Unknown Time-varying Parameters Research Articles

Adaptive control for full-states constrained nonlinear systems with unknown control direction using Barrier Lyapunov Functionals

In this paper, a new adaptive back-stepping (BS) control technique based on barrier Lyapunov functions (BLFs) is proposed to manage a class of full-state constrained nonlinear systems subject to totally unknown directions and uncertain time-varying parameters. BLFs guarantee that all the system states are constrained in a predefined compact set and the tracking error can converge to a small zero neighborhood. Nussbaum’s gain technique is utilized to tackle the unknown control direction issue. Besides, a sufficiently smooth projection algorithm is adopted to estimate the unknown time-varying parameters, so as to ensure that the adaption laws are differentiable and bounded. The developed controller not only makes all the system states restrained in the compact set but also assures the smoothness and boundedness of all the signals of the closed-loop system. In addition, the sufficiently smooth projection algorithm and Nussbaum gain technique are combined with the BLF-BS control method for the nonlinear systems. Finally, the simulation example results verify the effectiveness and feasibility of the proposed control scheme.

Adaptive Formation Tracking Control for First-Order Agents With a Time-Varying Flow Parameter

A novel adaptive method to achieve both path following and formation moving along desired orbits in the presence of a spatio-temporal flowfield is presented. The flowfield is a spatio-temporal general flow with unknown time-varying parameters. The so-called \emph{congelation of variables} method is used to estimate the time-varying flow parameters, which do not have any restrictions on the rate of their variation. The asymptotic properties of the resulting adaptive system are studied in detail. Simulation results demonstrate the effectiveness of the proposed method.

Fault-Tolerant Reduced-Attitude Control for Spacecraft Constrained Boresight Reorientation

This paper is devoted to investigating the fault-tolerant reduced-attitude control problem for boresight reorientation of an uncertain spacecraft subject to pointing and angular velocity constraints. First, the stereographic projection is used to transform this problem to an obstacle avoidance problem on a two-dimensional Euclidean sphere world with circular obstacles. Then, an adaptive fault-tolerant control strategy is proposed to solve the transformed problem, by designing two potential functions for constraint handling in conjunction with a sliding vector containing hyperbolic tangent functions. Stability analysis shows that the derived controller can achieve asymptotic convergence of the gradient of the obstacle avoidance potential and angular velocities, while ensuring the satisfaction of both pointing and angular velocity constraints, despite the presence of unknown time-varying inertia parameters, disturbances, and actuator faults. In particular, benefiting from incorporating the spacecraft principal moments of inertia into the potential field design, the risk of the system losing strong controllability under multiplicative actuator faults is greatly reduced. To accommodate actuator faults under input saturation, the adaptive fault-tolerant controller is further extended to a saturated counterpart, which is capable of making full use of the remaining actuation power to react to actuator faults. Finally, simulation results are presented to demonstrate our theoretical findings.

An Overview on Modelling of Complex Interconnected Nonlinear Systems

This paper proposes new mathematical models of representation, which can describe the dynamic behavior of large-scale nonlinear systems, such as an extended mathematical model of Volterra series, interconnected Hammerstein structures, and interconnected Wiener structures. In this research, we focus on the class of large-scale nonlinear systems, which are composed of several interconnected nonlinear subsystems. In this context, a discrete nonlinear mathematical model with unknown time-varying parameters, mono-variable, characterizes each interconnected subsystem operating in a deterministic or stochastic environment. An illustrative numerical simulation example of two interconnected nonlinear processes is provided to prove the validity and the performance of the developed theoretical results.

Adaptive Decentralized Asymptotic Tracking Control for Large-Scale Nonlinear Systems With Unknown Strong Interconnections

An adaptive decentralized asymptotic tracking control scheme is developed in this paper for a class of large-scale nonlinear systems with unknown strong interconnections, unknown time-varying parameters, and disturbances. First, by employing the intrinsic properties of Gaussian functions for the interconnection terms for the first time, all extra signals in the framework of decentralized control are filtered out, thereby removing all additional assumptions imposed on the interconnections, such as upper bounding functions and matching conditions. Second, by introducing two integral bounded functions, asymptotic tracking control is realized. Moreover, the nonlinear filters with the compensation terms are introduced to circumvent the issue of “explosion of complexity”. It is shown that all the closed-loop signals are bounded and the tracking errors converge to zero asymptotically. In the end, a simulation example is carried out to demonstrate the effectiveness of the proposed approach.

