Time-varying Uncertain Parameters Research Articles

Decentralized Adaptive Secure Control of Uncertain Nonlinear Time-Varying Interconnected Systems Against Sensor and Actuator Attacks.

In this article, the decentralized adaptive secure control problem for cyber-physical systems (CPSs) against deception attacks is investigated. The CPSs are formed as a type of nonlinear interconnected strict-feedback systems with uncertain time-varying parameters. The attack affects the information transmission between sensor and actuator in a multiplicative manner. A novel decentralized adaptive backstepping secure control strategy is established by exploiting a particular kind of Nussbaum functions and a flat-zone Lyapunov function analysis approach. It is shown that all of closed-loop signals remain globally bounded, and each output signal eventually converges into a small neighborhood of the origin. Simulation results on an illustrative example are provided to display the effectiveness of the proposed control scheme.

Input delay compensation of nonlinear systems with uncertain time-varying parameters

A robust adaptive control law is designed for the class of nonlinear systems with uncertain time-varying parametric dynamics and input delays. The Constitution of control law design is based on filtered tracking errors, previous values of control input and estimate of uncertain parameters which is updated by the update law. An arbitrary large input delay compensation is guaranteed by deriving sufficient control gain conditions using Lyapunov-Krassovskii based stability analysis. The efficacy of the design is verified by Simulation results of two-link robot manipulator dynamical system.

Event-triggered adaptive prescribed-time control for nonlinear systems with uncertain time-varying parameters

The problem of event-based adaptive prescribed-time control for a class of nonlinear systems with uncertain time-varying parameters is considered in this paper. The existence of uncertain time-varying parameters makes the system in question intrinsically different from that in prescribed-time stabilization or event-triggered control. Moreover, the existing prescribed-time control methods require the real-time continuous control input. For this reason, a novel event-based adaptive prescribed-time control strategy is presented by skillfully utilizing a key scaling technique and a new event-triggering mechanism. It is proved that the proposed event-triggering mechanism can enlarge the trigger time interval and effectively reduce the number of trigger moments compared with the existing event-triggered control methods. An important stability criterion is proposed based on the defined prescribed-time adjustment function. Furthermore, the proposed control algorithm can effectively reduce the computational burden and save the control effort. Finally, a numerical simulation verifies the effectiveness of the proposed prescribed-time control algorithm.

Intelligent vibration control for ultra-high-speed elevators: A type 2 variable universe fuzzy neural network method with input saturation

When elevators accelerate to ultra-high speed, the horizontal vibration suppression is significantly challenged by the complex coupled excitation and uncertain time-varying parameters. Therefore, this paper proposes an intelligent control method with type 2 variable universe fuzzy neural network considering input saturation. Firstly, considering the multilevel relationship of the guide rails, guide shoes, frame and car, a horizontal vibration dynamic model is constructed. To improve the tolerance and adaptability of the control system to the uncertain parameters, the type 2 variable universe fuzzy control is used as the main controller. The discourse of universe is adjusted by the T-S fuzzy neural network, and the anti-saturation controller is designed to compensate for the over-saturation problem aggravated by the networks. The non-parametric inverse model of intelligent adjustable dampers represented by the magnetorheological damper is constructed to accurately calculate the ideal output damping force. The effectiveness of the proposed control method is verified by the elevator experimental data and the bidirectional gas-solid coupling aerodynamic excitation. The results show that the proposed intelligent control method can significantly improve the mean values, peak values and comfort indexes of the horizontal vibration acceleration and tilt angle acceleration of the elevator car. The research provides a new intelligent control scheme for high-speed/ultra-high-speed elevators and other similar vibration suppression systems.

Interval observer–based compensators design for linear systems with uncertain time-varying parameters

This paper proposes a novel approach to design interval observer–based compensator for linear systems with uncertain parameters and measurement noises. Based on monotone system theory, existence decoupled conditions of observers gain design to guarantee cooperativity and input-to-state stability of error dynamics system are proposed in terms of a set of linear matrix inequalities. Moreover, a compensator consisting of the observers and output feedback controller is designed within interval observer design framework. Such an observer-based compensator has a simple separation structure, which shows that interval observers and feedback controller can be simultaneously designed based on separation principle. The developed techniques on observer-based compensator design are illustrated through a practical example.

