Time-varying Full State Constraints Research Articles

Adaptive Dynamic Surface Control Based on Observer for Switched Non-Strict Feedback Systems With Full State Constraints

As we all know, it is very difficult to design the controller and prove the stability for switched nonlinear systems. Therefore, the engineering application of switching system and the development of switching control theory are limited. In order to solve the control problem for constrained switched system, an adaptive output feedback control scheme based on backstepping technology is studied in this paper for switched non-strict feedback nonlinear systems with asymmetric time-varying full state constraints and unknown external disturbances. A switched state observer based on fuzzy logic system is designed to estimate the unmeasurable states of the uncertain switched system. Asymmetric time-varying barrier Lyapunov functions are adopted to keep the full states of the system satisfying their asymmetric time-varying constraints. A variable separation approach is used to address the algebraic loop problem of non-strict feedback structure. The stability of the closed-loop system and the semi-globally uniformly ultimately bounds of the signals are proved by the Lyapunov method and average dwell time theory. Finally, simulation results are given to show the effectiveness of the proposed control scheme. Different from the existing results, this paper is the first to investigate adaptive control for switched non-strict feedback systems with full state time-varying constraints, unmeasurable states and unknown disturbances, which is a more general case in real systems.

Adaptive control design for MIMO switched nonlinear systems with full state constraints

SummaryThis paper presents an adaptive fuzzy control approach of multiple‐input–multiple‐output (MIMO) switched uncertain systems, which involve time‐varying full state constraints (TFSCs) and unknown disturbances. In the design procedure, the fuzzy logic systems are adopted to approximate the unknown functions in the systems. The adaptive fuzzy controller is set up by backstepping technique. According to the tangent barrier Lyapunov function (BLF‐Tan), a novel adaptive MIMO switched nonlinear control algorithm is designed. Under the rule of arbitrary switchings and the proposed control laws, it is demonstrated that all signals in the resulted system are semiglobally uniformly ultimately bounded (SGUUB) and the tracking error converges to a small neighborhood of zero with TFSCs. Furthermore, the simulation example validates the effectiveness of presented control strategy.

Adaptive neural dynamic surface control of MIMO uncertain nonlinear systems with time-varying full state constraints and disturbances

In order to stabilize multiple-input–multiple-output uncertain strict feedback nonlinear systems with time-varying full-state constraints and external disturbances, an adaptive neural dynamic surface control method is investigated in this paper. A new compensator is proposed, which combines approximation error based adaptive radial basis function neural networks (RBFNNs) and nonlinear disturbance observer (NDOB) to improve the compensate performance of unmodeled dynamics and external disturbances. To prevent that the time-varying full state constraints are violated, the controller is designed via asymmetric time-varying barrier Lyapunov function (ATBLF). Meanwhile, the dynamic surface control is established to avoid the problem of “explosion of complexity” in traditional backstepping design. All closed-loop signals are proved to be semiglobally uniformly ultimate bounded through stability analysis. Finally, the simulation for six degrees of freedom (6-DOF) model unmanned airship are given to illustrate the effectiveness of the proposed control method.

TABLF-based adaptive control for uncertain nonlinear systems with time-varying asymmetric full-state constraints

ABSTRACT In this paper, we investigate the tracking control problem for a class of strict-feedback nonlinear systems with parametric uncertainties and time-varying asymmetric full-state constraints. By introducing novel tan-type time-varying asymmetric barrier Lyapunov function (TABLF) in each step of backstepping design, the boundedness of the fictitious state tracking errors are ensured. A novel adaptive backstepping control design based on tuning function is given, which successfully eliminates the effect of uncertainties. In addition, only one parameter needs to be adjusted online in the control design, which greatly alleviates the computation burden. Based on the proposed control scheme the asymptotic convergence of system output tracking error is realised and the time-varying full-state constraints are not violated for all the time. A numerical example is given to illustrate the effectiveness of the proposed control scheme.

Adaptive neural network-based control of uncertain nonlinear systems with time-varying full-state constraints and input constraint

This paper investigates the problem of state-constraint adaptive neural network-based tracking control for a class of nonlinear systems with input saturation constraint. The considered systems are with uncertain nonlinearities which are not required to be globally Lipschitz or be with a prior knowledge of the structure. To facilitate the stability analysis, radial basis function neural networks (RBFNNs) are first utilized to approximate the unknown nonlinear terms. The constraint problem of input saturation often appears in the control system. To solve above issue, a novel adaptive control scheme is proposed with the help of an augmented function with auxiliary control signal, which ensures that all the closed-loop signals are semi-globally uniformly ultimately bounded. On the other hand, to guarantee better transient performance under input saturation, an improved barrier Lyapunov function with time-varying barriers is developed, which makes the tracking errors preserve within the specified constraint bounds. Simulation results are given to demonstrate the effectiveness of the proposed approach.

Adaptive Neural Network Learning Controller Design for a Class of Nonlinear Systems With Time-Varying State Constraints

This paper studies an adaptive neural network (NN) tracking control method for a class of uncertain nonlinear strict-feedback systems with time-varying full-state constraints. As we all know, the states are inevitably constrained in the actual systems because of the safety and performance factors. The main contributions of this paper are that: 1) in order to ensure that the states do not violate the asymmetric time-varying constraint regions, an adaptive NN controller is constructed by introducing the asymmetric time-varying barrier Lyapunov function (TVBLF) and 2) the amount of the learning parameters is reduced by introducing a TVBLF at each step of the backstepping. Based on the Lyapunov stability analysis, it can be proven that all the signals in the closed-loop system are the semiglobal ultimately uniformly bounded and the time-varying full-state constraints are never violated. Finally, a numerical simulation is given, and the effectiveness of this adaptive control method can be verified.

