Unknown Time-varying Control Coefficients Research Articles

Global practical tracking for uncertain nonlinear systems with unknown control coefficients and polynomial growth

This paper studies the problem of global output-feedback tracking control for a class of uncertain nonlinear systems. The system studied in this paper has unknown time-varying control coefficients and unknown reference signal. Notably, the nonlinearities of the system are bounded by the lower triangular linear unmeasured states multiplying the unknown constant, the polynomial-of-output and the polynomial-of-input growth rates, which indicates the presence of serious uncertainties. Motivated by the closely related works, by combining the ideas of universal control and deadzone with backstepping technique, this paper presents a new adaptive tracking control scheme based on two dynamic high-gains in the new forms. The proposed control scheme ensures that the tracking error converges to a specified arbitrarily small interval range after a finite time while the state of the resulting closed-loop system is globally bounded. Finally, the effectiveness of the control scheme is verified by an illustrative example.

Global adaptive neural network control of nonlinear time-varying systems with unknown control coefficients and model uncertainties

This paper investigates the adaptive control problem for the strict-feedback nonlinear time-varying system (NTVS) with unknown control coefficients and model uncertainties. To address the problem that the neural network (NN) can only achieve local approximation of unknown nonlinear functions, a novel NN control scheme is proposed. The scheme consists of a NN controller that operates inside the approximation domain and a robust controller that operates outside the approximation domain, and a novel switching function is designed to enable the two controllers to switch smoothly in the vicinity of the approximation domain to ensure that all signals of the closed-loop system are globally uniformly ultimately bounded. To address the problem that unknown time-varying control coefficients are difficult to handle, an adaptive fault-tolerant control scheme is proposed in combination with the congelation of variables method. The scheme employs classical adaptive control to adapt to the variation of unknown control coefficients and robust control to eliminate the time-varying disturbance terms, and introduces a positive integrable time-varying function to achieve asymptotic tracking of an arbitrary reference signal. The combination of these two schemes constitutes a global adaptive neural network control (GANNC) method for the NTVS with unknown control coefficients and model uncertainties. Finally, an adaptive attitude fault-tolerant controller for launch vehicles is designed by using the GANNC method, which can realize the accurate tracking of the attitude control system to the reference command under normal status, strong disturbances and actuator failures, and comparative experiments prove the effectiveness and superiority of the controller.

Multiple adaptive fuzzy Nussbaum-type functions design for stochastic nonlinear systems with fixed-time performance

Nussbaum design has been successfully exploited to deal with uncertain systems with a single unknown control coefficient. However, it is challenging for the traditional Nussbaum method to efficiently handle the feedback control design with multiple unknown time-varying control coefficients because the multiple Nussbaum-type gains might mutually cancel out, which makes the Lyapunov-based stability analysis infeasible. To tackle this issue, a novel type of Nussbaum function is designed for the tracking problem of a class of stochastic strict-feedback nonlinear systems. In the presented Nussbaum design, the multiple unknown control coefficients are separately compensated, where the effect of mutual cancellation no longer exists and the Lyapunov stability analysis can be directly applied. Moreover, the proposed Nussbaum design is combined with the fixed-time stability theory, which ensures the settling time is bounded and independent of the initial condition. Within the adaptive fuzzy backstepping framework, it is shown that all signals in the closed-loop system remain bounded through the theoretical discussions. The simulation experiment is conducted to verify the effectiveness of the presented design for the continuous-time stochastic nonlinear dynamical system.

Global event-triggered output-feedback stabilization for switched nonlinear systems with time-delay and measurement sensitivity

In this paper, the problem of adaptive event-triggered output-feedback stabilization is addressed for a class of switched nonlinear systems with time-delay and output measurement sensitivity. With the assistance of the dynamic high gain technology and a novel event-triggered control mechanism, we overcome the design complexities arising from unknown polynomial growth rate with respect to the output, unknown large measurement sensitivity, unknown time-varying control coefficient and time-delay. Then, an effective constructive method is provided to design switched observers and a common event-triggered controller. Through introducing two key matrix inequalities and constructing a common Lyapunov-Krasovskii functional, sufficient conditions are given to get rid of Zeno behavior, and ensure that all the signals are bounded and the closed-loop system states converge to zero under arbitrary switchings. Two simulation studies are conducted for verifying the effectiveness of proposed scheme.