Optimal resource allocation and adaptive robust control of technology innovation ecosystems based on cooperative game theory

This paper addresses a problem of optimal resource allocation for technology innovation ecosystem. Two layers goal are realized. First, an uncertain dynamical system is constructed with the Lotka–Volterra model for the description of the dynamics of the concerned innovation ecosystem, in which the growth rate and the symbiosis coefficient are specially treated as possibly (fast) time-varying uncertain parameters. Second, an adaptive robust resource allocation strategy is designed to drive the errors between the populations and the desired populations to be uniformly bounded and uniformly ultimately bounded, such that the first layer (basic) goal of resource allocation is achieved. Third, a two-player cooperative game is formulated for the seeking of the optimal control parameters, in which two (static) cost functions and a comprehensive performance index are constructed by performance analysis, and then the optimal control parameters (i.e., the Pareto-optimality) are obtained by minimizing the comprehensive performance index, such that the second layer (further) goal of optimal balance between the control inputs and the system performance is achieved. This work should be the first effort that addresses the optimal resource allocation and control for technology innovation ecosystem through a creative combination of dynamic modeling, control theory and game theory.

A new adaptive iterative learning control of finite-time hybrid function projective synchronization for unknown time-varying chaotic systems

A new adaptive iterative learning control (AILC) scheme is proposed to solve the finite-time hybrid function projective synchronization (HFPS) problem of chaotic systems with unknown periodic time-varying parameters. Fourier series expansion (FSE) is introduced to deal with the problem of uncertain time-varying parameters. The bound of the expanded remaining items is unknown. A typical convergent series is used to deal with the unknown bound in the design process of the controller. The adaptive iterative learning synchronization controller and parameter update laws are designed. Two different chaotic systems are synchronized asymptotically according to different proportional functions on a finite time interval by Lyapunov stability analysis. The simulation example proves the feasibility and effectiveness of the proposed method.

Integrated Localization and Tracking for AUV With Model Uncertainties via Scalable Sampling-Based Reinforcement Learning Approach

This article studies the joint localization and tracking issue for the autonomous underwater vehicle (AUV), with the constraints of asynchronous time clock in cyberchannels and model uncertainty in physical channels. More specifically, we develop a reinforcement learning (RL)-based asynchronous localization algorithm to localize the position of AUV, where the time clock of AUV is not required to be well synchronized with the real time. Based on the estimated position, a scalable sampling strategy called multivariate probabilistic collocation method with orthogonal fractional factorial design (M-PCM-OFFD) is employed to evaluate the time-varying uncertain model parameters of AUV. After that, an RL-based tracking controller is designed to drive AUV to the desired target point. Besides that, the performance analyses for the integration solution are also presented. Of note, the advantages of our solution are highlighted as: 1) the RL-based localization algorithm can avoid local optimal in traditional least-square methods; 2) the M-PCM-OFFD-based sampling strategy can address the model uncertainty and reduce the computational cost; and 3) the integration design of localization and tracking can reduce the communication energy consumption. Finally, simulation and experiment demonstrate that the proposed localization algorithm can effectively eliminate the impact of asynchronous clock, and more importantly, the integration of M-PCM-OFFD in the RL-based tracking controller can find accurate optimization solutions with limited computational costs.

Adaptive Control of Time-Varying Parameter Systems With Asymptotic Tracking

A continuous adaptive controller is developed for nonlinear dynamical systems with linearly parameterizable uncertainty involving time-varying uncertain parameters. Through a unique stability analysis strategy, a new adaptive feedforward term is developed along with specialized feedback terms, to yield an asymptotic tracking error convergence result by compensating for the time-varying nature of the uncertain parameters. A Lyapunov-based stability analysis is shown for Euler–Lagrange systems, which ensures asymptotic tracking error convergence and boundedness of the closed-loop signals. Additionally, the time-varying uncertain function approximation error is shown to converge to zero. A simulation example of a two-link manipulator is provided to demonstrate the asymptotic tracking result.

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.

