Asymmetric Output Constraints Research Articles

Output-feedback finite-time stabilization of a class of constrained planar systems

This work has addressed the output-feedback finite-time stabilization issue for a type of asymmetric output-constrained planar systems. The innovation involved in the results of the work owes to the construction of a barrier Lyapunov function (BLF) to the handling of the asymmetric output constraint. By incorporated the BLF into the backstepping-like technique, a state feedback controller is first developed. An implementable observer is subsequently designed to estimate the unmeasurable system state. Lastly, an observer-based finite-time output feedback controller is explicitly proposed. Theoretically, the Lyapunov stability theory is adopted to show that the system states are finite-time stabilized under the presented control scheme. Meanwhile, the violation of a pre-established asymmetric output constraint is circumvented. To testify the derived theoretical results, the case studies of a permanent magnet linear motor system are offered.

Fixed-time SOSM controller design subject to an asymmetric output constraint

This paper addresses the problem of fixed-time controller design for the second-order sliding mode (SOSM) dynamics with asymmetric output constraints. Based on the construction of a barrier Lyapunov function (BLF) and the technique of adding a power integrator, a fixed-time SOSM controller that can be used to handle the asymmetric output constraint issue is developed. A strict Lyapunov stability analysis shows that the developed SOSM controller guarantees that the sliding variable can converge to the origin within a fixed time that is irrelevant to the system initial conditions. Meanwhile, the system output will never invade the boundary of the preset asymmetric constrained area. Finally, two examples are given to verify the effectiveness and the feasibility of the proposed scheme.

Fixed-time stabilization for interconnected high-order nonlinear systems with dead-zone input and output constraint

This paper deals with the problem of fixed-time stabilization for a class of high-order nonlinear systems with time-varying output constraint (also known as p-normal form systems). Compared with the existing results, the order of the systems can be less than 1, which is more relaxed. Moreover, each subsystem is with the dead-zone input and interconnected nonlinearity. We design a new decentralized fixed-time controller based on the recursive design method by revamping the technique of adding a power integrator and using the tan-type barrier Lyapunov function. The proposed controller is also effective for the systems with asymmetric output constraints. Based on Lyapunov stability theory, it is proved that the decentralized controller can realize that the outputs are strictly constrained within predefined boundaries and all state variables converge to zero in a fixed time, where the bound of reaching time is independent of the initial conditions. Finally, simulation examples are given to illustrate the effectiveness of the proposed method.

Design of high‐order sliding mode controller under asymmetric output constraints

AbstractThis article is devoted to the design issue of high‐order sliding mode (HOSM) controller subject to asymmetric output constraints. A barrier Lyapunov function (BLF) is first developed to deal with the constraints. Subsequently, by implanting the BLF into the modified adding a power integrator technique, a HOSM control algorithm, which is able to handle the closed‐loop system simultaneously with and without asymmetric output constraints, has been presented. It has been shown on the basis of the rigorous mathematical proof that under the proposed control strategy, the finite‐time stability of the considered system with the asymmetric output constraints is ensured. Meanwhile, the proposed algorithm also satisfies the requirement of the preset asymmetric output constraint. At last, an illustrative example is given to demonstrate the effectiveness of the presented algorithm.

Adaptive neural output-feedback control for a class of output-constrained switched stochastic nonlinear systems

In this paper, a neural network-based adaptive output-feedback control problem is investigated for a class of output-constrained switched stochastic nonlinear systems. By introducing nonlinear mapping, the asymmetric and symmetric output constrained stochastic nonlinear system is transformed into a new system without any constraint. It is the first time that a switching system is used to convert symmetric and asymmetric output constraints in the same system. An adaptive neural output-feedback controller is developed based on the backstepping technique. A state observer is designed to estimate the unmeasurable system state signals. An adaptive controller is designed to ensure that the output tracking error converges to a small region of the origin. The control scheme ensures that all signals in the closed-loop systems are semi-global uniformly ultimately bounded. Results of simulation cases are presented to prove the effectiveness of the theoretical analysis.

