Output feedback based simultaneous stabilization of two Port-controlled Hamiltonian systems with disturbances

In motor system control design, a single controller is usually employed to simultaneously control two or more motors for saving costs, which also achieves the computational simplification of control. In practical Hamiltonian systems control, more systems also need to be stabilized by a single controller under some working conditions. Thus, this paper studies simultaneous stabilization problem of two nonlinear Port-controlled Hamiltonian (PCH) systems with disturbances by a composite controller. Based on the Hamiltonian structure properties, two PCH systems are combined together to generate an augmented PCH system by utilizing output feedbacks firstly. Then, to estimate disturbances effectively, it is essential to design a nonlinear disturbance observer (NDOB) and the estimate is employed to feedforward compensate the effects of disturbances. Next, combining the output feedback part and the disturbance compensation part together, a simultaneous stabilization controller is developed. Subsequently, it is proved that the closed-loop system under the proposed controller is asymptotically stable. Finally, an example with simulations reveals that the proposed method is effective.     

Adaptive fuzzy asymptotically tracking control of full state constrained nonlinear system based on a novel Nussbaum-type function

This study carries out the problem of adaptive backstepping fuzzy tracking control for a class of full state constrained uncertain nonlinear system with unknown control directions. Based on Nussbaum-type functions and tan-type Barrier Lyapunov functions, a novel adaptive fuzzy tracking controller is proposed to guarantee that the system output tracking error asymptotically converges to zero, while the constraints on the states of system will not be violated during operation. Compared with the existing results, a better convergence effect is obtained for this class of systems. Stability analysis of the proposed closed-loop control system is supported by the Lyapunov stability theory. Finally, a simulation example is presented to illustrate the effectiveness of the proposed control strategy.     

Sampled observer-based adaptive decentralized control for strict-feedback interconnected nonlinear systems

This paper investigates the decentralized tracking control problem for a class of strict-feedback interconnected nonlinear systems with unknown parameters, where the system states are unmeasurable and the interconnections are unknown. Different from the existing results, where the output is available all the time, we consider the case that the output is only available at the sampled instants, which means the failure of existing methods. By introducing a kind of sampled observer for each subsystem, the system states and unknown parameters are jointly estimated. Based on which, a totally decentralized output feedback control scheme is developed to achieve the desired tracking performance by applying backstepping technique, where a compensation mechanism is utilized to address the unknown interconnections from other subsystems. Subsequently, by using Lyapunov stability theory, it is proved that all the signals in the closed-loop system are bounded and the tracking errors converge to an adjustable neighbourhood of the origin. Finally, an example is used to illustrate the effectiveness of the proposed method.     

Sampled observer-based adaptive output feedback fault-tolerant control for a class of strict-feedback nonlinear systems

This paper studies the sampled outputs-based adaptive fault-tolerant control problem for a class of strict-feedback uncertain nonlinear systems, where the nonlinear functions are allowed to include the unmeasured system states. Within the framework, a sampled output observer is introduced to jointly estimate the system states and parameters. By combining the estimated states and the supervisory switching strategy, an adaptive fault-tolerant controller is designed to achieve the desirable tracking performance. By using Lyapunov stability theory, it is proved that all the signals of the closed-loop systems are bounded and the tracking error converges to an adjustable neighbourhood of the origin eventually both in the fault free and faulty cases. Especially, if the outputs are available all the time, the proposed output feedback fault-tolerant control method can ensure the tracking error satisfy the prescribed performance bounds regardless of the faults. Finally, two examples are used to illustrate the effectiveness of the proposed method.     

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.     

Adaptive fuzzy output feedback fault-tolerant tracking control of switched uncertain nonlinear systems with sensor faults

This paper investigates the adaptive fuzzy output feedback fault-tolerant tracking control problem for a class of switched uncertain nonlinear systems with unknown sensor faults. In this paper, since the sensor may suffer from an unknown constant loss scaling failure, only actual output can be used for feedback design. A failure factor is employed to represent the loss of effectiveness faults. Then, an adaptive estimation coefficient is introduced to estimate the failure factor, and a state observer based on the actual output is constructed to estimate the system states. Fuzzy logic systems are used to approximate the unknown nonlinear functions. Based on the Lyapunov function method and the backstepping technique, the proposed control scheme with average dwell time constraints can guarantee that all states of the closed-loop system are bounded and the tracking error can converge to a small neighborhood of zero. Finally, two simulation examples are given to illustrate the effectiveness of the proposed scheme.     