Optimal guaranteed cost intermittent control to the efficient movement of freight trains

Freight train system is under constant pressure to optimize operational efficiency, a factor that has led the sector to spearhead many new technologies. To address this, the optimal guaranteed cost intermittent cruise control of freight train system with time-varying uncertain parameters is investigated. In particular, the guaranteed cost intermittent control approach is proposed, which can achieve both advantages of guaranteed cost control and intermittent control methods. In addition, the acceptable conditions for the guaranteed cost control laws are weakened to insure that the proposed strategy is suitable for the application in freight train systems. Moreover, to promote the optimal control design in the freight train system, the proposed optimal guaranteed cost intermittent control for the nonlinear system subjected to norm bounded parametric uncertainties is addressed. The results of numerical experiments are presented to ascertain the effectiveness of the proposed freight train control methodology and to compare it to prior methods.

Guaranteed Cost Impulsive Synchronization of Uncertain Multiplex Networks

This brief mainly deals with the issue of guaranteed cost impulsive synchronization of uncertain multi-agent systems from the multiplex network prospective, where the uncertain time-varying system parameters are supposed to be norm-bounded. By means of a group of linear matrix inequalities, the effective guaranteed cost impulsive control is designed to not only ensure that the trajectories of all followers synchronize with the leader, but also guarantee that the control cost is no higher than an upper bound of the quadratic guaranteed cost function. Numerical example demonstrates the feasibility of theoretical results.

Robust indirect adaptive control of electromechanical servo systems with uncertain time-varying parameters

This paper focuses on high-accuracy motion control for electromechanical servo systems with time-varying parameter estimation. A robust indirect adaptive controller based on a nonlinear X-swapping technique is proposed to achieve the online estimation of the time-varying parameters. The time-varying parametric uncertainties can be well compensated via the adaptive feedforward cancellation technique, and the residual model uncertainties are suppressed by a nonlinear robust control law. The Lyapunov-based stability analysis illustrates that the proposed method obtains a prescribed estimating result and an excellent asymptotic tracking performance. Extensive experimental results are acquired to affirm the applicability of the proposed control strategy.

Adaptive augmented torque control of a quadcopter with an aerial manipulator

A quadcopter manipulator system is an aerial robot consisting of a quadcopter with a robotic arm attached to it. The system has coupled nonlinear dynamics with uncertain time-varying parameters. The work in this paper focuses on designing an adaptive nonlinear controller to facilitate the uncertain system’s trajectory tracking and stability. The novelty of the proposed work is the design and implementation of an adaptive feedback linearization controller, called adaptive augmented torque (AAT) control, for the aerial robot. The control law is based on a feedback linearization controller with model reference adaptive controller and a tracking error-based augmented term. Using the input-to-state stability concept, a bound on the parameter estimation error is also developed. In the presented methodology, the controller uses estimated values of system parameters obtained from the adaptive mechanism and the tracking error to compute the control input using the AAT control law. An adaptive law for estimating unknown parameters is obtained using the strictly positive real-Lyapunov method. The asymptotic stability of the closed-loop system is analyzed via the Lyapunov theory. Simulations implemented in MATLAB and ROS/Gazebo and preliminary hardware experiments are presented to validate the theoretical results and to corroborate the performance of the AAT control law.

Robust State-Feedback Controller for Linear Parameter Varying Systems with Time-Invariant Uncertainties

In this paper, the robust gain-scheduled state-feedback controller problem is studied for uncertain linear parameter-varying systems whose state-space representations are the linear combination of the uncertain time-varying parameters including time-invariant parametric uncertainties (TIPU). It is supposed that these uncertainties are bounded by the given intervals and cannot be pulled out as an uncertain block. It is considered a serious challenge because the exact information about the plant dynamics cannot be extracted from the uncertain time-varying parameters. This is while; the gain-scheduled controllers need to have the exact information about the plant dynamics to satisfy the desired control purposes. To handle this challenge, we introduce a state-feedback gain, which is formed by a set of the new scheduling parameters and a secondary time-varying term. The stabilization conditions are obtained in terms of the linear matrix inequalities (LMIs). The effectiveness of the proposed method is shown using an example.