Distributed event triggering control for six-rotor UAV systems with asymmetric time-varying output constraints

Distributed event triggering control for six-rotor UAV systems with asymmetric time-varying output constraints

Finite-time stabilization via output feedback for high-order planar systems subjected to an asymmetric output constraint

This article addresses the problem of finite-time stabilization via output feedback for high-order planar systems subjected to an asymmetric output constraint. By delicately exploring the features of nonlinearities and utilizing skillful manipulations of signum functions, a new fraction-type asymmetric barrier Lyapunov function and a distinctive non-smooth state observer are developed. On the basis of the proposed barrier Lyapunov function along with the state observer, the celebrated adding a power integrator technique is elegantly renovated to develop a novel approach by which a continuous output feedback finite-time stabilizer is constructed in a systematic fashion while ensuring the fulfillment of a pre-specified asymmetric output constraint. The presented scheme is a unification approach able to achieve the finite-time stabilization via output feedback for systems subjected to or free from output constraints simultaneously, without needing to change both the controller and observer structures. A numerical is provided to illustrate the superiority of the developed method.

HOSM controller design with asymmetric output constraints

HOSM controller design with asymmetric output constraints

Three-dimensional vibration suppression for an Euler–Bernoulli beam with asymmetric output constraint

A vibration control strategy is addressed for the three-dimensional vibration suppression of an Euler-Bernoulli beam (EBB) subject to asymmetric output constraints in this paper. A special piecewise barrier Lyapunov function candidate is provided to prevent the asymmetric output constraint violation, and a model-based boundary control (MBC) is developed subsequently to ensure the coupled vibration reduction. Moreover, considering the parameter uncertainties, an adaptive law is designed to estimate the uncertain parameter and to update the vibration controller. The main challenge of this work is to consider the asymmetric output constraint in a nonlinear and coupled infinite-dimensional system. Finally, numerical simulations are made to present the system performance under the proposed vibration controllers which maintain the output being restrained in the predefined scope.

Adaptive Fuzzy Fault Tolerant Control of Uncertain MIMO Nonlinear Systems With Output Constraints and Unknown Control Directions

This article studies the adaptive fuzzy fault tolerant control (FTC) problem for a class of uncertain multi-input multi-output (MIMO) nonlinear systems with unknown control directions in the presence of time-varying asymmetric output constraints. Our contribution includes a step forward beyond usual FTC results to exhibit that the system output of nonsquare and square MIMO systems is uniformly bounded against actuator faults by a novel FTC methodology without the fault detection unit, as well as stay in the preselected constraints. To obtain new results, an equivalent unconstrained system is established by employing an error transformation technique. Furthermore, a learning-based switching function scheme is proposed to automatically activate different groups of actuators without human intervention for attenuating the influence of faulty actuators. By this means, no explicit fault detection and isolation units are needed to result in reducing the risk of false alarm or missed detections and expediting the responsiveness of the controller. Moreover, the obstacle caused by unknown control directions is circumvented by a novel technique combining the matrix decomposition technique and Nussbaum-type function. It is proved that the desired tracking performance with prescribed output bounds and the boundedness of all the signals in the closed-loop system can be guaranteed via an improved average dwell time approach. Finally, simulation results demonstrate the merits of the proposed controller.

Fixed-time stabilisation for switched stochastic nonlinear systems with asymmetric output constraints

In this paper, the fixed-time stabilisation problem is investigated for switched stochastic nonlinear systems with asymmetric output constraints. A novel universal barrier Lyapunov function is proposed to not only handle systems with asymmetric output constraints but also work for systems with symmetric constraints or without constraints, without reshaping the controller framework. On the basis of the stochastic fixed-time stability theorem and adding a power integrator strategy, an elaborate control method is established to ensure that the system state fixed-time converges to zero almost surely without the knowledge of initial conditions. Meanwhile, the system output is always retained in the preset asymmetric region in probability. A practical example is utilised to verify the validity of the proposed theory.