Robust Time-Varying Parameters Estimation Based on I-DREM Procedure

We consider a class of systems with time-varying parameters, which are represented in the form of linear regressions with bounded disturbances. The task is to estimate such parameters under the condition that the regressor is finitely exciting (FE). Considering such a problem statement, a new robust method is proposed to identify the time-varying parameters with bounded error, which could be reduced to the finite limit. For this purpose, unknown time-varying parameters are expanded into the Taylor series in order to transform the task into the estimation of the piecewise-constant parameters. This results in the increase of the dimensionality of the identification problem. Then, the I-DREM procedure with exponential forgetting, resetting, and normalization of the regressor, which has been proposed earlier by the authors, is applied to the obtained regression. In contrast to the known solutions, this allows one to get the dimensionality of the problem back to the initial one and provide the required exponential convergence of the parameter error to a bounded set with adjustable bound under the FE condition. In addition, proposed method guarantees that the parameter error is bounded beyond the regressor excitation interval. The above properties are proved analytically and demonstrated via numerical experiments.

Adaptive observer design for time-varying systems with relaxed excitation conditions*

In this paper we are interested in the problem of adaptive state observation of linear time-varying (LTV) systems where the system and the input matrices depend on unknown time-varying parameters which described unknown LTI dynamics with unknown initial conditions. Our main contribution is to propose a globally convergent state observer that requires only a weak excitation assumption on the system.

State Observation of Affine-in-the-States Systems with Unknown Time-Varying Parameters and Output Delay

In this paper we address the problem of adaptive state observation of affine-in-the-states time-varying systems with delayed measurements and unknown parameters. The development of the results proposed in the [Bobtsov et al. 2021a] and in the [Bobtsov et al. 2021c] is considered. The case with known parameters has been studied by many researchers—see [Sanz et al. 2019, Bobtsov et al. 2021b] and references therein—where, similarly to the approach adopted here, the system is treated as a linear time-varying system. We show that the parameter estimation-based observer (PEBO) design proposed in [Ortega et al. 2015, 2021] provides a very simple solution for the unknown parameter case. Moreover, when PEBO is combined with the dynamic regressor extension and mixing (DREM) estimation technique [Aranovskiy et al. 2016, Ortega et al. 2019], the estimated state converges in fixed-time with extremely weak excitation assumptions.

Anti-saturation adaptive fault-tolerant control with fixed-time prescribed performance for UAV under AOA asymmetric constraint

This paper presents an anti-saturation adaptive fault-tolerant control scheme with fixed-time prescribed performance for the longitudinal model of fixed wing UAV under actuator faults, control input saturation, angle of attack (AOA) asymmetric constraint and uncertainties. First, by introducing equivalent error transformation technique, the error transformed models of the altitude and airspeed tracking subsystems are strictly constructed. Second, asymmetric saturation function, auxiliary system and barrier Lyapunov function (BLF) are incorporated to guarantee AOA maintain in the asymmetric constraint. Then, neural network approximation structures are combined with adaptive robust terms to handle the lumped disturbances. Furthermore, Nussbaum-type gain technique is adopted to deal with the unknown time-varying parameter arising from input saturation and actuator faults. According to the stability analysis, the altitude and airspeed tracking errors evolve strictly inside the fixed-time performance envelops, while the AOA remains in asymmetric constraint and all signals in closed-loop system are uniformly ultimately bounded. Finally, numerical simulation is presented to verify the effectiveness and superiority of proposed control scheme.

Simultaneously Robust Chaos Synchronization and Identification of Unknown Parameters for Nonlinear Gyro System

This paper concerns robust synchronization and parameter identification for nonlinear gyroscope systems. Gyros are widely utilized in navigational applications where synchronization plays a vital role. A system of nonlinear dynamical equations with some parameters presents a model of gyro systems. The parameters of gyro can vary in time, which can lead to desynchronization of the gyro systems. In this paper, we assume that a gyro system has bounded time-varying unknown parameters and the synchronization problem is considered in two situations. First, the synchronization of two gyroscopes with identical dynamical model and, second, the synchronization of a gyroscope with the Rossler system. The Lyapunov stability theory with control terms is employed to cope with the problem. Also, the identification of time-varying unknown parameters is the side goal of the paper. The proposed scheme synchronizes chaotic nonlinear systems in both situations appropriately. In addition, the slave parameters converge to the nominal values of master parameters despite uncertainty. Simulation results illustrate the superiority of the proposed method.

