Output Tracking Control Research Articles

Practical tracking control for a class of uncertain MIMO nonlinear systems with unmatched disturbances

This paper studies the output tracking control problem for a class of uncertain MIMO nonlinear systems. The motivation comes from how to deal with unknown coupling system dynamics between subsystems and achieve the desired tracking when the system has parameter uncertainties and external disturbances. The difficulty is to guarantee that tracking errors enter an arbitrarily prescribed neighbourhood within a finite time. Based on the construction of a time-varying dynamic gain associated with tracking errors and the effective manipulation of nonlinear parametrization, a novel robust feedback controller is built up to ensure the boundedness of all closed-loop signals and the convergence of tracking errors to a small neighborhood approaching the origin in a finite time. Finally, the feasibility of control strategy is verified by numerical and practical examples.

Adaptive fuzzy fixed-time control for uncertain switched nonlinear systems with non-symmetrical dead-zone

This paper addresses fuzzy adaptive fixed-time tracking control problem for uncertain switched nonlinear systems with non-symmetrical dead-zone, even if the tracking control problem for subsystems is not solvable. A fixed-time stability criterion for switched nonlinear systems using MLF(multiple Lyapunov functions) method is presented. Then, it is applied to fixed-time tracking control of uncertain strict-feedback switched nonlinear systems. The design methods of fuzzy adaptive feedback controllers and a state-dependent switching law are given to achieve the boundedness of all the signals of the resulting closed-loop system and the fixed-time output tracking control. Nonsymmetrical dead-zone model is used to estimate an adaptive factor through less parameters, which related to fixed-time tracking control for the uncertain switched nonlinear systems. Two examples are given to verify the effectiveness of the proposed design method.

Learning-based robust output tracking control for unknown discrete-time nonlinear systems with dynamic uncertainty

Although numerous approximate dynamic programming (ADP) methods have been proposed and applied to robust control problems, research on the use of ADP methods for robust tracking control in nonlinear systems remains limited, especially for discrete time (DT) nonlinear systems. In this paper, we propose an efficient robust learning-based output tracking control method, referred to as r-LTC, for a class of unknown DT nonlinear systems with dynamic uncertainty. The objectives are achieved by: 1) using a system identification technique based on network-type coefficients Auto-Regressive with eXogenous variables (ARX) model to identify completely unknown systems; 2) reformulating the identified model into a state space model in terms of deviations from the reference trajectory, such that the robust tracking problem can be converted into a robust regulation problem; 3) transforming the robust regulation problem into an equivalent optimal regulation problem for a nominal system with a modified utility function; 4) alternately implementing the performance evaluation and control policy update through two neural networks (NNs) to numerically solve DT Hamilton-Jacobi-Bellman (HJB) equation, such that the approximated optimal feedback control inputs for nominal system can be obtained, allowing for realization of all unknown bounded uncertainties. The proposed method does not require a state observer and any steady state knowledge, only the measurable system input and output data are utilized. The convergence of NNs’ approximate weights and stability of the closed-loop uncertain systems are rigorously proven using the Lyapunov method. Lastly, a case study is performed using real data collected from the Shenzhen Metro Line 12 tunneling project to examine the performance of the proposed r-LTC algorithm in terms of the set value tracking accuracy, control system stability, and robustness against different types of disturbances.

Robust Funnel Model Predictive Control for Output Tracking with Prescribed Performance

Robust Funnel Model Predictive Control for Output Tracking with Prescribed Performance

[formula omitted] output tracking control for polynomial parameter-varying systems via homogeneous Lyapunov methods

This paper investigates the H∞ output tracking control for polynomial parameter-varying systems—a class of nonlinear parameter-varying systems. Based on the homogeneous polynomial Lyapunov function (HPLF), a state feedback controller is presented to make the augmented system (composed of the original system and the tracking error system) robust exponentially stable, so that the output of the original system can track the reference signal and satisfy the H∞ output tracking performance. The conservativeness of the theoretical results is reduced due to the following facts: (1) the HPLF can depend on the full states and time-varying parameters; and (2) there are no constraints on the input coefficient matrix and the inverse of the Lyapunov matrix. In particular, when the system states and time-varying parameters are confined to a compact set, local results are obtained based on the generalized S-procedure. The solvable conditions are given in terms of state-and-parameter-dependent linear matrix inequalities, which can be solved by sum of squares (SOS) techniques. Finally, the feasibility and effectiveness of the proposed method are verified by a numerical example and the heading control of unmanned surface vehicle.

Observer-based fuzzy tracking control of nonlinear systems with intermittent output constraints

This paper pays attention to the output tracking control problem of nonlinear systems where the output is uniquely measurable and subject to an intermittent constraint. A multiplicative transformation based on the shifting-replaying function is introduced together with barrier Lyapunov function to solve the intermittent output constraint. A state observer independent of the matching condition of control gains is designed via the non-uniform state transformation to relax the assumption of full-state measurability. By virtue of the estimated states, we propose an output feedback controller that only involves one fuzzy adaptive parameter to restrain the effect of unknown system nonlinearities. Through Lyapunov stability analysis, it is proved that the proposed controller can make all signals in the closed-loop system remain semi-globally uniformly ultimately bounded. Two simulation examples are provided to verify the effectiveness of the proposed method, and also the superiority over the existing ones.

