Fuzzy adaptive output-feedback tracking control for nonlinear strict-feedback systems in prescribed finite time

The current paper addresses the fuzzy adaptive tracking control via output feedback for single-input single-output (SISO) nonlinear systems in strict-feedback form. Under the situation of system states being unavailable, the system output is used to set up the state observer to estimate the real system states. Furthermore, the estimation states are employed to design controller. During the control design process, fuzzy logic systems (FLSs) are used to model the unknown nonlinearities. A novel observer-based finite-time tracking control scheme is proposed via fuzzy adaptive backstepping and barrier Lyapunov function approach. The suggested fuzzy adaptive output feedback controller can force the output tracking error to meet the pre-specified accuracy in a fixed time. Meanwhile, all the closed-loop variables are bounded. Compared to some existing finite-time output feedback control schemes, the developed control strategy guarantees that the settling time and the error accuracy are independent of the uncertainties and can be specified by the designer. At last, the effectiveness and feasibility of the proposed control scheme are demonstrated by two simulation examples.     

Cooperative output feedback control of a mobile dual flexible manipulator

This paper addresses the cooperative output feedback control of a mobile dual flexible manipulator, which is mounted at a moving platform to grasp and move a rigid object. We derive the distributed parameter model with geometric constraints for the dual flexible manipulator system by utilizing the Lagrange multiplier method and the Hamilton’s principle, which avoids the problem of control spillover. This paper considers a case where the states of system are difficult to measure directly and exploits the high gain observer theory to design the state observers for estimating the unavailable states. Then the cooperative output feedback control scheme is developed by the Lyapunov’s method, which enables the cooperative control of the flexible manipulator system. Furthermore, under the cooperative output feedback control scheme, we prove that the states of the system are uniformly bounded. Finally, the feasibility of the designed cooperative output feedback controllers is verified by numerical simulation.     

Fault-tolerant practical tracking control for uncertain robotic system with general reference trajectory and output constraint

This paper is devoted to the fault-tolerant tracking control for a class of uncertain robotic systems under time-varying output constraints. Notably, both actuator fault and the disturbances are present while all the dynamic matrices are not necessarily to be parameterized by unknown parameters or have known nominal parts, and moreover, the reference trajectories as well as the output constraints functions are not necessarily twice continuously differentiable without any time derivatives of them being available for feedback. These remarkable characteristics greatly relax the corresponding assumptions of the related literature and in turn to bring the ineffectiveness of the traditional schemes on this topic. For this, a powerful adaptive control methodology is established by incorporating adaptive dynamic compensation technique into the backstepping framework based on Barrier Lyapunov functions. Then, an adaptive state feedback controller with the smart choices of adaptive law and virtual controls is designed which guarantees that all the states of the closed-loop system are bounded and the system output practically tracks the reference trajectory while not violates the output constraints.     

Model reference control of LPV systems

This paper deals with the problem of model reference control for linear parameter varying (LPV) systems. The LPV systems under consideration depend on a set of parameters that are bounded and available online. The main contribution of this paper is to design an LPV model reference control scheme for LPV systems whose state-space matrices depend affinely on a set of time-varying parameters that are bounded and available online. The design problem is divided into two subproblems: the design of the coefficient matrices of the controller and the design of the gain of the state feedback controller for LPV systems. The singular value decomposition is used to obtain the coefficient matrices, while the linear matrix inequality methodology is used to obtain the parameter-dependent state feedback gain of the control scheme. A simple numerical example is used to illustrate the proposed design and a coupled-tank process example is used to demonstrate the usefulness and practicality of the proposed design. Simulation and experimental results indicate that the proposed scheme works well.     