Adaptive decentralised control for large‐scale non‐linear non‐strict‐feedback interconnected systems with time‐varying asymmetric output constraints and dead‐zone inputs

This study investigates the neural-network (NN)-based adaptive decentralised controller design issue for a class of large-scale non-linear non-strict-feedback interconnected systems with time-varying asymmetric output constraints and dead-zone inputs. The existences of the non-strict-feedback structure, time-varying asymmetric output constraints, and dead-zone inputs lead to the construction of the controller of each subsystem is very difficult. By applying the inherent property of Gaussian functions employed in radical basis function NNs, the non-strict-feedback structure is skillfully handled, and the adaptive backstepping method is used to construct the desired controllers of all subsystems. Furthermore, Lyapunov stability analysis shows that all the signals of the closed-loop system are ultimately bounded, and each subsystem output can converge to an arbitrarily small and predefined time-varying range with the corresponding constraint is always satisfied by employing a barrier Lyapunov function. Finally, simulation results based on a practical example prove the effectiveness of the proposed design strategy.

Output feedback stabilization for planar switched nonlinear systems with asymmetric output constraints

In this paper, smooth output feedback controllers are presented to stabilize a class of planar switched nonlinear systems with asymmetric output constraints (AOCs). A new common barrier Lyapunov function (CBLF) is developed to prevent the switched system from violating AOCs. Combining the adding a power integrator technique (APIT) and the CBLF, state feedback controllers are designed. Then, reduced-order nonlinear observers are constructed and smooth output feedback controllers are proposed to globally stabilize planar switched nonlinear systems under arbitrary switchings. Meanwhile, the system output meets the prescribed AOCs during operation. The method proposed in this paper is a unified tool because it works not only for switched nonlinear systems with asymmetric or symmetric output constrains but also for those without output constraints. Simulations are presented to verify the proposed method.

Output Constrained Adaptive Controller Design for Nonlinear Saturation Systems

This paper considers the adaptive neuro-fuzzy control scheme to solve the output tracking problem for a class of strict-feedback nonlinear systems. Both asymmetric output constraints and input saturation are considered. An asymmetric barrier Lyapunov function with time-varying prescribed performance is presented to tackle the output-tracking error constraints. A high-gain observer is employed to relax the requirement of the Lipschitz continuity about the nonlinear dynamics. To avoid the “explosion of complexity”, the dynamic surface control (DSC) technique is employed to filter the virtual control signal of each subsystem. To deal with the actuator saturation, an additional auxiliary dynamical system is designed. It is theoretically investigated that the parameter estimation and output tracking error are semi-global uniformly ultimately bounded. Two simulation examples are conducted to verify the presented adaptive fuzzy controller design.

Finite-time adaptive neural control for nonstrict-feedback stochastic nonlinear systems with input delay and output constraints

This paper addresses a novel finite-time adaptive neural control (FTANC) problem for nonstrict-feedback stochastic nonlinear systems (NSFSNS), in which the input delay and output constrained problems are considered simultaneously. First, the Pade approximation technique is adopted to transform the delay input system into a delay-free one. Second, the stochastic nonlinear mapping technique is developed to solve the symmetric and asymmetric output constraints in the system. Then, the adaptive neural controller is designed based on backstepping technique, such that the closed-loop systems are semi-globally practical finite-time stable (SGPFTS) in probability, and the tracking error converges to a small neighborhood of the origin after a finite period of time. Two simulation examples show the effectiveness of the proposed approach.

Low-Cost Approximation-Based Adaptive Tracking Control of Output-Constrained Nonlinear Systems.

