Asymptotic Output Tracking Research Articles

Fuzzy approximation-based reparametrization and adaptive control design of nonlinear aircraft dynamics

This paper conducts a new study on fuzzy approximation-based reparametrization and adaptive control design of non-canonical nonlinear aircraft dynamics, with particular focus on emphasizing the expansion of linearization-based adaptive flight control designs from local to semi-global scopes. The linearization-based adaptive control method has been employed for managing non-canonical nonlinear aircraft systems, owing to its capability in handling the complexity of aircraft system dynamics. To enhance the operational range of the linearization-based approach, this paper focuses on the aircraft longitudinal dynamic model in general non-canonical forms. A semi-global linearization-based adaptive control method is developed for this kind of system. Firstly, a new reparametrization is devised, leveraging local linearized models and a concept of relative degree. Subsequently, adaptive controllers are designed to guarantee stable and asymptotic output tracking for aircraft systems with various relative degrees. The efficiency of the newly developed adaptive control approach is validated through simulation outcomes.

Enhancing pressure control of low-friction pneumatic actuator with eddy current damper via valve dead-zone compensation

This article addresses the high-performance pressure control of a pneumatic actuator that incorporates an air-bearing piston and an eddy current damper (ECD). After optimizing the pneumatic actuator, achieving precise pressure control relies on maintaining an accurate and stable airflow through the control valve. A terminal sliding mode adaptive control method (TSMAC) is proposed, proficiently integrating considerations for dead zone nonlinearities in the proportional valve and the effects of unmodeled disturbances in the pneumatic actuator. Using the opening area of the proportional valve as the input to the pneumatic system greatly simplifies the control process and reduces the workload required for valve parameter calibration. The Lyapunov-based stability analysis demonstrates that excellent asymptotic output tracking can be achieved with low steady-state error simply by knowing the boundaries of the valve opening area. The control effect of the proposed control strategy is compared with an adaptive backstepping sliding mode control method based on a linearly fitted proportional valve model on an established constant pressure control test bench. Experimental results under various loads and operating conditions illustrate the effectiveness of the proposed approach.

Singularity-free adaptive control of discrete-time linear systems without prior knowledge of the high-frequency gain

This paper proposes a new output feedback model reference adaptive control (MRAC) method for discrete-time linear time-invariant systems with arbitrary relative degrees. The proposed method does not require any prior knowledge of the high-frequency gain represented by kp, thereby completely eliminating the common design condition in the traditional discrete-time MRAC framework: the sign of kp is known, as well as an upper bound on |kp|. Specifically, an output feedback adaptive control law is developed, which incorporates a time-varying gain function to effectively address the singularity issue. The developed adaptive control law leads to the derivation of a linear estimation error equation for the closed-loop system. Consequently, a gradient algorithm based parameter update law is directly formulated by utilizing the estimation error and some other available signals without requiring any prior knowledge of kp. In comparison to the traditional MRAC and Nussbaum function-based methods, it does not necessitate any additional design conditions or involve any transient performance issues, while still ensuring closed-loop stability and asymptotic output tracking for any given bounded reference signal. The simulation study showcases the design procedure and evaluates the efficacy of the proposed control method.

Robust Adaptive Control of the Offshore Produced Water Treatment Process: An Improved Multivariable MRAC-Based Approach

The application of deoiling hydrocyclone systems as the downstream of three-phase gravity separator (TPGS) systems is one of the most commonly deployed produced water treatment processes in offshore oil and gas production. Due to the compact system’s complexity and tailor-made features, it is always challenging to develop some optimally coordinated control solution for the coupled hydrocyclone and TPGS systems. It is obvious that coordinated control can better fulfill legislative discharge regulation by robustly maintaining high separation efficiencies. This paper presents a new control solution for a set of integrated hydrocyclone and TPGS systems by applying an improved multi-variable model reference adaptive control (MV-MRAC) approach with the aim of achieving both asymptotic output tracking and unknown disturbance rejection. A robust MV-MRAC controller design is proposed based on a control parameterization derived from a factorization of a high-frequency gain matrix Kp=LDS as a product of three matrices, where L represents unity lower triangular, D=sign(D) represents diagonal, and S represents positive definite, and a teaching–learning-based optimization (TLBO) algorithm for optimizing the adaption rates. The developed solution is analyzed and compared with a commonly deployed PI control solution on a model that is derived from a lab-scale produced water treatment process. This simulation study demonstrates the promising potential of the proposed control solution compared with the currently deployed PI control solution.

