Robust Tracking Problem Research Articles

Observer-based tracking control design for periodic piecewise time-varying systems

In this study, the problem of robust tracking problem for continuous-time periodic piecewise time-varying delay systems with disturbances and uncertainties has been examined by using observer-based H∞ tracking control protocol. Precisely, the state space representation of the system is formulated to reconstruct the unmeasurable states via the available informations of input/output dynamics. Based on the suitable Lyapunov-Krasovskii functional with periodic piecewise time-varying Lyapunov matrix, a set of sufficient conditions in the form of linear matrix inequalities is derived which affirms the robust asymptotic tracking performance and satisfactory disturbance attenuation for the addressed model. Particularly, the matrix polynomial approach is utilized which makes the analysis to be more flexible and amenable to convex optimization tool. Accordingly, the period time-varying controller and observer gains are computed through the feasible solution of derived matrix inequalities. Conclusively, the simulation results are presented to confirm the efficiency and applicability of the theoretical outcomes.

Nonlinearity compensation based robust tracking control of nonlinear nonminimum phase hypersonic flight vehicles

This paper introduces a nonlinearity compensation based robust tracking controller for hypersonic flight vehicles. The controller focuses on robust control design with respect to the nonminimum phase feature and system uncertainties for the control-oriented model. Firstly, following the principle of decomposing the complex control problem into two simpler problems, the original robust tracking problem for nonlinear nonminimum phase hypersonic flight vehicles is decomposed into a simpler robust tracking problem for a linear nonminimum phase system with disturbances and a stabilization problem for a nonlinear system without disturbances. After the problem decomposition, a proportional–integral tracking controller and a feedback linearization controller are designed for the linear system and the nonlinear system, respectively. Then, the addition of the two designed controllers gives the final controller. By compensating for the system nonlinearity using the secondary system and its controller, the proposed control method can satisfy the robust tracking control requirements for nonlinear nonminimum phase hypersonic flight vehicles. The simulation results show, compared with a feedback linearization control method and a composite neural learning control method, the proposed method has superior tracking accuracy and robustness against system uncertainties and external disturbances.

Model reference adaptive control: A finite‐time approach

SummaryThis article contributes with a finite‐time model reference adaptive control approach to solve the robust tracking problem for a class of disturbed scalar linear systems. A nonlinear continuous control law, composed of nonlinear adaptive gains, provides a finite‐time rate of convergence. For the ideal case, that is, without external disturbances, the tracking and the parameter (ideal control gains) identification error converge to zero in a finite time. For the disturbed case, the tracking and the parameter identification error dynamics are finite‐time input‐to‐state stable with respect to the external disturbance. The corresponding convergence proofs and the robustness analysis are based on a Lyapunov function approach, input‐to‐state stability theory, and homogeneity theory. Finally, simulation and experimental results show the feasibility of the proposed scheme.

Design of robust tracking and disturbance attenuation control for stochastic control systems

The focus of current research is to address the problem of robust output tracking, input delay compensation and disturbance attenuation performance for a family of stochastic systems by implementing the improved-equivalent-input-disturbance (IEID) estimator and the extended Smith predictor (ESP) technique. By integrating the observer and IEID-estimator together with ESP, a new closed-loop configuration is presented. Then, Lyapunov based mean-square asymptotic stability criterion is obtained. According to attained stability criterion, an IEID and ESP based-controller is designed, which ultimately guarantees the exact output tracking. Simulation studies of numerical examples are offered to expose the authenticity of IEID and ESP-based controller. Further, the proposed outcomes in comparison with existing results are presented to demonstrate the efficaciousness of the established control procedure.

Robust subspace tracking algorithms using fast adaptive Mahalanobis distance

We consider the problem of robust subspace tracking (RST) in burst noise which appears in some applications in array signal processing and wireless communication. Our approach is based on robust adaptive covariance matrix, thus avoiding parameter fine-tuning in existing methods in the literature. However, this involves the estimation of the Mahalanobis distance, which has a quadratic computational complexity. We propose a novel algorithm to efficiently estimate the adaptive Mahalanobis distance, with linear complexity thanks to exploiting noise characteristics and the data structure. This approach can be used to robustify many existing RST algorithms. Particularly, in this paper, based on two efficient but non-robust algorithms, called YAST and LORAF, we propose their robust counterparts – RYAST and ROBUSTQR –, robust to burst noise while having the same complexity order as that of the original ones. We illustrate the effectiveness of the proposed RST algorithms by comparing them to the state-of-the-art in different scenarios.