On hyper-exponential stability and stabilization of linear systems by bounded linear time-varying controllers

Hyper-exponential stability analysis and hyper-exponential stabilization of linear systems by bounded linear time-varying feedback are investigated in this paper. On the one hand, we propose some Lyapunov-like hyper-exponential stability theorems (both global and local) based on the comparison principle and the concepts of hyper-exponentially stable functions and hyper-exponentially increasing functions. On the other hand, we establish methods to design bounded linear time-varying controllers such that hyper-exponential stability of linear time-invariant systems can be guaranteed. The key design tool is the utilization of a time-varying parameter contained in the controller and the properties of solution to a parametric Lyapunov equation. Both state feedback and observer-based output feedback are accommodated. As a further result, hyper-exponential semi-global stabilization for linear systems by bounded controls is discussed. Finally, the validity of the proposed schemes is illustrated through numerical simulations on spacecraft rendezvous control system.     

Global practical tracking for nonlinear systems with uncertain dead-zone input via output feedback

In this paper, global practical tracking is investigated via output feedback for a class of uncertain nonlinear systems subject to unknown dead-zone input. The nonlinear systems under consideration allow more general growth restriction, where the growth rate includes unknown constant and output polynomial function. Without the precise priori knowledge of dead-zone characteristic, an input-driven observer is designed by introducing a novel dynamic gain. Based on non-separation principle, a universal adaptive output feedback controller is proposed by combining dynamic high-gain scaling approach with backstepping method. The controller proposed guarantees that the closed-loop output can track any smooth and bounded reference signal by any small pre-given tracking error, while all closed-loop signals are globally bounded. Finally, simulation examples are given to illustrate the effectiveness of our dynamic output feedback control scheme.     

Robust adaptive tracking with an additional plant identifier for a class of nonlinear systems

In this paper, we develop two new model reference adaptive control (MRAC) schemes for a class of nonlinear dynamic systems that is robust with respect to an uncertain state (output) dependent nonlinear perturbations and/or external disturbances with unknown bounds. The design is based on a controller parametrization with an adaptive integral action. Two types of adaptive controllers are considered—the state feedback controller with a plant parameter identifier, and the output feedback controller with a linear observer.     

Approximate decoupling and output tracking for MIMO nonlinear systems with mismatched uncertainties via ADRC approach

In this paper, we consider output tracking for a class of MIMO nonlinear systems which are composed of coupled subsystems with vast mismatched uncertainties. First, all uncertainties influencing the performance of controlled outputs, which include internal unmodelled dynamics, external disturbances, and uncertain nonlinear interactions between subsystems, are refined into the total disturbance in the control channels of subsystems. The total disturbance is shown to be sufficiently reflected in the measured output of each subsystem so that it can be estimated in real time by an extended state observer (ESO) in terms of the measured outputs. Second, we decouple approximately the MIMO systems by cancelling the total disturbance based on ESO estimation so that each subsystem becomes approximately independent linear time invariant one without uncertainty and interaction with other subsystems. Finally, we design an ESO based output feedback for each subsystem separately to ensure that the closed-loop state is bounded, and the closed-loop output of each subsystem tracks practically a given reference signal. This is completely in comply with the spirit of active disturbance rejection control (ADRC). Some numerical simulations are presented to demonstrate the effectiveness of the proposed output feedback control scheme.     

Incremental passivity-based output regulation for switched nonlinear systems via average dwell-time method

This paper investigates the output regulation problem for a class of switched nonlinear systems with at least a feedback incrementally passive subsystem via average dwell time method. First, the output regulation problem for switched nonlinear system via full information feedback is solved. The stabilizing controllers consist of the state feedback controllers and linear output feedback controllers. In some particular cases, it is unnecessary to verify that all the solutions of the switched nonlinear system converge to the bounded steady-state solution, while we only have to verify the regulated outputs converge to zero directly. Second, a dynamic error-feedback stabilizer for each subsystem and a switched internal model whose subsystems all are incrementally passive are designed to solve the output regulation problem for the switched nonlinear system under a composite switching signal with average dwell times. The stabilizer and the internal model are interconnected in a more simple way and allowed to switch asynchronously. Finally, two examples are provided to show the effectiveness of the obtained results.     