Output Adaptive Observers Design for Linear Non-Stationary Systems with Polynomial Parameters

The article deals with the problem of state observer design for a linear time-varying plant. To solve this problem, a number of realistic assumptions are considered, assuming that the model parameters are polynomial functions of time with unknown coefficients. The problem of observer design is solved in the class of identification approaches, which provide transformation of the original mathematical model of the plant to a static linear regression equation, in which, instead of unknown constant parameters, there are state variables of generators that model non-stationary parameters. To recover the unknown functions of the regression model, we use the recently well-established method of dynamic regressor extension and mixing (DREM), which allows to obtain monotone estimates, as well as to accelerate the convergence of estimates to the true values. Despite the fact that the article deals with the problem of state observer design, it is worth noting the possibility of using the proposed approach to solve an independent and actual estimation problem of unknown time-varying parameters.

Simultaneous Perturbation Stochastic Approximation-Based Consensus for Tracking Under Unknown-But-Bounded Disturbances

We consider a setup where a distributed set of sensors working cooperatively can estimate an unknown signal of interest, whereas any individual sensor cannot fulfill the task due to lack of necessary information diversity. This article deals with these kinds of estimation and tracking problems and focuses on a class of simultaneous perturbation stochastic approximation (SPSA)-based consensus algorithms for the cases when the corrupted observations of sensors are transmitted between sensors with communication noise and the communication protocol has to satisfy a prespecified cost constraints on the network topology. Sufficient conditions are introduced to guarantee the stability of estimates obtained in this way, without resorting to commonly used but stringent conventional statistical assumptions about the observation noise, such as randomness, independence, and zero mean. We derive an upper bound of the mean square error of the estimates in the problem of unknown time-varying parameters tracking under unknown-but-bounded observation errors and noisy communication channels. The result is illustrated by a practical application to the multisensor multitarget tracking problem.

Adaptive Iterative Learning Control for High-Speed Train: A Multi-Agent Approach

The precise tracking control of high-speed train is an essential prerequisite to ensure the safety and comfort of the train. In this paper, an adaptive iterative learning control (ILC) scheme for the velocity and displacement tracking of high-speed train is proposed to handle the unknown time-varying parameters and lumped uncertainties. The composite energy function (CEF) method is used to analyze the stability of closed-loop system. Since the train usually runs on the same railway periodically, such as the same tunnels, slopes, bridges, etc., ILC is an inherent method for designing the tracking controller that is able to improve the operation performance of train iteratively. To the best of our knowledge, it is the first time that the multi-agent framework and ILC methodology are considered simultaneously in a single train, which can better reveal the coupled characteristic of adjacent cars and impose the repetitive operation pattern of train. The results of numerical simulations show that the tracking performance of the train toward the reference trajectory is significantly improved along with the increase of the number of operations.

Adaptive state estimation of state-affine systems with unknown time-varying parameters

In this paper we provide two significant extensions to the recently developed parameter estimation-based observer design technique for state-affine systems. First, we consider the case when the full state of the system is reconstructed in spite of the presence of unknown, time-varying parameters entering into the system dynamics. Second, we address the problem of reduced order observers with finite convergence time. For the first problem, we propose a simple gradient-based adaptive observer that converges asymptotically under the assumption of generalised persistent excitation. For the reduced order observer we invoke the advanced dynamic regressor extension and mixing parameter estimator technique to show that we can achieve finite convergence time under the weak interval excitation assumption. Simulation results that illustrate the performance of the proposed adaptive observers are given. This include, an unobservable system, an example reported in the literature and the widely popular, and difficult to control, single-ended primary inductor converter.

Auxiliary Constrained Control of a Class of Fault-Tolerant Systems

This paper is concerned with the robust constrained control problem for a class of fault-tolerant time-varying systems against actuator faults and input amplitude saturation. An adaptive technique is proposed to compensate for the impacts of actuator bias faults and partial loss of control effectiveness, as well as to eliminate the effects of unknown time-varying parameters of the systems. An auxiliary system is developed to ensure that the actuator behaves within the limitation of the actuator amplitude. Based on the compensation strategies and auxiliary signals, a novel adaptive fault-tolerant constrained controller is constructed to guarantee the convergence of the system states into a small stability domain in the presence of actuator faults, actuator amplitude limitations, and unknown system parameters. An example of F-18 flight control systems is given to illustrate the proposed procedures and its effectiveness.