Adaptive dynamic surface control using nonlinear disturbance observers for position tracking of electro-hydraulic servo systems

In this article, an adaptive dynamic surface control method with nonlinear disturbance observers is proposed for accurate position tracking of an electro-hydraulic servo system with unknown time-varying inner or external disturbances. The dynamic surface control approach adopted in the proposed controller is used to ameliorate the inherent complexity differentiation explosion of traditional backstepping method, which significantly simplifies the controller design process. The designed nonlinear disturbance observers are exploited to online estimate the inner or external disturbances of electro-hydraulic servo systems, and the performance degradation resulted from unknown time-varying disturbances is effectively suppressed. To further compensate for the system’s time-varying uncertain parameters, parameter adaptive updating laws are designed and combined in the proposed controller for accurate position tracking of electro-hydraulic servo systems. The closed-loop stability of the proposed controller is theoretically guaranteed by rigorous Lyapunov analysis. Comparative experimental results are carried out on a typical single-degree-of-freedom electro-hydraulic servo system, and the feasibility together with the superiority of the proposed controller is experimentally validated.

Fixed-time control of nonlinear discrete-time systems with time-varying delay and uncertain parameters: state and output feedback approaches

Fixed-time control of nonlinear discrete-time systems with time-varying delay and uncertain parameters: state and output feedback approaches

Designing controller parameters of an LPV system via design space exploration

This paper deals with the stabilizability problem of liner parameter varying (LPV) systems. It is assumed that LPV models affinely depend on time-varying uncertain and time-invariant design parameters. The uncertain parameters, their time-derivations, and design parameters belong to polygonal convex spaces. The stabilizability problem of such systems is studied. Extending the stability conditions to stabilizability conditions generally causes nonlinearity issues due to the coupling between the Lyapunov and design variables. To cope with this issue, a design space exploration algorithm (DSEA) is proposed to accurately determine the design parameters with a feasibility performance similar to stability analysis approaches. DSEA removes the undesired parts of the design subspace that cannot stabilize the model. Then, it checks the corner points of the remaining subspaces to find a stabilizing point. This procedure continues until a stabilizing point is found or the whole design subspaces are detected to be undesirable. Three hundred random LPV systems are generated to compare the feasibility performance of DSEA with existing approaches. Also, the proposed approach is used to stabilize the LPV model of a microgrid consisting of several distributed generation units and energy storage systems. The simulation results show the superiority of DSEA over the existing approaches.

Aerodynamic and gravity gradient based attitude control for CubeSats in the presence of environmental and spacecraft uncertainties

In this paper, the problem of controlling the attitude of a CubeSat in low Earth orbit using only the environmental torques is considered. The CubeSat is equipped with a Drag Maneuvering Device (DMD) that enables the spacecraft to modulate its experienced aerodynamic and gravity gradient torques. An adaptive controller is designed to achieve attitude tracking of the spacecraft in the presence of uncertain parameters such as the atmospheric density, drag and lift coefficients, and the time-varying location of the Center of Mass (CoM). The proposed controller also accounts for modeling inaccuracy of the inertia matrix of the spacecraft. A Lyapunov-based analysis is used to prove that the quaternion-based attitude trajectory tracking error is uniformly ultimately bounded. The designed controller is also examined through numerical simulations for a spacecraft with time-varying uncertain drag, lift coefficients and CoM location parameters and the NRLMSISE-00 model for the atmospheric density.

Non-probabilistic interval process method for analyzing two-stage straight bevel gear system with uncertain time-varying parameters

A two-stage straight bevel gear system is a gear system that can be used in various applications. The straight bevel gear is known for its complex tooth geometry. Due to the variation of the number of pairs of teeth in contact, the mesh stiffness function can be considered as a time-varying function. However, the mesh stiffness for the straight bevel gear is sensitive to measurement and modeling errors. Thus, at each time step, its value can not assigned to deterministic one. Generally, the uncertain parameters are assumed to be time-independent. In this paper, the interval process method has been used to represent the time-varying uncertain parameters, whose bounds are determined through the potential energy method. The lumped parameter model of two-stage straight bevel gear has been proposed. We have considered that the masses of the straight bevel gear system components and bearing stiffnesses along with time-varying mesh stiffnesses are uncertain parameters which can be represented by the interval process model. The Chebyshev polynomial expansion has been used to approximate the response of the two-stage straight bevel gear system with respect to the interval variables. The lower and higher bounds of the eigenvalues of the system have been determined. The bounds of dynamic displacements of the straight bevel gear system have been computed and compared with those computed by the Monte Carlo method.