Stability of a forced system with a single nonlinear element in the feedback path

This paper presents a numerical technique to determine the stability of a nonlinear feedback control system with a single nonlinear element in the feedback path. By expressing the output explicitly in terms of the input the bounded inputand bounded output stability criterion of the nonlinear system is investigated.     

Anti-disturbance stabilization for a hybrid system of non-uniform elastic string

This paper is concerned with the anti-disturbance boundary feedback stabilization for a hybrid system coupling a non-uniform elastic string with a rigid body at one end by the active disturbance rejection control technology. An infinite-dimensional disturbance estimator and a Luenberger state observer are designed to estimate the disturbance and state of the system, respectively, based on which, a boundary output feedback control is further proposed to stabilize the system. The control consists of two parts: one part is for the stabilization of system without external disturbance, and the other part is for the rejection of the disturbance by virtue of the disturbance estimator. The well-posedness and exponential stability of the closed-loop system are proved by employing the semigroup theories and frequency domain method. Besides, all the signals of the closed-loop system are shown to be uniformly bounded. Finally, some numerical simulations are presented to validate the effectiveness of the proposed control strategy.     

Observer-based adaptive fuzzy control of a class of MIMO non-strict feedback nonlinear systems

This paper investigates the adaptive fuzzy control design problem of multi-input and multi-output (MIMO) non-strict feedback nonlinear systems. The considered control systems contain unknown control directions and dead zones. Fuzzy logic systems (FLSs) are utilized to approximate the unknown nonlinear functions, and the state observers are designed to estimate immeasurable states. By constructing a dead zone compensator and introducing a Nussbaum gain function into the backstepping technique, an adaptive fuzzy output feedback control method is developed. The proposed adaptive fuzzy controller is proved to guarantee the semi-globally uniformly ultimately bounded (SGUUB) of the closed-loop system, and can solve the control design problems of unmeasured states, unknown control directions and dead zones. The simulation results are given to demonstrate the effectiveness of the proposed control method.     

Distributed adaptive observer-based prescribed finite-time control of constrained multi-agent systems

This work considers a distributed adaptive output feedback control problem for nonlinear constrained multi-agent systems (MAS) in the prescribed finite time. To begin with, a state observer is constructed to estimate the unmeasurable state. Then, we develop a novel observer based distributed adaptive prescribed finite time output feedback control algorithm by incorporating the prescribed finite-time control technique into the backstepping design method. Through Lyapunov stability theory, it can be shown that all signals of MASs are bounded, the tracking errors converge to the adjustable regions around the origin within the pre-given error accuracy and settling time, and all states keep in the prescribed constraint regions. Finally, a simulation example verifies the efficacy of the obtained theoretical results.     

Adaptive output feedback control of large-scale nonlinear time-delay systems with uncertain output equations

For a class of large-scale nonlinear time-delay systems with uncertain output equations, the problem of global state asymptotic regulation is addressed by output feedback. The class of systems under consideration are subject to feedforward growth conditions with unknown growth rate and time delays in inputs and outputs. To deal with the system uncertainties and the unknown delays, a novel low-gain observer with adaptive gain is firstly proposed; next, an adaptive output feedback delay-free controller is constructed by combining Lyapunov-Krasovskii functional with backstepping algorithm. Compared with the existing results, the controllers proposed are capable of handling both the uncertain output functions and the unknown time delays in inputs and outputs. With the help of dynamic scaling technique, it is shown that the closed-loop states converge asymptotically to zero, while the adaptive gain is bounded globally. Finally, the effectiveness of our control schemes are illustrated by three examples.     

Output feedback gain scheduled control of actuator saturated linear systems with applications to the spacecraft rendezvous

The problem of stabilization of a linear system that is asymptotic null controllable with bounded control is studied in this paper. By combining the parametric Lyapunov equation approach and the gain scheduling technique, a new observer-based output feedback gain scheduling controller is proposed to solve the semi-global stabilization problem for a linear system subject to actuator saturation. By scheduling the design parameters online the convergence rate of the state can be improved. Numerical simulations for a spacecraft rendezvous system show the effectiveness of the proposed approaches.     