Asymptotic Output Tracking With Malfunctioning Actuators and Twisted/Biased Feedback

Asymptotic Output Tracking With Malfunctioning Actuators and Twisted/Biased Feedback

Asymptotic Output Tracking Control of a Class of Linear Systems by Finite-and-Quantized Output Feedback

This paper presents a novel finite-and-quantized output feedback asymptotic tracking control method for a general class of continuous-time linear time-invariant systems. First, we construct a finite quantizer with time-varying thresholds and design a pole placement control law that exclusively utilizes the finite-and-quantized output signal and an external reference signal. Then, we establish the boundedness of all closed-loop signals and prove the asymptotic convergence of the output tracking error to zero. The proposed method combines the advantages of classical pole placement control technique and finite quantization feedback technique. It not only reduces the requirement for feedback information compared with existing tracking control methods but also effectively handles unstable poles and zeros in controlled systems, thereby achieving asymptotic output tracking. Finally, we provide a representative example to validate the effectiveness and new features of our proposed method.

Asymptotic output tracking in a class of non‐minimum phase nonlinear systems via learning‐based inversion

AbstractAsymptotic output tracking of non‐minimum phase (NMP) nonlinear systems has been a popular topic in control theory and applications. Many approaches have focused on finding solutions under minimal assumptions either in the target system or desired trajectories, as there is no general solution available. In this article, we propose a practical and simple solution for cases where the reference trajectory is periodic in time. Our approach employs a learning‐based scheme to iteratively determine the desired feedforward input. Unlike previous learning‐based frameworks, our method only requires the output tracking error to update the feedforward input iteratively and can be applicable to NMP systems. Our method retains the key advantages of the learning‐based framework, including robustness to parameter uncertainties and periodic disturbances. We evaluate the effectiveness of our algorithm using simulation results with an inverted pendulum on a cart, a typical NMP nonlinear system.

Model reference adaptive disturbance rejection control using partial-state feedback

In this paper, we propose a partial-state feedback model reference adaptive control strategy for uncertain linear time-invariant systems with unmatched disturbances. The new control design is based on parametrization and observer technique. The control structure and output matching of nominal partial-state feedback disturbance rejection are presented. The adaptive partial-state feedback disturbance rejection scheme guarantees closed-loop system stability and asymptotic output tracking. A simulation example indicates the effectiveness of the presented adaptive partial-state feedback control design.

Reinforcement learning based adaptive control for uncertain mechanical systems with asymptotic tracking

This paper mainly focuses on the development of a learning-based controller for a class of uncertain mechanical systems modeled by the Euler-Lagrange formulation. The considered system can depict the behavior of a large class of engineering systems, such as vehicular systems, robot manipulators and satellites. All these systems are often characterized by highly nonlinear characteristics, heavy modeling uncertainties and unknown perturbations, therefore, accurate-model-based nonlinear control approaches become unavailable. Motivated by the challenge, a reinforcement learning (RL) adaptive control methodology based on the actor-critic framework is investigated to compensate the uncertain mechanical dynamics. The approximation inaccuracies caused by RL and the exogenous unknown disturbances are circumvented via a continuous robust integral of the sign of the error (RISE) control approach. Different from a classical RISE control law, a tanh(·) function is utilized instead of a sign(·) function to acquire a more smooth control signal. The developed controller requires very little prior knowledge of the dynamic model, is robust to unknown dynamics and exogenous disturbances, and can achieve asymptotic output tracking. Eventually, co-simulations through ADAMS and MATLAB/Simulink on a three degrees-of-freedom (3-DOF) manipulator and experiments on a real-time electromechanical servo system are performed to verify the performance of the proposed approach.

Singularity-free adaptive control of MIMO discrete-time nonlinear systems with general vector relative degrees

This paper develops a singularity-free adaptive tracking control scheme for a general class of multi-input and multi-output uncertain discrete-time nonlinear systems with non-canonical control gain matrices. The estimation of the control gain matrices, especially in some non-canonical forms, may be singular during parameter adaptation, which leads to the singularity problems of the adaptive control laws. This paper employs the matrix decomposition technique to solve the problem under a linearly parameterized adaptive control framework. The state and output feedback cases are addressed, respectively, to ensure closed-loop stability and asymptotic output tracking. Compared with the existing results, the features of the proposed adaptive control scheme include: (i) the proposed control laws do not involve the high-gain issue commonly encountered in robust control methods; (ii) two different filtered tracking error signals are introduced for the state and output feedback cases, respectively. These filters are crucial to avoid causality contradiction of the adaptive control laws commonly encountered in adaptive control of discrete-time systems; and (iii) a future time signal estimation-based adaptive control law is developed to ensure asymptotic output tracking for the output feedback case without requiring the high-gain observer. Finally, an illustrative example is given to verify the validity of the proposed control scheme.

