Output Tracking Of Systems Research Articles

Output Tracking and Regulation of Networked Control Systems Under Finite Bandwidth Constraints and Its Applications

Output Tracking and Regulation of Networked Control Systems Under Finite Bandwidth Constraints and Its Applications

Enhanced robust output tracking of nonlinear systems with dynamic event-triggering using neural network-based method

Enhanced robust output tracking of nonlinear systems with dynamic event-triggering using neural network-based method

Improved Command Filtered Backstepping Control for Uncertain Nonlinear Systems with Time-Delay

This paper presents an alternative method to solve the control problem of an uncertain nonlinear system in strict-feedback form with a time delay. Instead of using Lyapunov–Krasovskii functionals, ordinary Lyapunov functionals are used to design the controllers. In order to address the completely unknown uncertainties of the system, including the unmodeled dynamics, time-delay nonlinearities, and external disturbances, command filters are applied to reconstruct the estimations of such uncertainties, and the negative feedback of these estimations can be used to reduce the influence of such uncertainties on the system. With the help of the backstepping technique and the Lyapunov stability criterion, it is proved that the system output tracks the target signal with a small error, and contrastive simulation results verify our method’s effectiveness.

Infinite-time robust optimal output tracking of continuous-time linear systems using undiscounted reinforcement learning

This research paper focuses on addressing the challenge of infinite-time linear quadratic tracking control (LQT) for linear systems with parametric uncertainty. Traditional solutions to the LQT problem often involve using a discount factor to prevent the cost function from growing unbounded over time. However, this approach can introduce instability in the closed-loop system. To overcome this issue, this paper proposes an alternative approach using an undiscounted cost function that ensures the asymptotic stability of the uncertain closed-loop system. To design a control scheme without requiring precise knowledge of the system dynamics, reinforcement learning (RL) algorithms are employed. However, for systems with uncertain parameters that may lead to instability, the convergence of RL algorithms to a stabilising solution is not guaranteed. To address this limitation, a robust optimal control structure is developed using on-policy and off-policy reinforcement learning algorithms, resulting in a model-free controller. The effectiveness of the proposed robust optimal controller is validated through comparative simulations on an uncertain model of a DC–DC buck converter connected to a constant power load. These simulations demonstrate the advantages and benefits of the robust optimal controller in handling parametric uncertainty and ensuring stability in the control system.

Novel quantized iterative learning control based on spherical polar coordinates

AbstractThis study investigates the iterative learning control method for discrete‐time systems with data quantization, and it employs a quantizer based on spherical polar coordinates. The quantizer uses spherical polar coordinates to transform an unquantized signal into one with a predetermined quantization level. The quantization capability is dependent on the size of the support sphere, which is dynamically adjustable. In the scenarios of system output quantization, general quantization, and tracking error quantization, the learning control schemes are developed with consideration of the smallest sphere quantization features. The radii of the support spheres are designed independently based on the characteristics of the quantized signals (system output, control input, tracking error). The findings suggest that the system can achieve a bounded error convergence in the scenarios of system output and general quantization. In the context of quantization in tracking error, it is achievable to attain tracking performance with zero error. The example of a permanent magnet synchronous motor is provided to illustrate the findings of the study.

Photovoltaic System Output Analysis and Tracking Method Based on the Surveyed Data

Photovoltaic System Output Analysis and Tracking Method Based on the Surveyed Data

Adaptive neural network finite‐time control for fractional‐order nonlinear systems with external disturbance

AbstractThis paper is concerned with the finite‐time tracking control problem of fractional‐order nonlinear systems (FONSs) with uncertainty and external disturbance. A novel design scheme of the adaptive neural network finite‐time controller (ANNFTC) is developed by utilizing the theory of finite‐time stability and fractional‐order dynamic surface control (DSC) scheme combined with backstepping method. Radial basis function neural networks (RBF NNs) are employed to estimate the unknown nonlinear function. Furthermore, an auxiliary function is introduced to approximate the unknown upper bounds of the approximation error in RBF NNs and external disturbance. The ANNFTC ensures the finite‐time boundedness of all signals in FONSs and enhances the system output's tracking performance. The effectiveness of the proposed approach is demonstrated through a simulation example, providing empirical evidence to support the theoretical framework presented in this paper.

Segmented hybrid event‐triggered control for underactuated autonomous underwater vehicles with an asymmetrical prescribed performance constraint

AbstractIn this technical article, the trajectory‐tracking problem of event‐based adaptive prescribed performance control for underactuated autonomous underwater vehicles (AUVs) is considered. The primary innovation of this article is the proposal of a segmented event‐triggered mechanism (SETM) that incorporates preselected convergence time. This mechanism allows for the regulation of communication frequency in the control channel (controller‐to‐actuator) according to the dynamic characteristics of the AUV system at different stages. In addition to presenting new design scheme based on SETM, an enhanced vision known as segmented hybrid event‐triggered mechanism (SHETM) is introduced. Notably, the minimum and maximum triggering intervals (MITI and MATI) for these two ETMs can be calculated from the corresponding resettable dynamic variables presented in the trigger conditions. Subsequently, by utilizing the proposed asymmetrical prescribed performance control (APPC) strategy, the system's output tracking error behaviors in both transient and steady‐state stages can be qualitatively predetermined through design parameters within the boundary function. Moreover, the minimum learning parameter (MLP) based RBFNN adaptive control law is developed to counteract the effects of model uncertainties and ocean current perturbations. Finally, rigorous theoretical analysis and simulation results confirm the viability of the proposed scheme.