Distributed fault-tolerant tracking control for heterogeneous nonlinear multi-agent systems under sampled intermittent communications

This paper studies the distributed fault-tolerant control (FTC) problem for heterogeneous nonlinear multi-agent systems (MASs) under sampled intermittent communications. First, in order to estimate the state of leader under sampled intermittent communications, the distributed intermittent observer for each follower is constructed. By using the tool from switching system theory, the estimation error converges to zero exponentially if the communication rate is larger than a threshold value even under the impact of sampled intermittent communications. Then, by applying model reference adaptive tracking technique, a robust FTC protocol is developed to track the distributed intermittent observer. Two algorithms are presented to choose the feedback gain of the distributed intermittent observer and the tracking feedback gain of the fault-tolerant tracking controller. It is proved that the global consensus tracking error is bounded under the developed distributed control protocol. Finally, an example with the coupled pendulums is provided to verify the efficiency of the designed method.     

Robust self-triggered MPC with fast convergence for constrained linear systems

In this paper, a robust self-triggered model predictive control (MPC) scheme is proposed for linear discrete-time systems subject to additive disturbances, state and control constraints. To reduce the amount of computation on controller sides, MPC optimization problems are only solved at certain sampling instants which are determined by a novel self-triggering mechanism. The main idea of the self-triggering mechanism is to choose inter-sampling times by guaranteeing a fast decrease in optimal costs. It implies a fast convergence of system states to a compact set where it is ultimately bounded and a reduction of computation times to stabilize the system. Once the state enters a terminal region, the system can be stabilized to a robust invariant set by a state feedback controller. Robust constraint satisfaction is ensured by utilizing the worst-case set-valued predictions of future states in such a way that recursive feasibility is guaranteed for all possible realisations of disturbances. In the case where a priority is given to reducing communication costs rather than improvement in control performance in a neighborhood of the origin, a feedback control law based on nominal state predictions is designed in the terminal region to avoid frequent feedback. Performances of the closed-loop system are demonstrated by a simulation example.     

Observer-based decentralized adaptive control for large-scale nonlinear systems with mixed dynamic interaction

The problem of decentralized adaptive control is investigated for a class of large-scale nonstrict-feedback nonlinear systems subject to dynamic interaction and unmeasurable states, where the dynamic interaction is related to both input and output items. First, the fuzzy logic system is utilized to tackle unknown nonlinear function with nonstrict-feedback structure. Then, by combining adaptive and backstepping technology, the proper output feedback controller is designed. Meanwhile, a fuzzy state observer is proposed to estimate the unmeasurable states. The proposed controller could guarantee that all the signals of the resulting closed-loop systems are bounded. Finally, the applicability of the proposed controller is well carried out by a simulation example.     

Event-triggered adaptive control of multi-agent systems with saturated input and partial state constraints

In this paper, we study the consensus tracking control problem of a class of strict-feedback multi-agent systems (MASs) with uncertain nonlinear dynamics, input saturation, output and partial state constraints (PSCs) which are assumed to be time-varying. An adaptive distributed control scheme is proposed for consensus achievement via output feedback and event-triggered strategy in directed networks containing a spanning tree. To handle saturated control inputs, a linear form of the control input is adopted by transforming the saturation function. The radial basis function neural network (RBFNN) is applied to approximate the uncertain nonlinear dynamics. Since the system outputs are the only available data, a high-gain adaptive observer based on RBFNN is constructed to estimate the unmeasurable states. To ensure that the constraints of system outputs and partial states are never violated, a barrier Lyapunov function (BLF) with time-varying boundary function is constructed. Event-triggered control (ETC) strategy is applied to save communication resources. By using backstepping design method, the proposed distributed controller can guarantee the boundedness of all system signals, consensus tracking with a bounded error and avoidance of Zeno behavior. Finally, the correctness of the theoretical results is verified by computer simulation.