Global regulation of feedforward nonlinear systems with unknown time-varying control coefficients and growth rate

In this paper, we consider a regulation problem for a class of feedforward nonlinear systems with unknown control coefficients and unknown growth rate. More specifically, the unknown control coefficients are assumed to be time-varying and belong to ranges with unknown upper and lower bounds. Due to the described control coefficients with uncertain feedfoward nonlinearities, our considered system is the natural extension of the related existing results. In solving our control problem, a new adaptive controller is derived by constructing a Lyapunov function in backstepping-like procedure and utilizing appropriate parameters based on the gain scaling technique and Nussbaum function. The uniquely designed exponents of a dynamic gain overcome the difficulties caused from the unknown sign and unknown ranges of the control coefficients and uncertain nonlinearities and thus play a key role in system regulation. We give the rigorous system analysis and simulation results of the numerical example to certify our control method.

Adaptive Uniform Performance Control of Strict-Feedback Nonlinear Systems With Time-Varying Control Gain

In this paper, we present a novel adaptive performance control approach for strict-feedback nonparametric systems with unknown time-varying control coefficients, which mainly includes the following steps. Firstly, by introducing several key transformation functions and selecting the initial value of the time-varying scaling function, the symmetric prescribed performance with global and semi-global properties can be handled uniformly, without the need for control re-design. Secondly, to handle the problem of unknown time-varying control coefficient with an unknown sign, we propose an enhanced Nussbaum function (ENF) bearing some unique properties and characteristics, with which the complex stability analysis based on specific Nussbaum functions as commonly used is no longer required. Thirdly, by utilizing the core-function information technique, the non-parametric uncertainties in the system are gracefully handled so that no approximator is required. Furthermore, simulation results verify the effectiveness and benefits of the approach.

Type-B Nussbaum function-based fault-tolerant control for a class of strict-feedback nonlinear systems

This paper studies the fault-tolerant control (FTC) problem of a class of strict-feedback nonlinear systems. First, we put forward a key theorem which shows that type-B Nussbaum functions can be extended to the cases containing multiple Nussbaum functions in the same Lyapunov inequality under certain conditions. Then, by using the techniques of Nussbaum functions and adaptive control, a new fault-tolerant control scheme is proposed. Compared with the previous work, this paper considers unknown time-varying control coefficients and unknown time-varying fault coefficients of actuators. It is proved that all the signals of the closed-loop system are globally bounded and the tracking error converges to zero asymptotically. Finally, simulations are provided to verify the effectiveness of the proposed control scheme.

Stabilization for time-delay nonlinear systems with unknown time-varying control coefficients

A control scheme based on dynamic gains is proposed for the time-varying nonlinear time-delay systems with unknown control coefficients. A class of Nussbaum functions are introduced to deal with the problem of unknown control directions. Dynamic gains technique and Lyapunov–Krasovskii functional are developed to handle the time delays in nonlinear system. It is shown that the system state is regulated to origin asymptotically, and the boundedness of all closed-loop signals is guaranteed. Simulation results are provided to demonstrate the effectiveness of the proposed methodology.

Distributed control of nonlinear systems with unknown time-varying control coefficients: A novel Nussbaum function approach

In this paper, distributed control of uncertain multi-agent systems (MAS) with completely unknown nonlinearities, unknown time-varying control coefficients and multiple unknown control directions is investigated. Firstly, a new theorem with a series of novel Nussbaum functions are presented, which solve the outstanding problem in control of nonlinear systems with unknown time-varying control coefficients and unknown signs. Secondly, global consensus of MAS with unknown time-varying control coefficients and unknown system nonlinearities under directed graph is firstly achieved, and the transient tracking performance is also guaranteed. Thirdly, a novel filter is proposed for each agent which does not require a prior knowledge of time derivative of leader. Finally, simulation results show the effectiveness of the proposed control schemes.