BLF-based asymptotic tracking control for a class of time-varying full state constrained nonlinear systems

This paper presents an adaptive control based on a tan-type barrier Lyapunov function for time-varying state constrained strict-feedback nonlinear systems to achieve asymptotic output tracking. The design procedure is constructive and yields a continuous actual control law, which guarantees that asymptotic output tracking is achieved. Furthermore, we show that the time-varying full state constraints are not violated for all time and that all closed-loop signals are bounded provided that some conditions on the initial states and control parameters are satisfied. Three simulation examples are provided to illustrate the performance of the proposed control scheme. One is a comparison study simulation, another is a practical single-link robot system and the last is a three-order nonlinear system.

Neural Network Controller Design for a Class of Nonlinear Delayed Systems With Time-Varying Full-State Constraints.

This paper proposes an adaptive neural control method for a class of nonlinear time-varying delayed systems with time-varying full-state constraints. To address the problems of the time-varying full-state constraints and time-varying delays in a unified framework, an adaptive neural control method is investigated for the first time. The problems of time delay and constraint are the main factors of limiting the system performance severely and even cause system instability. The effect of unknown time-varying delays is eliminated by using appropriate Lyapunov-Krasovskii functionals. In addition, the constant constraint is the only special case of time-varying constraint which leads to more complex and difficult tasks. To guarantee the full state always within the time-varying constrained interval, the time-varying asymmetric barrier Lyapunov function is employed. Finally, two simulation examples are given to confirm the effectiveness of the presented control scheme.

Tracking control of uncertain nonlinear systems with deferred asymmetric time-varying full state constraints

In this paper, we investigate the tracking control problem of uncertain strict-feedback systems under deferred and asymmetric yet time-varying (DATV) constraints. We show that such type of constraints, occurring some time after (rather than from the beginning of) system operation, are frequently encountered in practice that have not been adequately addressed in existing works. By utilizing an error-shifting transformation, together with a new asymmetric Barrier Lyapunov Function with variational barrier bounds, we develop a tracking control method capable of dealing with DATV full state constraints under completely unknown initial tracking condition, leading to a control solution to the underlying problem. We also show that, with the proposed method, full state constraints being violated initially (rendering the previous methods inapplicable) can be made satisfied within a pre-specified finite time. The benefits and effectiveness of the proposed control are theoretically authenticated and numerically validated.

Adaptive neural network-based control for a class of nonlinear pure-feedback systems with time-varying full state constraints

In this paper, an adaptive neural network &#x0028 NN &#x0029 control approach is proposed for nonlinear pure-feedback systems with time-varying full state constraints. The pure-feedback systems of this paper are assumed to possess nonlinear function uncertainties. By using the mean value theorem, pure-feedback systems can be transformed into strict feedback forms. For the newly generated systems, NNs are employed to approximate unknown items. Based on the adaptive control scheme and backstepping algorithm, an intelligent controller is designed. At the same time, time-varying Barrier Lyapunov functions &#x0028 BLFs &#x0029 with error variables are adopted to avoid violating full state constraints in every step of the backstepping design. All closedloop signals are uniformly ultimately bounded and the output tracking error converges to the neighborhood of zero, which can be verified by using the Lyapunov stability theorem. Two simulation examples reveal the performance of the adaptive NN control approach.

Neuroadaptive Robotic Control Under Time-Varying Asymmetric Motion Constraints: A Feasibility-Condition-Free Approach.

This paper presents a neuroadaptive tracking control approach for uncertain robotic manipulators subject to asymmetric yet time-varying full-state constraints without involving feasibility conditions. Existing control algorithms either ignore motion constraints or impose additional feasibility conditions. In this paper, by integrating a nonlinear state-dependent transformation into each step of backstepping design, we develop a control scheme that not only directly accommodates asymmetric yet time-varying motion (position and velocity) constraints but also removes the feasibility conditions on virtual controllers, simplifying design process, and making implementation less demanding. Neural network (NN) unit accounting for system uncertainties is included in the loop during the entire system operational envelope in which the precondition on the NN training inputs is always ensured. The effectiveness and benefits of the proposed control method for robotic manipulator are validated via computer simulation.

Tracking control for strict-feedback nonlinear systems with time-varying full state constraints

This paper focuses on the tracking control problem for strict-feedback nonlinear systems subject to asymmetric time-varying full state constraints. Time-varying asymmetric barrier Lyapunov functions are employed to ensure time-varying constraint satisfaction. By allowing the barriers to vary with the desired trajectory in time, the initial condition requirements are relaxed. High-order coupling terms caused by backstepping are cancelled through a novel variable substitution for the first time. Besides the normal case, where the full knowledge of the system is available, we also handle scenarios of parametric uncertainties. Asymptotic tracking is achieved without violation of any constraints, and all signals in the closed-loop system are ultimately bounded. State-constrained systems with input saturation and bounded disturbances are also considered; the tracking error converges to a bounded set around zero. The performance of the asymmetric-barrier-Lyapunov-function-based control is illustrated through a numerical example.

Barrier Lyapunov functions-based adaptive control for nonlinear pure-feedback systems with time-varying full state constraints

This paper studies the problem of controller design for pure-feedback nonlinear systems with asymmetric time-varying full state constraints. The mean value theorem is employed to transform a pure-feedback system into a strict-feedback structure with non-affine terms. For the transformed system, a time-varying asymmetric Barrier Lyapunov Function (ABLF) with the error variables is employed to ensure the time-varying constraints satisfaction. By allowing the barriers to vary with the desired trajectory in time, the initial condition requirements are relaxed efficiently. The presented control scheme can guarantee that all signals in the closed-loop system are ultimately bounded. It is also proved that the tracking error converges to an adjustable neighborhood of the origin even in the presence of disturbance. The performance of the ABLF-based control are illustrated through two examples.