Dual design of control law and switching law for turbofan systems under multiple disturbances

In this paper, an anti-disturbance output tracking control strategy is proposed for turbofan systems with multiple disturbances. The considered turbofan models are described by switched systems. For the unmeasured disturbances, a disturbance observer is designed. Then, the observer-based controller is proposed such that the system output tracks the desired signal and multiple disturbances are successfully suppressed. Applying the multiple Lyapunov functions method, the stability of the closed-loop system with H∞ control performance is analyzed and proved. Finally, a simulation example of turbofan system is presented to illustrate the effectiveness of the proposed method.

Data-driven robust iterative learning control of linear systems

We propose a data-driven robust iterative learning control (ILC) technique to multi-input-multi-output (MIMO) linear systems. Control of MIMO linear systems, particularly with strong cross-axis coupling, is challenging as modeling of a MIMO system can be complicated, time-consuming, and often requires a trade-off between robustness and performance. As such, limitations exist in current ILC techniques. The aim of this paper is to develop an efficient and easy-to-use data-driven ILC technique to output tracking of MIMO linear systems under random disturbance. Through the proposed technique, the complicated modeling process and the robustness-accuracy trade-off are avoided, and the up-to-now system dynamics is captured by constructing and updating the iteration gain using the input and output data in the last iteration. It is shown that monotonic convergence of the ILC algorithm is guaranteed, and an optimal gain can be obtained to maximize the convergence rate and minimize the residual tracking error. The proposed technique is illustrated through experiments on a three-input three-output piezoelectric actuator system, with comparison to the adaptive multi-axis inversion-based iterative control (A-MAIIC) technique. The experimental results show rapid convergence and improved formance of the proposed technique when the cross-axis coupling is strong.

Specified convergence rate guaranteed output tracking of discrete-time systems via reinforcement learning

Toward the aim of zero tracking error and user-specified convergence rate, a data-driven output tracking design for unknown linear discrete-time systems is investigated in this work. For policy learning, we customize a virtual auxiliary system, based on which an enhanced Bellman equation with the user-specified convergence rate is derived. This allows us not to explicitly measure the time for the system evolution, while only the input–output data are sufficient in our design. By utilizing the robust output regulation technique, we can learn an optimal tracker for such an auxiliary system via policy iteration and value iteration. It is proved that the output tracking error of the original discrete-time system converges to zero at the specified convergence rate. The effectiveness of the proposed algorithms is illustrated by a simulation example.

Boundary Output Tracking of Nonlinear Parabolic Differential Systems via Fuzzy PID Control

Boundary Output Tracking of Nonlinear Parabolic Differential Systems via Fuzzy PID Control

Integral BLF-Based Adaptive Neural Constrained Regulation for Switched Systems With Unknown Bounds on Control Gain.

In this article, an integral barrier Lyapunov-function (IBLF)-based adaptive tracking controller is proposed for a class of switched nonlinear systems under the arbitrary switching rule, in which the unknown terms are approximated by radial basis function neural networks (RBFNNs). The IBLF method is used to solve the problem of state constraint. This method constrains states directly and avoids the verification of feasibility conditions. In addition, a completely unknown control gain is considered, which makes it impossible to directly apply previous existing methods. To offset the effect of the unknown control gain, the lower bound of the control gain is added into the barrier Lyapunov function, and a regulating term is introduced into the controller. The proposed control strategy realizes three control objectives: 1) all the signals in the resulting system are bounded; 2) the system output tracks the reference signal to a arbitrarily small compact set; and 3) all the constraint conditions for system states are not violated. Finally, a simulation example is used to show the effectiveness of the proposed method.

Adaptive robust output tracking of uncertain strict-feedback nonlinear systems with full state constraints via control schemes with simple structure

In this paper, the problem of output tracking control is considered for a class of uncertain strict-feedback nonlinear systems with virtual control coefficients and full state constraints. It is assumed only that the nonlinear uncertainties of the systems are some smooth functions enough to guarantee the existence of solutions to the differential equations which describe uncertain systems, and that the virtual control coefficients are unknown. Based on backstepping algorithm, by combining the barrier Lyapunov function with an integral inequality reported in the current control literature, a design method is presented whereby a simple adaptive robust output tracking control scheme can be synthesised. The presented design method can evade the repeated differentiation problem appearing in using backstepping algorithm, and need not know all the nonlinear upper bounds of uncertainties, which are repeatedly employed at each step of backstepping procedure. It is also shown that the output tracking error of the uncertain nonlinear systems with both unknown virtual control coefficients and full state constraints can converge uniformly exponentially towards a ball which can be as small as desired. Finally, a numerical example is given, and the corresponding simulations are also implemented to demonstrate the simplicity of the proposed method and the validity of the theoretical results.