Robust trajectory tracking with adjustable performance of underactuated surface vessels via quantized state feedback

This paper investigates a robust quantized state feedback tracking problem with preselected performance of uncertain underactuated surface vessels (USVs) with state and input quantization under a band-limited network. With the feedback of all quantized states and control inputs, a preselected-performance-based tracking strategy using quantized states is proposed to achieve robust tracking that does not require any knowledge of the USV dynamics and function approximators. Design conditions of performance functions are introduced to ensure the stability of the closed-loop system using quantized feedback. In the Lyapunov sense, it is analyzed that all error surfaces remain within the preselected performance functions for all time. Finally, some convincing simulation comparison results are provided to illustrate the theoretical results.

Towards Robust WiFi Fingerprint-Based Vehicle Tracking in Dynamic Indoor Parking Environments: An Online Learning Framework

The variation of wireless signal in dynamic indoor parking environments may seriously compromise the performance of fingerprint-based localization methods. In this regard, this paper investigates the problem of robust WiFi fingerprint-based vehicle tracking in dynamic indoor parking environments, aiming at designing an online learning framework to continuously train the localization model and counteract the effect of signal variation. Specifically, a Hidden Markov Model (HMM) based Online Evaluation (HOE) method is firstly proposed to assess the accuracy of localization results by measuring the inconsistency of locations inferred by WiFi fingerprinting and Dead Reckoning (DR). Further, an Online Transfer Learning (OTL) algorithm is designed to improve the robustness of the fingerprinting localization, which consists of a weight allocation scheme to combine two classification models (i.e., the batch model and the online model) and an instance-based transferring scheme to resample the offline fingerprints and retrain the batch model. Finally, we implement the system prototype and give comprehensive performance evaluation, which demonstrates that the proposed solutions can outperform the state-of-the-art localization algorithms around 28&#x0025; <inline-formula><tex-math notation="LaTeX">$\sim$</tex-math></inline-formula> 58&#x0025; on vehicle tracking accuracy in dynamic indoor parking environments.

Optimal consensus for uncertain high‐order multi‐agent systems by output feedback

AbstractThe distributed optimal output consensus problem for high‐order multi‐agent systems has been studied recently. In this article, we further focus on the same problem for high‐order multi‐agent systems subject to parametric uncertainties and aim at distributed robust controllers by measurement output feedback. We first develop a dynamic compensator to estimate the expected optimal consensus point and convert the problem into several decentralized robust tracking problems. Then, by combining the integral control technique and dirty derivative observer technique, we constructively propose a distributed output feedback integral controller to solve this problem under a mild graph connectivity condition.

Robust high-order iterative learning control approach for two-dimensional linear discrete time-varying Fornasini–Marchesini systems with iteration-dependent reference trajectory

This paper first investigates robust tracking problem of a high-order iterative learning control (HOILC) algorithm for two classes of two-dimensional linear discrete time-varying Fornasini–Marchesini systems (2-D LDTVFMS) and 2-D LDTVFMS with input delays with iteration-dependent reference trajectory described by a high-order internal model (HOIM) operator, boundary states and disturbances. An extended high-order linear discrete inequality is proposed to guarantee the ILC tracking error of 2-D LDTVFMS converge robustly to a bounded range, the bound of which is relied on iteration-dependent uncertainties from reference trajectory, boundary states and disturbances. A simulation example on a practical thermal process is used to validate the effectiveness and feasibility of the proposed HOILC law. Additionally, it is verified by theory analysis and simulation that no matter how the ILC controller gain is selected, the convergence condition in Theorem 2 of Wan and Li [(2021). High-order internal model based iterative learning control for 2-D linear FMMI systems with iteration-varying trajectory tracking. IEEE Transactions on Systems Man and Cybernetics: Systems, 51, 1462–1472] is not satisfied. Using the proposed HOILC law, perfect tracking result in Theorem 2 of Wan and Li (2021) can be obtained.