High-order fully actuated system approaches: Part V. Robust adaptive control

A type of high-order fully actuated (HOFA) systems with both nonlinear uncertainties and time-varying unknown parameters is considered, and a direct approach for the designs of robust adaptive stabilising controllers and robust adaptive tracking controllers is proposed based on the Lyapunov stability theory. The established controller is composed of three parts, the basic part cancels the known nonlinearities in the system and simultaneously assigns the linear dominant term in the closed-loop system, the robustness part overcomes the effects of the nonlinear uncertainties in the system, and the adaptation part adjusts online the controller to suit the effect of the unknown time-varying parameter vector. The proposed controller guarantees that the tracking error of the state to a given signal and the estimation error of the parameter vector finally converge globally into a bounded ellipsoid. Particularly, in the case that the unknown parameter vector is constant, an adaptive scheme that enables global asymptotical tracking is presented. An example demonstrates the effect of the proposed approach.

Adaptive NN tracking control with prespecified accuracy for a class of uncertain periodically time-varying and nonlinearly parameterized switching systems

This paper focuses on a tracking control issue for a class of uncertain switching nonlinear systems under arbitrary switching with unknown time-varying parameters. An approximator is designed by combining Multilayer neural network (MNN) with Fourier series expansion (FSE) to approximate the nonlinearly parameterized unknown functions. Then, a common Lyapunov function (CLF) is constructed and a novel adaptive neural network (NN) control scheme is proposed by using the adaptive Backstepping technique. It can be proven that the tracking error falls into a prespecified domain of equilibrium and the whole system is semi-globally uniformly ultimately bounded (SGUUB). The effectiveness of the designed approach is verified through two simulation examples.

Extracting Inherent Model Structures and Identifying Parameters of Time-Varying Systems Using Local Linear Neuro-Fuzzy Networks

The main challenges in identifying time-varying systems are to extract the inherent model structure and formulate a generic approach for various time-varying processes. In this article, a local linear neuro-fuzzy networks based approach is proposed for the first time to tackle this issue. The basic idea is to utilize the superior approximation capability of the fuzzy neural networks to expand the unknown time-varying parameters so that various nonlinear and discontinuous processes can be captured. In addition, the local linear model tree optimization algorithm is incorporated in our approach to optimize the network architecture. On one hand, the least number of neurons corresponding to the time-varying parameters can be automatically determined, thus avoiding the superfluous bases and the troublesome overfitting problem; on the other hand, the optimized distribution of the neurons could significantly increase the interpretability of the results, thus contributing to locating the domains where the parameters exhibit strong nonlinearity or change sharply. Moreover, we demonstrate that our approach could simultaneously extract the parsimonious model structure while identifying the time-varying parameters, without adding additional procedures or increasing computation burden. Considering the generality and the unique merits, our proposed approach could significantly advance the applications of artificial neural network techniques in system identification.

Adaptive bounded bilinear control of coupled first-order 1-D hyperbolic PDEs and infinite ODEs with unknown time-varying source term

ABSTRACT In this paper, we investigate the problem of bounded adaptive bilinear control of a system of coupled first-order 1-D hyperbolic PDE and infinite-dimensional ODE, with an unknown time-varying source term. Only boundary measurements are available, and the manipulated variable is the transport velocity. Moreover, input constraints have to be satisfied. Using boundary injection and an energy-like principle, a bounded adaptive output feedback controller is designed in the Lyapunov approach. This controller ensures the ultimate boundedness of the tracking, the state, and the parameter estimation errors while it respects the input constraints. A direct application of this study is the one-loop solar collector parabolic trough, where the solar irradiance is the unknown time-varying parameter and the flow rate is the manipulated variable. The measurements are provided by two sensors placed at the tube's inlet and outlet. Simulation results are provided to illustrate the performance of the theoretical findings.

Adaptive Monitoring of Biotechnological Processes Kinetics

In this paper, an approach for the monitoring of biotechnological process kinetics is proposed. The kinetics of each process state variable is presented as a function of two time-varying unknown parameters. For their estimation, a general software sensor is derived with on-line measurements as inputs that are accessible in practice. The stability analysis with a different number of inputs shows that stability can be guaranteed for fourth- and fifth-order software sensors only. As a case study, the monitoring of the kinetics of processes carried out in stirred tank reactors is investigated. A new tuning procedure is derived that results in a choice of only one design parameter. The effectiveness of the proposed procedure is demonstrated with experimental data from Bacillus subtilis fed-batch cultivations.