Adaptive output feedback control of nonlinear SISO systems via singular perturbation technique

Data-based adaptive neural network optimal output feedback control for nonlinear systems with actuator saturation

This paper focuses on the problem of adaptive output feedback tracking control for a class of non-strict-feedback nonlinear systems with unknown control coefficients. By employing a linear state transformation, the original system is transformed to a new system for which control design becomes feasible. Then, after the introduction of a simple input-driven observer, an adaptive output feedback controller which contains only one parameter is developed for such systems by using backstepping technique and variable separation method. The designed controller ensures that all the signals in the closed-loop systems are Semi-globally Uniformly Ultimately Bounded (SGUUB).

It is well recognized that an adaptive output feedback control based on almost strictly positive real‐ness (ASPR) or output feedback strictly passivity (OFSP) property of the system has strong robustness with respect to disturbances and uncertainty. However, most practical systems do not have such properties. In order to realize an augmented ASPR system for designing adaptive output feedback controller, a kind of adaptive parallel feedforward compensator (PFC) design schemes have been proposed for linear systems. In this paper, we propose an adaptive PFC design scheme by Kernel method for nonlinear systems and provide output feedback passivity based adaptive output feedback control for nonlinear systems. The effectiveness of the proposed method will be confirmed through numerical simulations. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

This paper deals with a design problem of an adaptive output feedback tracking control for systems with a parallel feedforward compensator (PFC) introduced in order to realize the output feedback exponential passive (OFEP) augmented control system. It is well known that one can easily design an adaptive output feedback control system for nonlinear systems satisfying the OFEP conditions. We adopt introduceing a PFC to make a non-OFEP nonlinear system OFEP and propose an adaptive control system design scheme which improves the control performance of the practical control system without the PFC. The effectiveness of the proposed method will be confirmed through experiments of a magnetic levitation system.

Tracking Control of PWM Non-affine Nonlinear Systems via Singular Perturbation Approach

Based on the backstepping technique, an adaptive neural network (NN) based output feedback controller is proposed to achieve a desired tracking performance for a class of discrete-time nonlinear systems, which are represented in non-strict-feedback form. The neural networks are utilized to approximate unknown functions in the systems. The adaptive output feedback controller needs only to adjust less adaptive parameters, therefore it is clear that the proposed approach can reduce on-line computation burden. It is proven that all the signals in the closed-loop system are semi-global uniformly ultimately bounded (SGUUB) and the tracking error converges to a small neighborhood of zero by choosing the design parameters appropriately. A simulation example is used to verify the effectiveness of the proposed approach.

In this paper, a hybrid fuzzy adaptive output feedback control design approach is proposed for a class of multiinput and multioutput strict-feedback nonlinear systems with unknown time-varying delays, unmeasured states, and input saturation. First, fuzzy logic systems are employed to approximate unknown nonlinear functions in the system. Next, a smooth function is used to approximate the input saturation and an adaptive fuzzy state observer is constructed to solve the problem of unmeasured states. Based on the designed adaptive fuzzy state observer, a serial-parallel estimation model is established. By applying adaptive fuzzy dynamic surface control technique and utilizing the prediction error between the system states observer model and the serial-parallel estimation model, a new fuzzy controller with the composite parameters adaptive laws is developed based on Lyapunov-Krasovskii functional. It is proved that all variables of the closed-loop system are bounded and the system outputs can follow the given bounded reference signals as close as possible. A simulation example is provided to further show the effectiveness of this novel control scheme.

This paper investigates adaptive output feedback control problem for switched uncertain nonlinear systems with input quantization, unmeasured system states and state constraints. Firstly, fuzzy logic systems are introduced to identify system uncertainties, then the fuzzy based observer is constructed to estimate unavailable states. Secondly, combing the backstepping technique and the barrier Lyapunov function method, an adaptive fuzzy output feedback control law is designed, which guarantees that all signals in the closed-loop system are bounded, the system output tracks the reference signal, and system states satisfy their corresponding constraint conditions. Finally, simulation results further show the good performances of the proposed control scheme.

Robust adaptive fuzzy filters output feedback control of strict-feedback nonlinear systemsIn this paper, an adaptive fuzzy robust output feedback control approach is proposed for a class of single input single output (SISO) strict-feedback nonlinear systems without measurements of states. The nonlinear systems addressed in this paper are assumed to possess unstructured uncertainties, unmodeled dynamics and dynamic disturbances, where the unstructured uncertainties are not linearly parameterized, and no prior knowledge of their bounds is available. In recursive design, fuzzy logic systems are used to approximate unstructured uncertainties, and K-filters are designed to estimate unmeasured states. By combining backstepping design and a small-gain theorem, a stable adaptive fuzzy output feedback control scheme is developed. It is proven that the proposed adaptive fuzzy control approach can guarantee the all the signals in the closed-loop system are uniformly ultimately bounded, and the output of the controlled system converges to a small neighborhood of the origin. The effectiveness of the proposed approach is illustrated by a simulation example and some comparisons.