Iterative learning control for consensus of second-order multi-agent systems with interval uncertain topologies

Abstract This paper is devoted to the robust consensus tracking problem of second-order nonlinear multi-agent systems (MASs) with the interval uncertain topologies. For the second-order MASs including one leader agent and multiple follower agents, a control protocol is proposed by combining the iterative learning control scheme with the sliding mode control method. By analyzing the convergence of sliding mode variables, the consensus conditions including the unknown eigenvalues and the undetermined weight coefficient are obtained. In order to deal with the difficulties of weight coefficient design caused by the unknown eigenvalues of graphs, a min-max optimization problem is formulated based on the fastest convergence of the λ-norm of sliding mode variables, then the optimal weight coefficient is obtained by solving the min-max optimization problem. Moreover, for the undirected and directed interval uncertain graphs, two algorithms about the optimal weight coefficients are proposed, respectively. Finally, three numerical simulation examples are presented to demonstrate the effectiveness of the proposed methods.

Adaptive optimal control approach to robust tracking of uncertain linear systems based on policy iteration

In this study, an optimal adaptive control approach is established to solve the robust output tracking problem of a class of continuous time uncertain linear systems based on the policy iteration (PI) in actor-critic algorithm. First, by augmenting the integral variables of the tracking error into state variables, the robust tracking problem is transformed into a robust control problem of an augmented uncertain linear system. It is proven that the robust control law of the augmented system enables the output of the considered system to track a polynomial time signal asymptotically. Second, an optimal control method in the corresponding auxiliary nominal system is established, and based on the Bellman optimality principle, PI algorithms are proposed to solve online tracking controllers for the matched and the mismatched uncertain systems. Finally, for testing the availability of the proposed approach and theoretical results, two numerical experiments are provided.

Robust LCEKF for Mismatched Nonlinear Systems with Non-Additive Noise/Inputs and Its Application to Robust Vehicle Navigation.

It is well known that the standard state estimation technique performance is particularly sensitive to perfect system knowledge, where the underlying assumptions are: (i) Process and measurement functions and parameters are known, (ii) inputs are known, and (iii) noise statistics are known. These are rather strong assumptions in real-life applications; therefore, a robust filtering solution must be designed to cope with model misspecifications. A possible way to design robust filters is to exploit linear constraints (LCs) within the filter formulation. In this contribution we further explore the use of LCs, derive a linearly constrained extended Kalman filter (LCEKF) for systems affected by non-additive noise and system inputs, and discuss its use for model mismatch mitigation. Numerical results for a robust tracking and navigation problem are provided to show the performance improvement of the proposed LCEKF, with respect to state-of-the-art techniques, that is, a benchmark EKF without mismatch and a misspecified EKF not accounting for the mismatch.

Control of Teleoperation Systems in the Presence of Varying Transmission Delay, Non-passive Interaction Forces, and Model Uncertainty

SUMMARYThis paper addresses robust stability and position tracking problems in teleoperation systems subject to varying delay in the communication medium, uncertainties in the models of manipulators, and non-passive interaction forces in the terminations. Fixed-structure nonlinear control law is developed based on the notion of Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) scheme. Then, utilizing the Lyapunov–Krasovskii theorem, sufficient conditions are derived in terms of Linear Matrix Inequalities (LMIs) to tune the controller parameters. Differently from literature, the objectives are achieved without requirement for any passive parts in the model of interaction forces. Comparative simulations and experimental results demonstrate the applicability and superiority of the proposed method.

