Nonlinear adaptive tracking‐control synthesis for functionally uncertain systems

The paper is concerned with a problem of adaptive tracking system control synthesis. It is assumed that a nonlinear object dynamics (model structure) is (partially) unknown and some of its nonlinear characteristics can be approximated by a sort of functional approximators. It has been proven that a nonlinear state feedback plus parameter adaptation are able to ensure its asymptotic stability. The proposed controller design is based on modified adaptive backstepping method. In this approach, as opposite to the standard backstepping, the design process has been reduced to a single iteration, which enables avoiding complicated recursive procedure. An extra task here is to find a control synthesis of linear-like, chained system. The solution of the last problem in general framework is also presented. The obtained thereby controller has several attractive features of both the feedback linearization and backstepping schemes.

This article deals with the problem of dissipative control synthesis for a class of descriptor systems with uncertainties in the derivative matrix. Attention is focused on the design of a proportional plus derivative (PD) state feedback, which guarantees that the closed-loop system is robustly stable and strict dissipative. Firstly, a sufficient condition for the closed-loop system is robustly stable and strict dissipative is presented by using a simple idea of changing the problem to the corresponding problem of an augmented uncertain system. Then, a PD controller is constructed by solving LMIs. Finally, a numerical example is given to demonstrate that the proposed method is effective.

Robust Adaptive Control

This paper aims to develop an adaptive control system for process monitoring, identification, and control in micro wire electrical discharge machining (wire-EDM). The proportion of short circuits in the total sparks defined as short circuit ratio is chosen as a control parameter for the adaptive control system. Pulse interval of each spark is adjusted in real-time according to the discrimination of gap status to improve the stability of machining operation. A self-organizing fuzzy sliding mode controller is then proposed for servo feed control. This intelligent control strategy has on-line learning capability and disturbance rejection robustness for responding to the nonlinear, stochastic, and time-varying characteristics of the micro wire-EDM process. Another fuzzy logic controller is designed to control the short circuit ratio at a pre-determined level through an on-line regulation of servo voltage for adaptive process control. Experimental results show that the developed adaptive control system results in faster machining and better machining stability than does a conventional control scheme.

The state model‐based transfer function models are applied for adaptation of linear controller and disturbance compensator in a feedback/feed‐forward control system of nonlinear process. An advantage of the presented adaptation method is the avoidance of artificial disturbances or iterative identification procedures for on‐line estimation of process dynamic parameters. The adaptation is based on linearization of the process model at each sampling time about the current state point, independent of the process being at steady‐state or transient conditions. The linear time‐varying dynamics model is updated on‐line using measured values of process variables and reduced to the first‐order plus time delay transfer function models in order to directly apply well‐developed controller tuning rules. Computational aspects of the adaptation method are discussed and computation algorithms are presented.The adaptive feedback/feed‐forward control system was applied for controlling temperature in industrial methane tank, dynamic parameters of which vary in a wide range due to variations of methane‐tank process load and external conditions. The heat balance‐based process state model is developed and validated using observation data of real plant. Computer simulation of the proposed control system performance under extreme operating conditions demonstrates fast adaptation of controller parameters, robust behaviour and significant improvement in the controllers' performance compared to that of fixed‐gain controllers. Copyright © 2007 John Wiley & Sons, Ltd.

SUMMARY In this paper, several concepts of switching frequency are introduced to analyze the properties and performance of switched systems in infinite as well as finite-time intervals. The observation is very motivating that different system properties and performances depend on different switching frequencies. Sufficient conditions ensuring asymptotic stability, l2 gain performance, and state boundness are derived on the basis of the notions of switching frequency, respectively. Then, on the basis of the analysis results, the control synthesis problems are addressed. LMI-based design algorithms are proposed to meet different control synthesis requirements. Numerical design examples are provided to demonstrate our results. Copyright © 2011 John Wiley & Sons, Ltd.

Combined Cooperative Adaptive Cruise Control using Collective Initial Excitation based Distributed Parameter Estimator

To address lateral vibration challenges in elevator systems during operation, a high‐fidelity coupled dynamic model integrating the elevator car‐guide rail structure and voice coil motor (VCM) actuator is developed. Building on this framework, a radial basis function (RBF) neural network‐compensated variable‐speed sliding mode control (VS‐SMC) strategy is proposed, where the RBF network enables real‐time identification and compensation of critical nonlinear states and disturbances. A dsat switching function with adaptive zero‐point slope is designed as the variable‐rate reaching law, The synergistic operation of RBF network’s real‐time nonlinear compensation and dsat function’s adaptive slope modulation enables high‐precision suppression of elevator vibrations, with closed‐loop stability rigorously proven via Lyapunov theory. Under VCM operational constraints, comparative simulations in MATLAB/Simulink evaluate four control schemes: passive control, PID, tanh‐RBF SMC, and the proposed dsat‐RBF SMC. Results demonstrate superior vibration suppression with 97%, 41%, and 78% displacement reduction under sinusoidal excitation, and 92%, 76%, and 68% reduction under Gaussian white noise, relative to passive, PID, tanh‐RBF methods. The proposed method achieves minimum displacement responses across all test scenarios, validating its robustness and precision in real‐world elevator dynamics. This study establishes a neural‐enhanced sliding mode paradigm for high‐performance vibration control, offering critical insights for safety‐critical vertical transport systems.