Practical tracking of uncertain nonlinear systems via adaptive event-triggered output feedback

This paper investigates the problem of global practical tracking by adaptive event-triggered output feedback for a class of uncertain nonlinear systems with unknown time-varying control coefficients. The nonlinear systems under consideration allow more general growth restriction, e.g., unknown constant and output-polynomial function coupled to the unmeasurable states. Based on non-separation principle, an adaptive event-triggered output feedback controller is proposed by combining dynamic high-gain scaling approach with backstepping method. It is worth emphasizing that a novel updating law of the high-gain is introduced to overcome the system nonlinearities and the serious uncertainties mentioned above. The controller proposed guarantees that the states of the resulting closed-loop systems are globally bounded, while the tracking error converges to a prescribed arbitrarily small neighborhood of the origin after a finite time. Finally, a numerical example is given to illustrate the effectiveness of the proposed approach.

On active disturbance rejection control for lower-triangular systems with mismatched nonlinear uncertainties and unknown time-varying control coefficients

On active disturbance rejection control for lower-triangular systems with mismatched nonlinear uncertainties and unknown time-varying control coefficients

Adaptive Fuzzy Output-Constrained Control for Nonlinear Stochastic Systems With Input Delay and Unknown Control Coefficients.

This article considers an adaptive fuzzy control problem for nonstrict-feedback nonlinear stochastic systems, which contain input delay, output constraints, and unknown control coefficients, simultaneously. First, an original stochastic nonlinear mapping and the Pade approximation transformation techniques are developed to solve the symmetric output constraints and input delay. Then, an adaptive fuzzy controller is designed for the unknown nonlinear systems, in which the Nussbaum function is employed to deal with the unknown time-varying control coefficients. Tracking errors are ensured to converge to a small neighborhood around the origin, and the system output does not violate the predefined constrained conditions. All the signals of the closed-loop systems have proven to remain bounded in probability. Moreover, the asymmetric output-constrained control is also studied. Two simulation examples are provided to show the effectiveness of the developed method.

Observer-Based Adaptive Consensus for a Class of Nonlinear Multiagent Systems

This paper investigates an adaptive consensus problem of a class of nonlinear multiagent systems in which the states are unmeasurable and the dynamics of all agents are supposed to be in strict-feedback form with unknown time-varying control coefficients. Due to the presence of uncertain nonlinearities in agents’ dynamics, radial basis function neural networks are used to approximate the unknown nonlinear functions, and a neural-network-based observer is designed to estimate the unmeasured states. The adaptive observer-based protocols are based on the relative output information of neighbors, and are constructed by adopting the dynamic surface control technique. It is proved that practical consensus of the system can be achieved with the proposed protocols. A simulation example is given to show the effectiveness of the proposed method.

Adaptive Robust Course-tracking Control of Time-varying Uncertain Ships with Disturbances

In this paper, we address the problem of course-tracking for ships with unknown time-varying parameters, completely unknown time-varying control coefficient, and unknown time-varying bounded environmental disturbances. Incorporating a Nussbaum function and an adaptive law into the backstepping design method, we propose a course-tracking control law. The strict stability analysis shows that the designed course-tracking control law makes the course-tracking error settle into an arbitrarily small compact and guarantees the global uniform ultimate boundedness of all signals of the resulting closed-loop system by appropriately choosing design parameters. Simulation results and simulation comparisons on two ships demonstrate the effectiveness and the superiority of the proposed course-tracking control law.

Adaptive Fuzzy Control for Nonlinear State Constrained Systems With Input Delay and Unknown Control Coefficients

In this paper, an adaptive fuzzy controller is investigated for a class of strict-feedback nonlinear state constrained systems with both input delay and unknown control coefficients. Nussbaum gain technique is employed in the design progress to deal with the unknown time-varying control coefficients. Pade approximation and an intermediate variable are applied to compensate for the effect of the input delay and the barrier Lyapunov functionals (BLFs) are used to guarantee the states to remain within their constraint sets. The unknown functions are approximated by Fuzzy logic systems (FLSs). It is proved that the tracking error can converge to a compact set of the origin without violating the state constraint, and all closed loop signals remain bounded. The effectiveness of the proposed controller is illustrated through two examples.