For pure-feedback nonlinear systems under asymmetric output constraint, we present a low-cost neuroadaptive tracking control solution with salient features benefited from two design steps. In the first step, a novel output-dependent universal barrier function (ODUBF) is constructed such that not only the restrictive condition on constraining boundaries/functions is removed but also both constrained and unconstrained cases can be handled uniformly without the need for changing the control structure. In the second step, to reduce the computational burden caused by the neural network (NN)-based approximators, a single parameter estimator is developed so that the number of adaptive law is independent of the system order and the dimension of system parameters, making the control design inexpensive in computation. Furthermore, it is shown that all signals in the closed-loop system are semiglobally uniformly ultimately bounded, the tracking error converges to an adjustable neighborhood of the origin, and the violation of output constraint is prevented. The effectiveness of the proposed method can be validated via numerical simulation.

Adaptive tracking control of high-order nonlinear systems under asymmetric output constraint

This paper addresses the tracking control problem of a class of high-order uncertain nonlinear systems under time-varying asymmetric output constraints. Most relevant results in the literature have two main restrictions: R1) some constraints need to be imposed on powers and growth conditions have to be established for the nonlinear functions of the system; R2) nonlinear bounding functions must be derived based on repeated derivations of virtual control variables during the design process. By integrating an improved technique of adding a power integrator with a dynamic surface control (DSC) method, we develop a systematic tracking control scheme that eliminates both of the above restrictions. Moreover, with an improved time-varying nonlinear transformed function introduced for high-order systems, the proposed scheme can be regarded as a unified tool in the sense that it works no matter whether the constraint is symmetric, asymmetric, or even without a constraint. The above results are also extended to systems with uncertain gain functions, and the proposed scheme estimates only one adaptive parameter. The simulation results of two deterministic practical applications show that the proposed control scheme is effective not only for high-order systems, but also for high-order-free systems.

Second-Order Sliding Mode Control Design Subject to an Asymmetric Output Constraint

In this brief, a novel second-order sliding mode (SOSM) control method is developed to solve the asymmetric output constraint problem by using a power integrator and barrier Lyapunov function (BLF). The new BLF is first constructed based on the asymmetric constraint condition. A novel SOSM algorithm is then constructed for the nonlinear systems with an asymmetric output constraint. Under the proposed SOSM algorithm, the output of the resulting closed-loop system will never escape from the asymmetric constraint. Finally, a pendulum system is adopted to verify the validity of the theoretical results.

Output feedback stabilization for a class of high‐order planar systems with an asymmetric output constraint

SummaryThis article is concerned with the problem of output feedback stabilization for a class of high‐order planar systems with an asymmetric output constraint. By fully extracting the characteristics of system nonlinearities and introducing a delicate manipulation of sign functions, a new tangent‐type asymmetric barrier Lyapunov function and an exquisite nonsmooth observer are proposed. Based on the presented barrier Lyapunov function as well as the nonsmooth observer, the technique of adding a power integrator, that is, a special version of the backstepping design, is skillfully revamped to establish a novel approach which systematically guides us in constructing a continuous output feedback stabilizer and achieving the requirement of a pre‐specified asymmetric output constraint. The developed approach is a unified design in the sense that it is capable of simultaneously performing the output feedback stabilization for systems with and without output constraints, without the need of changing the controller structure. An illustrative example is presented to demonstrate the effectiveness of the proposed strategy.

Adaptive output feedback control for a class of uncertain non-strict feedback systems with asymmetric time-varying output constraints

This study investigated a novel adaptive output feedback control scheme for non-strict feedback nonlinear systems with uncertainties, disturbances, and asymmetric time-varying output constraints. Because that the states of the system are unmeasurable, we used an adaptive fuzzy state observer to obtain the estimated values of the states. To make the output and tracking error satisfy their asymmetric time-varying constraints, an asymmetric time-varying barrier Lyapunov function was adopted. To overcome the “explosion of complexity” problem, we also adopted the dynamic surface control technology. The stability of the closed-loop system was proved by the Lyapunov method, and we give two simulation examples to show the effectiveness of the proposed control method.