Robust Visual Tracking Based on a Modified Flower Pollination Algorithm

In this study, a target tracking algorithm based on the flower pollination algorithm (FPA) is proposed. This method solves the problem of robust visual target tracking in different complex tracking scenes with the good global and local optimisation ability of the FPA. Meanwhile, with the aim of solving the problem of invalid background feature interference and the loss of effective features caused by the fixed scale of tracking frame in traditional tracking methods, a scale adaptive adjustment model of tracking frame is proposed. Considering that the FPA has good global and local optimization ability at simultaneously, the position update equation of the FPA is introduced as the main optimization method of target tracking. In addition, considering that the traditional FPA is similar to classical swarm intelligence algorithm (such as the particle swarm optimization algorithm), it also faces the problems of a high probability of falling into local extrema, a low efficiency of late convergence speed and a high probability of early maturity. Therefore, this work proposes the GTFPA, an advanced FPA based on the gravitational search algorithm (GSA) and mutation mechanism via a trigonometric function. We qualitatively, quantitatively and statistically compare the proposed method with other classical general tracking methods through two datasets, OTB2015 and VOT2018, which contain hundreds of video sequences and more than ten tracking scenes and can effectively test the success rate, accuracy and stability of the trackers. The results of a large number of tracking experiments in a variety of complex tracking scenarios prove that the proposed GTFPA tracker performs well with regards to efficiency, accuracy and robustness.

Robust finite-time tracking for a square fully actuated class of nonlinear systems

In this paper, the robust finite-time tracking problem is addressed for a square fully actuated class of nonlinear systems subjected to disturbances and uncertainties. Firstly, two applicable lemmas are derived and novel nonlinear sliding surfaces (manifolds) are defined by applying these lemmas. Secondly, by developing the nonsingular terminal sliding mode control, two different types of robust nonlinear control inputs are designed to meet and accomplish the aforementioned finite-time tracking objective. The global finite-time stability of the closed-loop nonlinear system is evaluated analytically and mathematically. The proposed control inputs are utilized to tackle and solve two interesting issues containing (a): the finite-time tracking problem of the unified chaotic system and (b): the finite-time synchronization of two non-identical hyperchaotic systems. Finally, based on MATLAB software, two numerical simulations are carried out to illustrate and demonstrate the effectiveness and performance of the proposed robust finite-time nonlinear control schemes.

An improved two‐loop model predictive control design for nonlinear robust reference tracking with practical advantages

SummaryIn this paper, the nonlinear robust reference tracking problem is considered and an Improved Two‐Loop Nonlinear Model Predictive Control (ITL‐NMPC) design is proposed for a pre‐controlled system with bounded uncertainties subject to input and state constraints. In the industry, this scheme leads the lower design cost and fewer implementation risks since (i) it allows the existing controller to remain unchanged without any manipulation, (ii) it does not need the open‐loop model of the pre‐controlled system, and (iii) it does not require the terminal cost and constraint definition. For the proposed ITL‐NMPC, a practical parameter tuning algorithm is introduced and its robust exponential stability, as well as recursive feasibility, are guaranteed. Simulation results are used to better illustrate the effectiveness of the proposed approach and show that the proposed method not only improves the control performance of the pre‐controlled system but also reduces the design cost while satisfying the constraints.

Fast Robust Subspace Tracking via PCA in Sparse Data-Dependent Noise

This work studies the robust subspace tracking (ST) problem. Robust ST can be simply understood as a (slow) time-varying subspace extension of robust PCA. It assumes that the true data lies in a low-dimensional subspace that is either fixed or changes slowly with time. The goal is to track the changing subspaces over time in the presence of additive sparse outliers and to do this quickly (with a short delay). We introduce a "fast" mini-batch robust ST solution that is provably correct under mild assumptions. Here "fast" means two things: (i) the subspace changes can be detected and the subspaces can be tracked with near-optimal delay, and (ii) the time complexity of doing this is the same as that of simple (non-robust) PCA. Our main result assumes piecewise constant subspaces (needed for identifiability), but we also provide a corollary for the case when there is a little change at each time. A second contribution is a novel non-asymptotic guarantee for PCA in linearly data-dependent noise. An important setting where this is useful is for linearly data dependent noise that is sparse with support that changes enough over time. The analysis of the subspace update step of our proposed robust ST solution uses this result.