Distributed cooperative adaptive tracking control for heterogeneous systems with hybrid nonlinear dynamics

The cooperative leader-following tracking for a group of heterogeneous mechanical systems with nonlinear hybrid order dynamics is studied. The controlled systems are considered to be composed of followers (agents) with hybrid first- and second-order time-varying dynamics. The leader is an unknown nonautonomous nonlinear system and can only give the state information of position and velocity to its neighboring followers. The followers are linked by the directed graph with fixed communication topology. And, not all of them have the information path to the leader directly. The directed information topology graph is required to have at least one spanning tree for position and velocity, respectively. Distributed cooperative adaptive control protocols are developed for all followers with first- or second-order dynamics to achieve the ultimate synchronization to the leader. The control protocols are designed based on the neural networks and the adaptive estimation algorithm for unknown time-varying functions and control coefficients. The convergence and boundedness of the synchronization error is proved by the Lyapunov theory. The simulation example verifies the correctness of the developed distributed control protocols.

Adaptive output-feedback bipartite consensus for nonstrict-feedback nonlinear multi-agent systems: A finite-time approach

Abstract Finite-time bipartite synchronization of multi-agent systems is assessed here. To cover a wide range of practical systems, the agents dynamics are modeled as nonlinear nonstrict-feedback dynamics with unknown time-varying control coefficients. Moreover, to conform to many real-world applications, the agents dynamics are assumed unknown and their state information is assumed not available for measurement. First, a virtual affine variable is introduced, and to eliminate the algebraic-loop in control design, neural network along with minimal learning parameter principle are employed to approximate composite uncertainties including unknown functions in the system dynamics, unknown control coefficients and control inputs. A local linear state-observer is then designed for each follower agent to estimate unmeasured states, and finally dynamic surface control scheme and finite-time approach are adopted in the distributed bipartite control design to guarantee finite convergence time. It is ensured that under this proposed protocol, the bipartite error surfaces and boundary error layers are converged to a neighborhood of the origin in the sense of finite-time stability. Finally, two simulation examples clarify the efficiency of the designed controller.

Adaptive tracking control for nonlinear time-varying delay systems with full state constraints and unknown control coefficients

This paper proposes an adaptive tracking control approach for a class of nonlinear state-constrained and time-varying delay systems with unknown time-varying control coefficients. As far as we know, there is no control method for such systems at present. To stabilize such a class of systems, the neural networks and a backstepping technique are utilized to structure an adaptive tracking controller. The Nussbaum gain technique is utilized to solve the problem of unknown time-varying control coefficients, and the Lyapunov–Krasovskii functionals (LKFs) are employed to eliminate the effect of unknown time-varying delays. In addition, the states are guaranteed to remain within their constraint sets based on the Barrier Lyapunov functions (BLFs). Finally, it can be proved that all signals in the closed-loop systems are bounded, the state constraints are never violated and the tracking errors fluctuate within the predetermined compact range around the zero. The simulation results are provided to illustrate the effectiveness of the proposed control strategy.

Adaptive Robust Backstepping Output Tracking Control for a Class of Uncertain Nonlinear Systems Using Neural Network

The problem of robust output tracking is studied for a class of uncertain nonlinear systems in the presence of structure uncertainties, external disturbances, and unknown time-varying virtual control coefficients. In this study, it is supposed that the upper bounds of external disturbances and that the upper and lower bounds of unknown time-varying virtual control coefficients are unknown. By employing a simple structure neural network (NN), the unknown structure uncertainties are approximated. A class of backstepping approach-based adaptive robust controllers is synthesized for such uncertain nonlinear systems. By making use of Lyapunov functional approach, it is also shown that the proposed adaptive robust backstepping output tracking controller can guarantee the tracking error between the system output and the desired reference signal to converge asymptotically to zero. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed controller.

Adaptive Cooperative Tracking Control of Multi-Agent Systems With Unknown Actuators Hysteresis

This paper considers cooperative tracking control of nonlinear multi-agent systems with actuators hysteresis over digraphs. Each agent is modeled by a higher-order nonlinear system in strict-feedback form with the generalized Prandtl–Ishlinskii hysteresis input and unknown time-varying virtual control coefficients. An online adaptive law is introduced for compensating the unknown hysteresis effect. A special Nussbaum-type function is developed to handle unknown time-varying virtual control coefficients. A switching mechanism is utilized to combine the neural networks approximation with an extra robust term, which can take over the authority outside the neural active region. In this sense, the globally uniformly ultimately bounded stability is guaranteed by the proposed distributed adaptive control law. Moreover, all agents ultimately synchronize to the leader node with bounded residual errors. Simulation results justify the proposed algorithm.