A new output feedback adaptive control method for fractional order systems with inaccessible state

In this paper, the output tracking control problem for fractional-order (FO) systems with inaccessible state is investigated, and a new fractional-order model reference adaptive control (FOMRAC) method is proposed. The designed FO adaptive update law is able to adjust the controller parameters online in real time according to the system output information. Compared with the classical output feedback FOMRAC method, the proposed FOMRAC strategy only needs the online updating of a scalar function, which significantly reduces the complexity of the controller design and the online computational burden, and can achieve better control effect. Furthermore, the scheme ensures the boundedness of the closed-loop signals and that the mean value of the squared norm of the output error converges to zero. Finally, simulation results are carried out to verify the effectiveness of the established approach.

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.

Optimal Tracking Control of Heterogeneous MASs Using Event-Driven Adaptive Observer and Reinforcement Learning.

This article considers the output tracking control problem of nonidentical linear multiagent systems (MASs) using a model-free reinforcement learning (RL) algorithm, where partial followers have no prior knowledge of the leader's information. To lower the communication and computing burden among agents, an event-driven adaptive distributed observer is proposed to predict the leader's system matrix and state, which consists of the estimated value of relative states governed by an edge-based predictor. Meanwhile, the integral input-based triggering condition is exploited to decide whether to transmit its private control input to its neighbors. Then, an RL-based state feedback controller for each agent is developed to solve the output tracking control problem, which is further converted into the optimal control problem by introducing a discounted performance function. Inhomogeneous algebraic Riccati equations (AREs) are derived to obtain the optimal solution of AREs. An off-policy RL algorithm is used to learn the solution of inhomogeneous AREs online without requiring any knowledge of the system dynamics. Rigorous analysis shows that under the proposed event-driven adaptive observer mechanism and RL algorithm, all followers are able to synchronize the leader's output asymptotically. Finally, a numerical simulation is demonstrated to verify the proposed approach in theory.

Adaptive Output Feedback Tracking Control for Nonlinear Systems with Unknown Growth Rate

Article Adaptive Output Feedback Tracking Control for Nonlinear Systems with Unknown Growth Rate Manman Yuan 1,2,*, and Wei Qian 1,2,* 1 School of Electrical Engineering and Automation, Henan Polytechnic University, Jiaozuo 454003, China 2 Henan Key Laboratory of Intelligent Detection and Control of Coal Mine Equipment, Jiaozuo 454003, China * Correspondence: ymmamhappy@163.com; qwei@hpu.edu.cn Received: 4 September 2023 Accepted: 7 November 2023 Published: 26 March 2024 Abstract: In this paper, the problem of adaptive output feedback tracking is considered for a class of nonlinear systems with lower-triangular structures. A novel dynamic gain is introduced to deal with the unknown growth rate. By coupling the dynamic gain with the observer and the controller, an adaptive output tracking controller is developed, which can guarantee that all signals of the closed-loop system are globally bounded. Finally, the effectiveness of the presented control scheme is illustrated by a numerical example.

Data-Efficient Off-Policy Learning for Distributed Optimal Tracking Control of HMAS With Unidentified Exosystem Dynamics.

In this article, a data-efficient off-policy reinforcement learning (RL) approach is proposed for distributed output tracking control of heterogeneous multiagent systems (HMASs) using approximate dynamic programming (ADP). Different from existing results that the kinematic model of the exosystem is addressable to partial or all agents, the dynamics of the exosystem are assumed to be completely unknown for all agents in this article. To solve this difficulty, an identifiable algorithm using the experience-replay method is designed for each agent to identify the system matrices of the novel reference model instead of the original exosystem. Then, an output-based distributed adaptive output observer is proposed to provide the estimations of the leader, and the proposed observer not only has a low dimension and less data transmission among agents but also is implemented in a fully distributed way. Besides, a data-efficient RL algorithm is given to design the optimal controller offline along with the system trajectories without solving output regulator equations. An ADP approach is developed to iteratively solve game algebraic Riccati equations (GAREs) using online information of state and input in an online way, which relaxes the requirement of knowing prior knowledge of agents' system matrices in an offline way. Finally, a numerical example is provided to verify the effectiveness of theoretical analysis.