Stochastic Relative Degree and Path-Wise Control of Nonlinear Stochastic Systems

In this article, we address the path-wise control of systems described by a set of nonlinear stochastic differential equations. For this class of systems, we introduce a notion of stochastic relative degree and a change of coordinates, which transforms the dynamics to a stochastic normal form. The normal form is instrumental for the design of a state-feedback control, which linearizes and makes the dynamics deterministic. We observe that this control is <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">idealistic</i> , i.e <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">.,</i> it is not practically implementable because it employs a feedback of the Brownian motion (which is never available) to cancel the noise. Using the idealistic control as a starting point, we introduce a hybrid control architecture, which achieves <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">practical</i> path-wise control. This hybrid controller uses measurements of the state to perform periodic compensations for the noise contribution to the dynamics. We prove that the hybrid controller retrieves the idealistic performances in the limit as the compensating period approaches zero. We address the problem of asymptotic output tracking, solving it in the idealistic and in the practical framework. We finally validate the theory by means of a numerical example.

Partial State Feedback Adaptive Disturbance Rejection Control

A unified disturbance rejection problem based on model reference adaptive control (MRAC) technique is addressed. When the full-state vector is not operational in feedback, we use partial-state signal y(t) to design a disturbance rejection controller. The parametrization and disturbance compensation techniques are necessary for designing adaptive control strategy to deal with systems uncertainties and unknown disturbances. This scheme guarantees the desired system performances, including closed-loop system stability as well as asymptotic output tracking. The proof progress of system stability is elaborated.

Discrete time partial‐state feedback model reference disturbance rejection control

SummaryThis article develops a disturbance rejection control strategy using partial‐state feedback model reference adaptive control for discrete‐time uncertain systems with unknown input disturbances. Adaptive control schemes are proposed for constant disturbances, sinusoidal disturbances, and generic bounded disturbances. The partial‐state feedback control is designed based on measurable signals and the parameterization method to counteract the effect of disturbances. The plant‐model output matching condition is established. The developed control law is more flexible for applications and has a more concise structure than output feedback control. Additionally, closed‐loop stability and asymptotic output tracking are derived. The effectiveness and the feasibility of partial‐state feedback disturbance rejection control are verified by simulation results.

Time-/Event-Triggered Adaptive Neural Asymptotic Tracking Control for Nonlinear Systems With Full-State Constraints and Application to a Single-Link Robot.

This study proposes the time-/event-triggered adaptive neural control strategies for the asymptotic tracking problem of a class of uncertain nonlinear systems with full-state constraints. First, we design a time-triggered strategy. The effect caused by the residuals of the estimation via radial basis function (RBF) neural networks (NNs), and the reasonable upper bounds on the first derivative of the reference signal and the derivative of each virtual control, can be eliminated by designing appropriate adaptive laws and utilizing the basic properties of RBF NNs. Moreover, the construction of the barrier Lyapunov functions (BLFs) in this work ensures the compliance of the full-state constraints and also holds the asymptotic output tracking performance. Then, based on the time-triggered strategy, we further design a relative threshold event-triggered strategy. The proposed event-triggered adaptive neural controller can solve the main control objective of this work, that is: 1) the full-state constraint requirements of the system are not violated and 2) the output signal asymptotically tracks the reference signal. Compared with the traditional method, the event-triggered strategy can improve the utilization of communication channels and resources and has greater practical significance. Finally, an example of single-link robot under the proposed two strategies illustrates the validity of the constructed controllers.

Hybrid Adaptive Output Feedback Tracking for Stable Systems With Unknown Input Constraints

The problem of global output tracking is addressed for stable minimum phase systems, with constant uncertain parameters and constant disturbances belonging to a known compact set, in the presence of input constraints such as amplitude saturation. The relative degree, the system order, and the sign of the high frequency gain are assumed to be known. A hybrid adaptive output feedback control is designed to achieve global asymptotic output tracking, provided that there exists an input within the input constraints capable of tracking exactly the output reference signal. By virtue of the hybrid control approach, the closed-loop system is linear within each time interval between parameter updating. Moreover, no information on input saturation is required by the controller. In addition to the standard assumptions in adaptive control design when inputs are unconstrained, further requirements on the reference signals, on system stability and on parameter bounds, are needed when inputs are constrained.

