Unknown High-frequency Gain Sign Research Articles

From adaptive control to variable structure systems – seeking harmony

From adaptive control to variable structure systems – seeking harmony

Output regulation of output feedback systems with unknown exosystem and unknown high-frequency gain sign

This paper discusses the global robust output regulation problem for a class of nonlinear output feedback systems. It is assumed that the exosystem and the high-frequency gain sign are unknown and that the unknown parameters can be arbitrarily large. To solve this problem, two major challenges are to be overcome. First, the concurrence of the unknown exosystem and the unknown high-frequency gain sign cannot be handled merely by designing estimators for the two unknown parameters respectively. Second, the conventional extended matching design approach cannot be directly implemented, owing to the arbitrarily large unknown parameters. To cope with these difficulties, a new estimator is developed, and the extended matching design approach is modified to obtain a suitable update law for the estimator. The effectiveness of the proposed adaptive controller is illustrated by an example.

Adaptive output feedback dynamic surface control of nonlinear systems with unmodeled dynamics and unknown high-frequency gain sign

In this paper, two adaptive output feedback control schemes are proposed for a class of nonlinear systems with unmodeled dynamics and unmeasured states as well as unknown high-frequency gain. Radial basis function (RBF) neural networks (NNs) are used to approximate the unknown nonlinear functions. K-filters are designed to estimate the unmeasured states. An available dynamic signal is introduced to dominate the unmodeled dynamics. By introducing the dynamic surface control (DSC) method, the bounded condition of the approximation error is removed, and the tracking control is achieved. Moreover, the number of adjustable parameters and the complexity of the design are both reduced. By theoretical analysis, the closed-loop system is shown to be semi-globally uniformly ultimately bounded (SGUUB). Simulation results are provided to illustrate the effectiveness of the proposed approach.

Adaptive nonlinear output-feedback dynamic surface control with unknown high-frequency gain sign

In this paper, an adaptive dynamic surface control (DSC) for a class of nonlinear systems with unknown high-frequency gain (HFG) sign is proposed. The novelty of our scheme is that we separate the first virtual control signal from the HFG, which enables us to estimate the HFG directly. As a result, the traditional Nussbaum function (NF) approach is abandoned. By using the proposed DSC, the adaptive laws are needed only at the first design step and the explosion of terms in backstepping control can be eliminated, which greatly reduces the computational burden. In particular, based on an initialisation technique, we prove that the performance of the system tracking error can be guaranteed even when the HFG sign is unknown. It is shown that all signals of the closed-loop system are semi-globally uniformly bounded. Simulation results illustrate that the proposed scheme is more applicable than that of the NF-based backstepping control.

Adaptive fuzzy backstepping output feedback control of nonlinear time-delay systems with unknown high-frequency gain sign

In this paper, an adaptive fuzzy robust feedback control approach is proposed for a class of single-input and single-output (SISO) strict-feedback nonlinear systems with unknown nonlinear functions, time delays, unknown high-frequency gain sign, and without the measurements of the states. In the backstepping recursive design, fuzzy logic systems are employed to approximate the unknown smooth nonlinear functions, K-filters is designed to estimate the unmeasured states, and Nussbaum gain functions are introduced to solve the problem of unknown sign of high-frequency gain. By combining adaptive fuzzy control theory and adaptive backstepping design, a stable adaptive fuzzy output feedback control scheme is developed. It has been proven that the proposed adaptive fuzzy robust control approach can guarantee that all the signals of the closed-loop system are uniformly ultimately bounded and the tracking error can converge to a small neighborhood of the origin by appropriately choosing design parameters. Simulation results have shown the effectiveness of the proposed method.

Adaptive Fuzzy Decentralized Control for Large-Scale Nonlinear Systems With Time-Varying Delays and Unknown High-Frequency Gain Sign

In this paper, an adaptive fuzzy decentralized robust output feedback control approach is proposed for a class of large-scale strict-feedback nonlinear systems without the measurements of the states. The nonlinear systems in this paper are assumed to possess unstructured uncertainties, time-varying delays, and unknown high-frequency gain sign. Fuzzy logic systems are used to approximate the unstructured uncertainties, K-filters are designed to estimate the unmeasured states, and a special Nussbaum gain function is introduced to solve the problem of unknown high-frequency gain sign. Combining the backstepping technique with adaptive fuzzy control theory, an adaptive fuzzy decentralized robust output feedback control scheme is developed. In order to obtain the stability of the closed-loop system, a new lemma is given and proved. Based on this lemma and Lyapunov-Krasovskii functions, it is proved that all the signals in the closed-loop system are uniformly ultimately bounded and that the tracking errors can converge to a small neighborhood of the origin. The effectiveness of the proposed approach is illustrated from simulation results.