Adaptive fuzzy tracking control for input and output constrained stochastic nonlinear systems: A NM-based approach

This paper investigates the tracking control problem for output constrained stochastic nonlinear systems under quantized input. The main challenge of considering such dynamics lies in the fact that theirs have both input and output constraints, making the standard backstepping technique fail. To address this challenge, the introduction of nonlinear mapping transforms the constrained nonlinear systems into unconstrained nonlinear systems, which not only avoids the emergence of feasibility conditions but also simplifies the structure of designed controller. The obstacle caused by quantized input is successfully resolved by exploiting the decomposition of hysteresis quantizer. Additionally, the uncertain nonlinearities are approximated by fuzzy logic systems during the control design process. Under the proposed quantized tracking control scheme, the output tracking error converges to an arbitrarily small neighborhood of origin and all signals in the closed-loop system remain bounded in probability. Simultaneously, it can make sure that the output constraint isn’t violated. Ultimately, both a numerical example and a practical example are provided to clarify the effectiveness of the control strategy.     

Protocol design for group output consensus of disturbed port-controlled Hamiltonian multi-agent systems

This paper considers the group output consensus problem for a class of disturbed port-controlled Hamiltonian multi-agent systems via a composite control method. The composite distributed control protocol is proposed by combining the damping injection and energy shaping method, the finite-time disturbance observer (FTDO) technique and distributed protocol, which makes the closed-loop Hamiltonian multi-agent systems asymptotically stable and the group outputs reach consensus. It is shown that many kinds of disturbances can be estimated accurately via the FTDO. The advantage is that this control scheme exhibits not only better robustness against disturbances, but also the nominal system recovery performance. Two illustrative examples reveal that the designed control protocol is effective.     

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.     

Event-triggered decentralized output-feedback control for interconnected nonlinear systems with input quantization

In this paper, the event-triggered decentralized control problem for interconnected nonlinear systems with input quantization is investigated. A state observer is constructed to estimate the unmeasurable states, and the state-dependent interconnections are accommodated by presenting some smooth functions. Then by employing backstepping technique and neural networks (NNs) approximation capability, a novel decentralized output feedback control strategy and an event-triggered mechanism are designed simultaneously. It is proved through Lyapunov theory that the closed-loop system is stable and the tracking property of all subsystems is guaranteed. Finally, the effectiveness of the proposed scheme is illustrated by an example.     

Predictive control of discrete-time high-order fully actuated systems with application to air-bearing spacecraft simulator

This paper addresses an output tracking problem for discrete-time high-order fully actuated (DHOFA) systems and its application in the control of air-bearing spacecraft (ABS) simulator. A HOFA system model, as a novel system representation, is applied to establish the dynamics of discrete-time control systems. Accordingly, a HOFA predictive control scheme is presented to deal with this problem, which is composed of a HOFA feedback for stabilization and a HOFA predictive control for tracking. In this scheme, a Diophantine equation is exploited to construct an incremental HOFA (IHOFA) prediction model to substitute a reduced-order prediction model, and then a cost function involving tracking performance is minimized by using multi-step output predictions. A sufficient and necessary condition is proposed to discuss the stability and tracking performance of the closed-loop DHOFA systems, it is simple to utilize in system analysis and extend in practice. Two experiments of the control of ABS simulator are shown to illustrate the feasibility of the presented HOFA predictive control scheme.     

Predefined-time tracking of nonlinear strict-feedback systems with time-varying output constraints

In this paper, the problem of the predefined-time tracking with time-varying output constraints (TVOC) is investigated for a class of nonlinear strict-feedback systems. First, the sufficient conditions for the studied problem are presented. Then, a recursive design algorithm of the controller is proposed by backstepping technique. A novel stabilizing function is constructed by adding a fractional term, which is capable of decreasing the asymmetric time-varying Barrier Lyapunov Function (BLF) to the origin within any desired settling time. After that, it is shown that under our proposed control, all the closed-loop signals are bounded, and the tracking error converges to zero within any desired settling time and remains zero thereafter without the violation of the output constraint. The settling time in this paper is not only independent of the design parameters, nor does it depend on the initial conditions, and can be set according to per our will. Finally, two examples are given to illustrate the effectiveness of the proposed method.     

Consensus of multi-agent systems with Luenberger observers

This paper studies the consensus problem of the multi-agent systems with parallel Luenberger observers. First, the structure of the cooperative system is established, where the output of the built-in Luenberger observer for each agent is used as its local control input and the cooperative control input combining with the cooperative measurement output is utilized as the input of the observers. Based on the structure of the closed-loop system, the consensus problem is then analyzed. In addition, two methods for designing the controller gains are provided. By virtue of the proposed structure, it is pointed out that the design of the controller gains and the observer parameters can be carried out separately. Finally, by resorting to the gradient flow method, an optimization algorithm is proposed to reduce the influence of the environmental noises. The effectiveness of the obtained results is shown through a numerical example.     