H∞$$ {H}_{\infty } $$ optimal output tracking control for Markov jump systems: A reinforcement learning‐based approach

AbstractIn this paper, the optimal output tracking control problem for Markov jump systems is investigated, where the two cases with known or completely unknown transition probabilities are both considered. Based on game theory and performance, quadratic cost is considered, where a discount parameter is introduced into the quadratic cost in order to track unstable systems and eliminate the assumption that the noise energy is bounded. The game coupled algebraic Riccati equation and the corresponding controller are presented by dynamic programming. The stochastic stability of the tracking error system is further investigated. Moreover, iterative and reinforcement learning‐based algorithms are proposed for solving the optimal tracking controller with known or completely unknown transition probabilities, respectively. Finally, some numerical simulations on a DC motor are performed to validate the effectiveness of the proposed results.

Asynchronous H∞ output tracking control for uncertain networked switched systems with mode-dependent average dwell time: an event-driven mechanism

This paper considers the problem of event-triggered H ∞ output tracking control for uncertain networked switched systems with both communication constraints and asynchronous switching. A new sampled delay-dependent error tracking uncertain networked switched system is constructed on the basis of event-triggered communication mechanism (ETCM) and the given reference model. By introducing a parameter-dependent Lyapunov–Krasovskii functional and employing the mode-dependent average dwell time (MDADT) method, results on exponential stability and robust H ∞ performance are proposed. Furthermore, the gains of the output tracking controller with matched system mode are obtained by solving a set of linear matrix inequalities (LIMs), at the same time, the parallel results with the mismatched case are also obtained. Simulation results show that the proposed design scheme not only guarantees tracking performance but also saves communication resources effectively.

Data-Based Collaborative Learning for Multiagent Systems Under Distributed Denial-of-Service Attacks

This paper employs a reinforcement learning (RL) technique to investigate the distributed output tracking control of heterogeneous multiagent systems (MASs) under multiple denial-of-service (DoS) attacks. Different from existing results where the dynamic of the leader is known for partial or all agents, the leader’s system matrix is completely unknown for each follower in this paper. To learn the leader system matrix, a data-based learning mechanism is first proposed using the idea of the data-driven method. Then, under the data-based learning mechanism, a resilient predictor subject to multiple DoS attacks is exploited to provide the estimation of the leader’s state for each agent, where adversaries attack different communication links independently. Moreover, a resilient dynamic output feedback controller is proposed to solve the output tracking control problem based on the output regulation theory. To consider the transient responses of agents, a RL-based dynamic output feedback controller is developed to realize the optimal output tracking control by solving discounted algebraic Riccati equations (AREs) in both offline and online ways. Theoretical analysis shows that the secure output tracking control of MASs can be achieved under the proposed data-based resilient learning control algorithm. Finally, a numerical example is provided to verify the effectiveness of theoretical analysis.

Reinforcement Learning Reduced H ∞ Output Tracking Control of Nonlinear Two-Time-Scale Industrial Systems

Reinforcement Learning Reduced <i>H</i> _∞ Output Tracking Control of Nonlinear Two-Time-Scale Industrial Systems

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.

Adaptive output observers-based distributed tracking

This paper proposes a novel adaptive output observer method for the distributed output tracking control of heterogeneous systems. Unlike the existing adaptive distributed state observer, an output-based adaptive distributed output observer (OADOO) that only relies on the leader’s output is proposed to estimate the leader’s information. Meanwhile, an input-based triggering mechanism is exploited to avoid continuous interactions between agents, and between the leader and its neighboring agents, respectively. Then, a local controller is developed to achieve the output tracking control. In comparison with the existing results for the similar research problem, our results not only handle the tracking control subject to only relative output measurement, but also considerably lower the data exchange traffic and dimension among agents of the developed OADOO.

Output Tracking Control of a Nonlinear System Based on Takagi-Sugeno Fuzzy Model: Generalized Partial Eigenstructure Assignment Approach

Output Tracking Control of a Nonlinear System Based on Takagi-Sugeno Fuzzy Model: Generalized Partial Eigenstructure Assignment Approach

Optimal Learning Output Tracking Control: A Model-Free Policy Optimization Method With Convergence Analysis.

Optimal learning output tracking control (OLOTC) in a model-free manner has received increasing attention in both the intelligent control and the reinforcement learning (RL) communities. Although the model-free tracking control has been achieved via off-policy learning and Q -learning, another popular RL idea of direct policy learning, with its easy-to-implement feature, is still rarely considered. To fill this gap, this article aims to develop a novel model-free policy optimization (PO) algorithm to achieve the OLOTC for unknown linear discrete-time (DT) systems. The iterative control policy is parameterized to directly improve the discounted value function of the augmented system via the gradient-based method. To implement this algorithm in a model-free manner, a model-free two-point policy gradient (PG) algorithm is designed to approximate the gradient of discounted value function by virtue of the sampled states and the reference trajectories. The global convergence of model-free PO algorithm to the optimal value function is demonstrated with the sufficient quantity of samples and proper conditions. Finally, numerical simulation results are provided to validate the effectiveness of the present method.

Nonlinear Model Inversion-Based Output Tracking Control for Battery Fast Charging

Nonlinear Model Inversion-Based Output Tracking Control for Battery Fast Charging