Robust trajectory tracking control of a marine surface vessel using asymmetric error constraints and output feedback

SummaryThis article investigates the problem of robust trajectory tracking for a marine surface vessel in the presence of asymmetrical error time‐varying constraints and output feedback. To deal with system uncertainties, adaptive neural networks (NNs) are used to approximate unknown dynamics model parameters and external disturbances. To obtain unmeasured velocities, a predictive observer based on output feedback is developed to estimate unknown velocities. A tan‐type asymmetric barrier Lyapunov function is used to deal with asymmetric error time‐varying constraints. The high‐frequency robust adaptive law is used to compensate for parameter estimation errors. The kinematic controller is designed based on the barrier Lyapunov function method, and the kinetics controller is designed base on an observer, an adaptive NN and a robust high‐frequency control. All signals of the closed‐loop systems are proved to be semiglobally uniformly and ultimately bounded via Lyapunov analysis, and the asymmetrical error constraints are not violated. Simulations are performed, and synthetic comparison is used to verify the feasibility and robustness of the proposed control law.

Robust Trajectory Tracking Control for Underactuated Autonomous Underwater Vehicles in Uncertain Environments

This article addresses the tracking control problem of 3-D trajectories for underactuated underwater robotic vehicles operating in a constrained workspace including obstacles. More specifically, a robust nonlinear model predictive control (NMPC) scheme is presented for the case of underactuated autonomous underwater vehicles (AUVs) (i.e., unicycle-like vehicles actuated only in the surge, heave, and yaw). The purpose of the controller is to steer the unicycle-like AUV to the desired trajectory with guaranteed input and state constraints (e.g., obstacles, predefined vehicle velocity bounds, and thruster saturations) inside a partially known and dynamic environment where the knowledge of the operating workspace is constantly updated via the vehicle’s onboard sensors. In particular, considering the sensing range of the vehicle, obstacle avoidance with any of the detected obstacles is guaranteed by the online generation of a collision-free trajectory tracking path, despite the model dynamic uncertainties and the presence of external disturbances representing ocean currents and waves. Finally, realistic simulation studies verify the performance and efficiency of the proposed framework. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This article was motivated by the problem of robust trajectory tracking for an autonomous underwater vehicle (AUV) operating in an uncertain environment where the knowledge of the operating workspace (e.g., obstacle positions) is constantly updated online via the vehicle’s onboard sensors (e.g., multibeam imaging sonars and laser-based vision systems). In addition, there may be other system limitations (e.g., thruster saturation limits) and other operational constraints, induced by the need of various common underwater tasks (e.g., a predefined vehicle speed limit for inspecting the seabed, and mosaicking), where it should also be considered into the control strategy. However, based on the existing trajectory tracking control approaches for underwater robotics, there is a lack of an autonomous control scheme that provides a complete and credible control strategy that takes the aforementioned issues into consideration. Based on this, we present a reliable control strategy that takes into account the aforementioned issues, along with dynamic uncertainties of the model and the presence of ocean currents. In future research, we will extend the proposed methodology for multiple AUV performing collaborative inspection tasks in an uncertain environment.

Robust controller design for marine electric propulsion system over controller area network

With the consistent tendency of electrification and intelligentization of marine systems in recent years, the electric propulsion system has been a prospective candidate for ships due to its potential in energy saving, environmental protection, high efficiency, and high reliability. However, time-varying delays of communication networks would be induced due to increasing information exchange requirement that caused by the increasing number of devices connecting to the communication networks as well as bandwidth limitation of marine network. Meanwhile, the propeller load is difficult to model due to the complexity of ship dynamics, which increases the uncertainty of marine electric propulsion system. Thus, robust control of the marine electric propulsion system is necessary and challenging. This paper presents a mixed H∞∕LQR robust controller design for marine electric propulsion system to address robust speed tracking problem under possible network-induced delays. The propeller dynamic model is built via open-water experimental data to reflect propeller load characteristics. Then, a delay-free model is established for the marine electric propulsion system by using system augmentation technique, with the random network-induced delay characterized by polytopic inclusions and Taylor series expansion. A mixed H∞∕LQR robust controller design is proposed for the marine electric propulsion system. Finally, based on a detailed controller area network model, the performance and effectiveness of the mixed H∞∕LQR robust controller are demonstrated by comparative simulation tests of a marine electric propulsion system with 4.088 MW permanent magnet synchronous motor (PMSM).