Neural Learning Control for Discrete-Time Strict-Feedback Systems: An Error Estimate Method

This paper addresses the issue of neural learning control for a kind of discrete-time strict-feedback system. Firstly, by using an error dynamics estimator, a new delay-free NN update law is proposed. Subsequently, after making the system output tracks a given recurrent tracking signal, the estimated NN weights can be demonstrated to converge to a small area of their ideal values, exponentially, which can be stored as constant NN weights. Then, a neural learning controller is proposed by using the constant NN weights and disturbance observer. Compared with the previous neural learning controller, the proposed scheme can not only avoid the chattering problem that may be caused by controller switching but also enhance the system robustness by implanting the disturbance observer.

Monotonically convergent iterative learning control by time varying learning gain revisited

This note considers the problem whether we can design a time-varying learning gain to ensure the monotone convergence of system output tracking errors (SOTEs) in the sense of unweighted 1/2/∞-norm for iterative learning control systems. Firstly, it points that the iterative learning control update law with the exponentially decaying learning factor considered in Moore et al. (2005) cannot ensure the monotonic convergence of SOTEs in the sense of unweighted 1-norm, 2-norm or ∞-norm. Secondly, it is strictly proven that there exists a time-varying learning gain to ensure the monotone convergence of SOTEs in the sense of unweighted ∞-norm and there is no time-varying learning gain to ensure the monotone convergence of SOTEs in the sense of unweighted 1-norm. Finally, this paper presents a sufficient condition under which there exists a time-varying learning gain to ensure the monotone convergence of SOTEs in the sense of unweighted 2-norm.

Comparison of REWS and LIDAR-based feedforward control for fatigue load mitigation in wind turbines

While optimizing wind energy harvesting has always been the principal goal of wind turbine control, extensive research has been conducted on the use of advanced control methodologies aiming to maximize the turbine’s power generation while also achieving secondary performance objectives, such as fatigue load minimization. Some recent studies have investigated the application of a classical control methodology known as exact output regulation for improved wind turbine control. This control method is designed to achieve the rejection of known input disturbances, while also ensuring the system output tracks a desired reference signal. These studies all assumed wind preview information from LIDAR measurements was available to support the controller design.In this paper we investigate the use of exact output regulation for turbine control, using wind speed estimates obtained from rotor speed measurements. Simulated performance comparisons conducted over a wide range of mean wind speeds show that the exact output regulation methodology using wind speed estimates derived from rotor measurements can deliver similar reductions in fatigue loads to those obtainable with LIDAR measurements, without compromising power generation.

Undiscounted reinforcement learning for infinite-time optimal output tracking and disturbance rejection of discrete-time LTI systems with unknown dynamics

This paper proposes a novel control structure to solve the infinite-time linear quadratic tracking (LQT) problem. The major challenge in the LQT problem is the boundedness issue of the cost function in an infinite time framework. In many studies, a discount factor is utilised to overcome the challenge. However, it can affect the stability of the closed-loop system and the steady-state error. This paper proposes an optimal control structure that guarantees zero steady-state error with bounded cost function without utilising the discount factor. The optimal gains of the proposed control structure are computed via model-based and model-free reinforcement learning (RL) algorithms. As a novelty in model-based RL algorithms, a model predictive RL algorithm is proposed to reduce the number of iterations in the learning phase. A model-free reinforcement learning algorithm is utilised to obtain optimal control for tracking the reference online and without any knowledge of system dynamics. Finally, the simulation results verify the advantages of the proposed optimal control structure.

A discontinuous integral action for robust output tracking in uncertain linear systems

AbstractIn this article, a solution to the output tracking problem is proposed for linear systems affected by external disturbances. The proposed robust control approach has a discontinuous integral term that provides exact and finite‐time convergence to zero of the output tracking error in the presence of external disturbances. The proposed nonlinear controller is non‐homogeneous. A constructive method to compute the controller gains is provided in order to ensure the convergence to zero of the output tracking error. Some simulation results are presented in order to illustrate the feasibility of the proposed robust control approach.

An integrated design method for active fault diagnosis and control

SummaryThe injection of an auxiliary input signal for active fault diagnosis may cause the change of system control performance in closed‐loop operation. This paper presents a novel integrated design method for active fault diagnosis and tracking control in order to facilitate the detection of incipient faults, meanwhile ensuring the normal operation of the closed‐loop system. First, a zonotopic filter is generated based on radius minimization method to estimate the uncertain bound set of systems states. Then, an auxiliary input signal is designed to separate the reachable sets of the system in healthy and faulty operation situations. Generally, the auxiliary input signal is required to be designed minimizing the system closed‐loop performance degradation. In this paper, a tracking controller is designed altogether with the auxiliary input signal to make the system output track a given reference. An optimal index is proposed to minimize simultaneously the energy of the auxiliary input signal and the output tracking error. Next, a fault detection logic is provided based on checking whether the closed‐loop system state belongs to healthy zonotope. Finally, the feasibility and advantages of this work are verified by means of a numerical example.