This paper is concerned with the issue of adaptive fuzzy sliding mode control for fuzzy underactuated translational oscillator with rotating actuator (TORA). Since the system considered in this paper is accompanied by strong inputs coupling and nonlinear characteristics, the feedback decoupling and fuzzy technique are introduced to establish a linear fuzzy underactuated TORA system. The two-order fuzzy sliding surface with adaptive parameters is designed, where the adaptive control is introduced to adjust the parameters of sliding surface such that the system performance could be improved. The sliding mode control law is synthesized to guarantee the sliding mode dynamics to be asymptotically stable and robust, and the reachability analysis is presented to ensure that the system trajectories can be driven onto the sliding mode surface and remain there for the subsequent time. Simulation results are provided to compare with the existing results and validate the effectiveness and feasibility of the proposed scheme.

We propose an adaptive iteratively linearized finite element method (AILFEM) in the context of strongly monotone nonlinear operators with energy structure in Hilbert spaces. The approach combines adaptive mesh-refinement with an energy-contractive linearization scheme (e.g., the Kačanov method) and a norm-contractive algebraic solver (e.g., an optimal geometric multigrid method). Crucially, a novel parameter-free algebraic stopping criterion is designed and we prove that it leads to a uniformly bounded number of algebraic solver steps. Unlike available results requiring sufficiently small adaptivity parameters to ensure even plain convergence, the new AILFEM algorithm guarantees full R-linear convergence for arbitrary adaptivity parameters. Thus, unconditional convergence is guaranteed. Moreover, for sufficiently small adaptive mesh-refinement parameter <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="theta"> <mml:semantics> <mml:mi>θ</mml:mi> <mml:annotation encoding="application/x-tex">\theta</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and linearization-stopping parameter <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="lamda Subscript normal l normal i normal n"> <mml:semantics> <mml:msub> <mml:mi>λ</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">l</mml:mi> <mml:mi mathvariant="normal">i</mml:mi> <mml:mi mathvariant="normal">n</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> <mml:annotation encoding="application/x-tex">\lambda _{\mathrm {lin}}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, the new adaptive algorithm guarantees optimal complexity, i.e., optimal convergence rates with respect to the overall computational cost and hence time.

Chapter 8 - Robust adaptive parameter estimation and control for vehicle active suspension systems

SummaryIn this study, we present a reinforcement learning (RL)‐based flight control system design method to improve the transient response performance of a closed‐loop reference model (CRM) adaptive control system. The methodology, known as RL‐CRM, relies on the generation of a dynamic adaption strategy by implementing RL on the variable factor in the feedback path gain matrix of the reference model. An actor‐critic RL agent is designed using the performance‐driven reward functions and tracking error observations from the environment. In the training phase, a deep deterministic policy gradient algorithm is utilized to learn the time‐varying adaptation strategy of the design parameter in the reference model feedback gain matrix. The proposed control structure provides the possibility to learn numerous adaptation strategies across a wide range of flight and vehicle conditions instead of being driven by high‐fidelity simulators or flight testing and real flight operations. The performance of the proposed system was evaluated on an identified and verified mathematical model of an agile quadrotor platform. Monte‐Carlo simulations and worst case analysis were also performed over a benchmark helicopter example model. In comparison to the classical model reference adaptive control and CRM‐adaptive control system designs, the proposed RL‐CRM adaptive flight control system design improves the transient response performance on all associated metrics and provides the capability to operate over a wide range of parametric uncertainties.

Disturbance-observer-based fuzzy model predictive control for nonlinear processes with disturbances and input constraints

Adaptive disturbance rejection neural output feedback control of hydraulic manipulator systems

This paper presents a feedforward disturbance compensation approach for the fast and precise positioning of table systems. In the micro-scopic displacement region of the table motion, since the friction behaves nonlinear spring characteristics depending on the displacement, the table positioning accuracy may be deteriorated according to the table motion such as inching and reciprocating motions, while the friction behaves Coulomb and viscous properties in the coarse displacement region. In this paper, a feedforward compensation approach for the nonlinear friction is proposed, where same structural mathematical disturbance model can compensate regardless of the displacement regions. The proposed positioning control approach with the disturbance modeling and compensation has been verified by experiments using a linear table system on machine stand.