In this paper, an adaptive fuzzy output feedback control approach is investigated for a class of stochastic nonlinear strict-feedback systems without the requirement of states measurement. The stochastic nonlinear system addressed in this paper is assumed to possess unstructured uncertainties (unknown nonlinear functions) and, in the presence of unmodeled dynamics, dynamics disturbances. Fuzzy logic systems are used to approximate the unstructured uncertainties, and a fuzzy state observer is designed to estimate the unmeasured states. By combining the backstepping design technique with the stochastic small-gain approach, a new adaptive fuzzy output feedback control approach is developed. It is proved that the proposed control approach can guarantee that the closed-loop system is input-state-practically stability (ISpS) in probability, and the observer errors and the output of the system converge to a small neighborhood of the origin by appropriate choice of the design parameters. Simulation results are included to indicate that the proposed adaptive fuzzy control approach has a satisfactory control performance. In addition, the simulation comparisons with the previous methods show that the proposed adaptive fuzzy control approach has robustness to the dynamical uncertainties.

In this article, an observer-based fuzzy adaptive inverse optimal output feedback control problem is studied for a class of nonlinear systems in strict-feedback form. The considered nonlinear systems contain unknown nonlinear dynamics and their states are not measured directly. Fuzzy logic systems are applied to identify the unknown nonlinear dynamics and an auxiliary nonlinear system is constructed. Based on this auxiliary system, a fuzzy state observer is first designed to estimate the immeasurable states. By using the inverse optimal principle and adaptive backstepping design theory, an observer-based fuzzy adaptive inverse optimal output feedback control scheme is then developed. The proposed inverse optimal control scheme need not assume that the states are measurable. It also guarantees that the closed-loop system is semiglobally uniformly ultimately bounded, and achieves the optimal control objective as well. Finally, two simulation examples are provided to check the validity of the presented control method.

Aims. We present an investigation into how the cooling of the background plasma influences the propagation of slow and fast MHD wave modes supported by an unbounded, homogenous plasma. Previous investigations have suggested that the cooling of the plasma and a reduction in density could lead to the damping of fast magneto-acoustic oscillations. We aim to investigate whether cooling of the background plasma at a constant density may be responsible for the damping of slow and fast modes. Methods. The plasma is assumed homogeneous and the background temperature (pressure) is decreasing with time. The temperature change is assumed to be due to optically thin radiation. A special case of the radiative function is chosen to allow an analytical assessment of the effects of cooling on magneto-acoustic MHD modes and ensures the temperature evolution of the background plasma due to this radiation also matches the observed cooling profile of coronal loops. Results. A time-dependent dispersion relation is obtained on the slow timescale of cooling and full time-dependent solutions are found. Leading order equations for the amplitude of the waves are obtained and solved analytically for the slow and fast MHD modes. The cooling of the plasma is found to cause the frequency of the magneto-acoustic modes to decrease with time. The slow modes are found to experience a greater change in frequency than the fast modes. More importantly, the radiative losses also provide a significant damping of the slow mode and a small damping of the component of the fast mode perpendicular to the magnetic field. The damping of the slow mode is found to be strong within typical lifetimes of oscillations observed in coronal structures. Cooling could have important consequences and needs to be assessed when trying to determine what mechanism is responsible for the observed damping of coronal oscillations.

This paper is concerned with the problem of adaptive neural output-feedback control for a class of nonlinear strict-feedback systems. In this research, radial basis function (RBF) neural networks (NNs) are used to approximate the unknown nonlinear functions and a state observer is constructed to estimate the immeasurable state variables. An adaptive neural output feedback control scheme is proposed via backstepping technique. The proposed design method can guarantee semi-global uniform ultimate boundedness (SGUUB) of all signals in the closed-loop system, and ensures the observer errors converge to a small neighborhood. At last, a simulation example is included to show the effectiveness of the proposed method.

Traffic congestion control for Aw–Rascle–Zhang model

The backstepping control design procedure has been used to develop stabilizing controllers for time invariant plants that are linear or belong to some class of nonlinear systems. The use of such a procedure to design stabilizing controllers for plants with time varying parameters has been an open problem. In this paper we consider the backstepping design procedure for linear time varying (LTV) plants with known and unknown parameters. We first show that a backstepping controller can be designed for an LTV plant by following the same steps as in the linear time-invariant (LTI) case and treating the plant parameters as constants at each time t. Its stability properties however cannot be established by using the same Lyapunov function and techniques as in the LTI case. We then introduce a new parametrization and filter structure that takes into account the plant parameter variations leading to a new backstepping controller. The new control design guarantees exponential convergence of the tracking error to zero if the plant parameters are exactly known. If the parameters are not precisely known but the time variations of the parameters associated with the system zeros are known, the appropriate choice of certain design parameters, without using any adaptive law, leads to closed-loop stability and perfect regulation. This new control design is modified and supplemented with an update law to be applicable to LTV plants with unknown parameters. In the adaptive control design, the notion of structured parameter variations is used in order to include possible a priori information about the plant parameter variations. With this formulation, only the unstructured plant parameters are estimated and are required to be slowly time varying, and the structured plant parameters are allowed to have any finite speed of variation. The adaptive controller is shown to be robust with respect to the unknown but slow parameter variations in the global sense. We derive performance bounds which can be used to select certain design parameters for performance improvement. The properties of the proposed control scheme are demonstrated using simulation results.