Robust adaptive precision motion control of tank horizontal stabilizer based on unknown actuator backlash compensation

Backlash nonlinearity inevitably exists in the actuator of tank horizontal stabilizer and has adverse effect on the system control performance, however, how to effectively eliminate its effect remains a pending issue. To solve this problem, a robust adaptive precision motion controller is presented in this paper to address uncertainties and unknown actuator backlash of tank horizontal actuator. The controller handles the modeling uncertainties including parameter uncertainties and unmodeled disturbances by integrating adaptive feedforward compensation and continuous nonlinear robust law. Based on the backstepping method, a smooth backlash inverse model is constructed by combining the adaptive idea. Meanwhile, the unknown backlash parameters of the system can be approximated through the parameter adaptation, and the impact of the actuator backlash nonlinearity is effectively compensated via the inverse operation, which can availably improve the tracking performance. Moreover, the adaptive law can update the disturbance ranges of tank horizontal stabilizer online in real time, which enhances the feasibility in practical engineering applications. Furthermore, the stability analysis based on Lyapunov function shows that with the existence of unmodeled disturbances and unknown actuator backlash, the designed controller guarantees excellent asymptotic output tracking performance. Extensive comparative results verify the effectiveness of the proposed control strategy.

A quantized output feedback MRAC scheme for discrete-time linear systems

This paper presents a quantized output feedback model reference adaptive control (MRAC) scheme for a class of single-input and single-output discrete-time linear time-invariant systems with unknown parameters. Our method, firstly, integrates the well-known MRAC and quantized control techniques to construct a quantized output feedback adaptive control law with parameter update laws. Then, some vital technical lemmas are developed, fundamentally applicable to finite and infinite quantized output feedback MRAC. Moreover, we prove that in the case of infinite quantization, appropriately choosing the output quantizer’s sensitivity affords the proposed adaptive control law to ensure closed-loop stability and achieve bounded or asymptotic output tracking. The significant advantage of the developed adaptive control scheme is combining the benefits of the classic MRAC and quantized control. Compared with current adaptive tracking control schemes, the developed scheme not only reduces the feedback information requirement, but also has full capability to achieve closed-loop stability and output tracking. The effectiveness of the proposed MRAC scheme is verified through several simulations.

Asymptotic Output Tracking of Non-minimum Phase Nonlinear Systems through Learning Based Inversion

Asymptotic Output Tracking of Non-minimum Phase Nonlinear Systems through Learning Based Inversion

Asymptotic output tracking control with prescribed transient performance of nonlinear systems in the presence of unknown dynamics

AbstractIn this article, we address the problem of asymptotic output tracking control with prescribed transient performance for a class of nonlinear systems in the presence of unknown dynamics. By fusing the funnel control approach and the tool of barrier Lyapunov function, a smooth adaptive tracking control strategy is developed in a recursive manner. In the proposed design, a new barrier Lyapunov function is adopted to eliminate the effects of unknown nonlinear dynamics, ensuring the prescribed transient behavior of the output tracking. The distinctive characteristic of the proposed method is that the designed control algorithm can guarantee not only prescribed output tracking performance but also global asymptotic stability without incorporating any prior knowledge of nonlinear dynamics or even corresponding bounding functions. Three illustrative examples are provided to testify the effectiveness of the proposed method.

Matrix Decomposition-Based Adaptive Control of Noncanonical Form MIMO DT Nonlinear Systems

This article presents a new study on adaptive control of multi-input and multi-output (MIMO) discrete-time nonlinear systems with a noncanonical form involving parametric uncertainties. The adaptive control scheme employs a vector relative degree formulation to reconstruct the noncanonical system dynamics and derives a normal form. Then, a new matrix decomposition-based adaptive control scheme is proposed for the controlled plant with a vector relative degree <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$[1, 1,{\ldots }, 1]$</tex-math></inline-formula> under some relaxed design conditions. In particular, the matrix decomposition technique is adopted to overcome the singularity problem during the adaptive estimation of an uncertain high-frequency gain matrix. The adaptive control scheme ensures closed-loop stability and asymptotic output tracking. An extension to the adaptive control of general canonical-form MIMO discrete-time nonlinear systems is also presented. Finally, through simulations, the effectiveness of the proposed control scheme is verified.