observation of the augmented ASS state. In addition, the solving time of the bench test satisfies the real-time requirements of the algorithm.

Nonlinear generalized predictive control with virtual unmodeled dynamics decomposition compensation and data driven

In this study, a novel nonlinear generalized predictive control (NGPC) method is proposed to tackle the tracking control problem which considers a mathematical model in conjunction with the virtual unmodeled dynamics decomposition compensation technology. First, data-modeling technology is adopted to take advantage of the input and output data information from the process to decompose the virtual unmodeled dynamics into the form of posterior measurement unmodeled dynamics and an unknown increment. Then, feedforward compensator is designed. The essential difference between the proposed data modeling algorithm and existing methods is that the effect of the measurement unmodeled dynamics is eliminated by the feedforward compensator. For the increment of the virtual unmodeled dynamics, a novel estimation algorithm is established through a data driven approach; A nonlinear compensator for the unknown increment of the virtual unmodeled dynamics is designed to suppress the effect of the increment of the virtual unmodeled dynamics on the closed-loop system. Second, the developed compensator is combined with the GPC algorithm to construct a nonlinear generalized predictive controller. Theoretical analysis proves that the proposed modeling and control algorithm have bounded-input bounded-output (BIBO) stability. Finally, an experimental study is conducted, which indicates the effectiveness of the proposed algorithm.

A novel Koopman-inspired method for the secondary control of microgrids with grid-forming and grid-following sources

This paper proposes an online data-driven Koopman-inspired identification and control method for microgrid secondary voltage and frequency control. Unlike typical data-driven methods, the proposed method requires no warm-up training yet with guaranteed bounded-input–bounded-output (BIBO) stability and even asymptotic stability under some mild conditions. The proposed method estimates the Koopman state space model adaptively so as to perform effective secondary voltage and frequency control that can handle microgrid nonlinearity and uncertainty. Case studies in the 4-bus and 13-bus microgrid test systems (with grid-forming and grid-following sources) demonstrate the effectiveness and robustness of the proposed identification and control method subject to the change of operating conditions and large disturbances (e.g., microgrid mode transitions, generation/load variations) even with measurement noises and time delays.

Data-driven prescribed performance control for satellite with large rotational component

In this paper, the high precision attitude control for satellite with large misaligned rotational component is investigated, proposing a novel model-free prescribed performance adaptive control (MF-PPAC) method. Based on the model-free adaptive control (MFAC) strategy, high-precision attitude control is achieved depending on the system measurement rather than the spacecraft mathematical model, which demonstrates the superiority in handling nonlinearity and uncertainty of the spacecraft system, especially for those with unbalance of the rotational component. Furthermore, the transient and the stable-state behavior of the tracking error using MFAC is constrained in the prescribed performance bounds and converges to zero gradually with the utilization of prescribed performance function (PPF) and error transformation method. Finally, the convergence and boundedness of the system error, the bounded-input bounded-output (BIBO) stability of the proposed MF-PPAC is demonstrated by the contraction mapping theory. Simulation and comparison with disturbance-observer-based PD control and MFAC illustrate the effectiveness of the proposed method.

Positive input observer‐based controller design for blood glucose regulation for type 1 diabetic patients: A backstepping approach

In practice, there are many physical systems that can have only positive inputs, such as physiological systems. Most conventional control methods cannot ensure that the main system input is positive. A positive input observer‐based controller is designed for an intravenous glucose tolerance test model of type 1 diabetes mellitus (T1DM). The backstepping (BS) approach is employed to design the feedback controller for artificial pancreas (AP) systems, based on the Extended Bergman's Minimal Model (EBMM). The EBMM represents the T1DM in terms of the blood glucose concentration (BGC), insulin concentration, and plasma level and the disturbance of insulin during medication due to either meal intake or burning sugar by doing some physical exercise. The insulin concentration and plasma level are estimated using observers, and these estimations are applied as feedback to the controller. The asymptotic stability of the observer‐based controller is proved using the Lyapunov theorem. Moreover, it is proved that the system is bounded input‐bounded output (BIBO) stable in the presence of uncertainties generated by uncertain parameters and external disturbance. For realistic situations, we consider only the BGC to be available for measurement and additionally inter‐and intra‐patient variability of system parameters is considered.

Funnel control by induced contraction

This note explores a property of the internal dynamics that is essential for the functioning of classical funnel control. We relax the property of internal dynamics bounded-input bounded-output (BIBO) stability by concentrating on a narrower class of output reference trajectories. Our ideas have a connection with the recently introduced concept of induced contraction, which is motivated by the phenomenon of noise-induced synchronization in neuronal oscillators. We remark that, contrary to previous works, we only have to modify the class of admissible output reference trajectories to handle non-minimum phase systems. We also propose a way (specific to nonlinear systems) to choose an output reference trajectory (possibly under output constraints) for classical funnel control to work for a certain class of unknown systems.

Analysis and Prediction of Electric Power System’s Stability Based on Virtual State Estimators

The stability of bilinear systems is investigated using spectral techniques such as selective modal analysis. Predictive models of bilinear systems based on inductive knowledge extracted by big data mining techniques are applied with associative search of statistical patterns. A method and an algorithm for the elementwise solution of the generalized matrix Lyapunov equation are developed for discrete bilinear systems. The method is based on calculating the sequence of values of a fixed element of the solution matrix, which depends on the product of the eigenvalues of the dynamics matrix of the linear part and the elements of the nonlinearity matrixes. A sufficient condition for the convergence of all sequences is obtained, which is also a BIBO (bounded input bounded output) systems stability condition for the bilinear system.