Output regulation control for stochastic systems with additive noise

This paper investigates the robust output regulation problem for stochastic systems with additive noises. As is known, for the output regulation control problem, a general method is to regard that the system is disturbed by an autonomous exosystem (which is consisted by external disturbances and reference signals), and for the system disturbed by the white noise, the stochastic differential equations (SDEs) should be utilized in modeling, accordingly, a controller with a feedforward regulator is constructed for the stochastic system with an exosystem, which can not only cancel the external disturbance, but also transform the trajectory tracking problem into the stabilization problem; In consideration of the state variables in stochastic systems cannot be measured completely, we embed an observer to the controller, such that the random interference can be suppressed, and the trajectory tracking can be achieved. Based on the stochastic control theory, the criteria of the exponential practical stability in the mean square is presented for the closed-loop system, finally, through tuning the controller parameters, the mean square of the tracking error can converge to an arbitrarily small neighborhood of the origin.     

Barrier Lyapunov function-based decentralized adaptive neural control for uncertain high-order stochastic nonlinear interconnected systems with output constraints

Decentralized adaptive neural backstepping control scheme is developed for uncertain high-order stochastic nonlinear systems with unknown interconnected nonlinearity and output constraints. For the control of high-order nonlinear interconnected systems, it is assumed that nonlinear system functions are unknown. It is for the first time to control stochastic nonlinear high-order systems with output constraints. Firstly, by constructing barrier Lyapunov functions, output constraints are handled. Secondly, at each recursive step, only one adaptive parameter is updated to overcome over-parameterization problems, and RBF neural networks are used to identify unknown nonlinear functions so that the difficulties caused by completely unknown system functions and stochastic disturbances are tackled. Finally, based on the Lyapunov stability method, the decentralized adaptive control scheme via neural networks approximator is proposed, ultimately reducing the number of learning parameters. It is shown that the designed controller can guarantee all the signals of the resulting closed-loop system to be semi-globally uniformly ultimately bounded (SGUUB), and the tracking errors for each subsystem are driven to a small neighborhood of zero. The simulation studies are performed to verify the effectiveness of the proposed control strategy.     

Robust distributed tracking control for linear multi-agent systems based on distributed intermediate estimator

This paper considers the distributed tracking control problem for linear multi-agent systems with disturbances and a leader whose control input is nonzero and not available to any follower. Based on the relative output measurements of neighboring agents, a novel distributed observer-based tracking protocol is proposed, where the distributed intermediate estimators are constructed to estimate the leader’s unknown control input and the states of the tracking error system simultaneously, then a distributed tracking protocol is designed based on the derived estimates. It is proved that the states of the tracking error system are uniformly ultimately bounded and an explicit tracking error bound is obtained. A simulation example of aircrafts verifies the effectiveness of the proposed method.     

Event-triggered adaptive tracking control of uncertain nonlinear systems with prescribed performance and actuator failures

This article studies adaptive prescribed performance tracking control problem for a class of strict-feedback nonlinear systems with parametric uncertainties and actuator failures. Firstly, in order to compensate the multiple uncertainties and eliminate the influence of actuator failure, a new adaptive tracking controller based on first-order filter technology will be proposed, which simplifies the algorithm design process. Then, by introducing an asymmetric state transition function, the transient and steady performances of the output tracking error are both constrained such that the predetermined performance control goal is achieved. Moreover, to reduce the communication burden from the controller to the actuator, the event-triggered mechanism is designed, and there will be no Zeno phenomenon. Based on Lyapunov stability theory, it is strictly proved that output signal can track the reference signal and all the signals of the closed-loop system are bounded. Finally, a simulation example is performed and the results demonstrate effectiveness of the proposed strategy.     

Fuzzy adaptive command filtered backstepping fault-tolerant control for a class of nonlinear systems with actuator fault

This paper investigates a class of nonlinear systems with actuator fault. In particular, fuzzy logic systems have been used to approximate the unknown nonlinear functions, backstepping procedure is adopted to design controller for the system with mismatched condition, command filter is utilized to eliminate the explosion of complexity of the backstepping and also to compensate the output of a filter subjected to the derivative of the virtual control. The stability of the closed-loop system and the convergence of the tracking error are proved via Lyapunov Theorem. In addition, two numerical simulation examples are illustrated the effectiveness of the proposed approach.     

Fuzzy adaptive fault-tolerant tracking control of MIMO stochastic pure-feedback nonlinear systems with actuator failures

This paper studies the adaptive fuzzy fault-tolerant control design problem for a class of stochastic multi-input and multi-output (MIMO) nonlinear systems in pure-feedback form. The nonlinear systems under study contain unknown functions, unmeasured states and actuator faults, which are described by the loss of effectiveness and lock-in-place modes. With the help of fuzzy logic systems identifying uncertain stochastic nonlinear systems, a fuzzy state observer is established for estimating the unmeasured states. Based on the backstepping design technique with the nonlinear tolerant-fault control theory, an adaptive fuzzy output feedback faults-tolerant control approach is developed. It is proved that the proposed fault-tolerant control approach can guarantee that all the signals of the resulting closed-loop system are bounded in probability. Moreover, the observer errors and tracking errors can be regulated to a small neighborhood of the origin by choosing design parameters appropriately. A simulation example is provided to show the effectiveness of the proposed approach.