Globally stable adaptive backstepping fuzzy control for output-feedback systems with unknown high-frequency gain sign

This paper addresses the problem of globally stable adaptive backstepping output-feedback tracking control for a class of nonlinear systems with unknown high-frequency gain sign. The fuzzy systems are used as feedforward compensators to model some system functions depending on the reference signal. Thus, the global stability of closed-loop system can be guaranteed under the assumption that the unknown system functions are bounded by partly known nonlinear functions. The other advantage of the proposed control scheme is that the designer can determine the approximation domain a priori via the bound of the reference signal, which is very important for the choice of the centers and widths of membership functions. Moreover, the Nussbaum-type function is employed to deal with the unknown high-frequency gain sign. Two simulation examples are provided to illustrate the feasibility of control scheme presented in this paper.

Variable Structure Model Reference Adaptive Control with Unknown High Frequency Gain Sign

A variable structure model reference adaptive control for plants with relative degree greater than one and unknown high frequency gain sign is proposed. A switching scheme is introduced based on a monitoring function designed for the first auxiliary error of the close loop system. It is shown that under the supervision of the monitoring function, the switching stops after at most a finite number of switchings and the tracking error converges to a residual set that can be made arbitrarily small by appropriately choosing some design parameters.

Adaptive Robust Stabilization of Output Feedback Systems With Application to Chua's Circuit

This brief studies the adaptive robust stabilization problem for nonlinear systems in output feedback form with the high-frequency gain sign unknown. The problem is solved by integrating the robust control method and the Nussbaum gain technique. Also, we show that the celebrated Chua's circuit is a nonlinear system in output feedback form, and apply our approach to design a control law to achieve global stability of the closed-loop system in the presence of uncertain parameters and unknown high-frequency gain sign

Global Robust Output Regulation of Output Feedback Systems With Unknown High-Frequency Gain Sign

The global robust output regulation problem for nonlinear systems in output feedback form has been solved under a key assumption that the high-frequency gain sign is known. This note shows that this assumption can be removed by incorporating the Nussbaum gain technique into the existing framework for handling the robust output regulation problem.

Adaptive nonlinear output-feedback control with unknown high-frequency gain sign

A global adaptive output-feedback control scheme, which does not require a priori knowledge of high-frequency gain sign, is proposed for general nonlinear systems in output-feedback form. Unlike in Ding (1998), the removal of a priori knowledge of the high-frequency gain sign is not at the price of making growth restrictions on system nonlinearities, and furthermore, only the minimal number of parameters needs to be updated.

Semiglobal output feedback control of uncertain nonlinear systems with unknown high frequency gain sign

We remove, for semiglobal output feedback control of uncertain nonlinear systems, a previous requirement that the high-frequency-gain sign be known a priori. Our proposed control scheme is also of the high-gain observer-type, but it involves a switching between two forms of control. The underlying idea is that with the help of the high gain observer, the high-frequency-gain sign can be identified online, provided the designed control satisfies some domination condition.

Comparison of hybrid and continuous sliding mode based control algorithms 1

Abstract The term hybrid systems designates those physical processes that exhibit both continuous and discrete aspects. On the other hand, some fully continuous systems can benefit from the introduction of an inherently event-based system such as an intelligent supervisor thus becoming hybrid themselves. In the present paper, the focus is on this last class of system. More precisely, a new control approach for continuous time systems with unknown high frequency gain sign is presented relying on a logic-driven sliding mode control. Such an approach is compared with a consolidated one based on the so-called Nussbaum function .

Model reference adaptive control with unknown high frequency gain sign

This paper presents an indirect model reference adaptive control for minimum phase linear systems of arbitrary order with unknown high frequency gain sign. It is proved that the (modified) estimate of the high frequency gain has a uniform positive lower bound. The problem has been solved by using the least squares covariance matrix properties to define an appropriate modification of the parameters estimates.