Adaptive multiple model control for a class of nonlinear discrete time systems: second-level adaption design approach

In this study, a multiple model control scheme based on a second-level adaption design approach is established for a class of nonlinear discrete time systems. The nonlinear function of systems is relaxed to zero-order bounded. In the first-level adaption, N identification models are employed to estimate unknown parameters, which can weaken the effect of unknown parameters. The convex hull property based on all identification models is constructed, which ensures that the convex hull identified parameters converge to the real value rapidly. Compared with the existing multiple model controller, the actual controller is developed by a convex hull for the identification of unknown parameters and it can avoid some potential drawbacks of the switch mechanism. In the constructed scheme, the discrete time system is bounded input bounded output (BIBO) and the tracking error is bounded. Finally, a simulation example is presented to validate the proposed scheme.

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.

Bounded-Input Bounded-Output Stability Tests for Two-Dimensional Continuous-Time Systems

This paper presents two efficient algorithms to determine whether a bivariate polynomial, possibly with complex coefficients, does not vanish in the cross product of two closed right-half planes (is “2-C stable”). A 2-C stable polynomial in the denominator of a two-dimensional analog filter has been proved (not long ago) to imply bounded-input bounded-output (BIBO) stability. The two algorithms are entirely different but both rely on a recently proposed fraction-free (FF) Routh test for complex polynomials in this transaction. The first algorithm tests the 2-C stability of a bivariate polynomial of degree (n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> ,n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ) in order n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sup> of elementary operations (when n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> =n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> =n). It is a “tabular type” two-dimensional stability test that can be regarded as a “Routh table” whose scalar entries were replaced by univariate polynomials. The second 2-C stability test is obtained from the first by its telepolation. It carries out the 2-C stability test by a finite collection of FF Routh tests and requires only order n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> elementary operations. Both algorithms possess an integer-preserving property that enhances them with additional merits including numerical error-free decision on 2-C stability.

Direct tuning of the data-driven controller considering closed-loop stability based on a fictitious reference signal

The direct tuning of controller parameters, which is based on data-driven control, has been attracting considerable attention because of the ease of its control system design. In practical use, it is important to consider the stability of the closed-loop system and model matching with few design parameters. In this study, we propose a direct tuning method based on a fictitious reference signal that considers the bounded-input bounded-output (BIBO) and model matching without repeating experiments. The proposed method includes two steps. In the first step, the BIBO stability is satisfied. The pole information is lost in the cost function of the conventional method using a fictitious reference signal. Then, we derive a new cost function that can prevent the loss of the pole information. This provides controller parameters that can stabilize the closed-loop system. The model matching between the reference model and the closed-loop system is considered in the second step. When model matching is achieved, the characteristics of the reference model almost match those of the closed-loop system, including the gain and phase margins. The parameters of the reference model are automatically tuned to realize model matching. Using the two-step method, we can obtain parameters considering BIBO stability and the model matching. In addition, there are no design parameters apart from the dealing noise. Two simulations and an experiment were performed on a system with dead time to verify the effectiveness of the proposed two-step method. The results showed that the proposed method provides BIBO stability and model-matched control parameters from the measured data through a one-time experiment without trial and error.

Application of quasi-f -power increasing sequence in absolute ph - |C, a, b; d; l| of infinite series

An increasing quasi-f-power sequence of a wider class has been used to establish a universal theorem on a least set of conditions, which is sufficient for an infinite series to be generalized ph-|C, a, b; d; l| k summable. Further, a set of new and well-known arbitrary results have been obtained by using the main theorem. Considering suitable conditions a previous result has been obtained, which validates the current findings. In this way, Bounded Input Bounded Output(BIBO) stability of impulse has been improved by finding a minimal set of sufficient condition for absolute summability because absolute summable is the necessary and sufficient conditions for BIBO stability.

A New Sufficient Criterion for the Stability of 2-D Discrete Systems

During the past few decades, two and higher dimensional systems have been extensively applied in many areas of research. The representation of the 2-D systems in the frequency domain is usually given by its transfer function. The bounded-input bounded-output (BIBO) stability of the two dimensional discrete systems depends on the zeros of the characteristic polynomial which is the denominator of this transfer function. In this paper, a new sufficient criterion for the stability of two-dimensional linear shift-invariant discrete systems is presented. The new criterion is based on the sufficient condition for stable polynomials with complex coefficients and the stability criterion for 2-D discrete systems proposed by Murray and Delsarte et al. . The new criterion is non-conservative for the stability testing of 2-D discrete systems. It is shown that the proposed sufficient criterion is simple enough to be applied for the stability checking of the 2-D discrete systems. The utility of the proposed criterion is demonstrated by examples.

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.

Uniform bounded input bounded output stability of fractional‐order delay nonlinear systems with input

SummaryThe bounded input bounded output (BIBO) stability for a nonlinear Caputo fractional system with time‐varying bounded delay and nonlinear output is studied. Utilizing the Razumikhin method, Lyapunov functions and appropriate fractional derivatives of Lyapunov functions some new bounded input bounded output stability criteria are derived. Also, explicit and independent on the initial time bounds of the output are provided. Uniform BIBO stability and uniform BIBO stability with input threshold are studied. A numerical simulation is carried out to show the system's dynamic response, and demonstrate the effectiveness of our theoretical results.