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This article is devoted to the global output‐feedback stabilization of nonlinear systems with unknown control directions and unmeasured states dependent growth whose rate is an unknown arbitrary function of output. In view of limited capability of continuous feedback in compensating system uncertainties and nonlinearities, a novel switching adaptive scheme is proposed. The scheme involves a logic‐based switching mechanism, based on which, a proper controller is selected (from a family of candidate controllers) to act on the system during its execution interval. The main differences between the proposed scheme and those in the related works are as follows. First, the set of candidate controllers is determined online, rather than specified in advance, which provides foundations for compensating arbitrary function‐of‐output growth rate. Second, an iterative function composed of system memory signals is introduced into the switching mechanism, aiming to evaluate the differences between the system states and observe states. Finally, when switching stops, only by introducing an extra transformation and adopting elaborate analysis, can the boundedness of the closed‐loop system signals be obtained, rather than those in the related works where the boundedness can be naturally established once switching stops. The constructed switching adaptive controller guarantees that all the signals of the resulting closed‐loop system are bounded and ultimately converge to zero. [ABSTRACT FROM AUTHOR]

This paper is devoted to the adaptive stabilization for uncertain hyperbolic PDE‐ODE cascade systems. Remarkably, unknown spatially varying and unknown constant parameters exist in the PDE and ODE subsystems, respectively. This brings essential difficulties in the design of compensator and boundary controller, and in the involved performance analysis. To solve the control problem, an infinite‐dimensional backstepping transformation (simplified as IDBT) and its inverse are first introduced to change the original system into a new system (called target system). Then, a state‐feedback boundary controller is constructed for the target system by incorporating the adaptive technique based on projection operator, which can guarantee the desirable stability of the resulting closed‐loop system. Finally, a simulation example is provided to illustrate the effectiveness of the proposed adaptive controller. [ABSTRACT FROM AUTHOR]

Summary: This article is devoted to the global practical tracking for a class of uncertain nonlinear systems. Notably, the input powers of the system are unknown and not required to be upper bounded by known constants. This means the presence of new type of serious uncertainties, which makes the problem under investigation largely challenging and urges us to develop a new powerful adaptive control scheme, particularly the compensation strategy to overcome the negative influence caused by the uncertainties. For this, a dual high‐gain‐based adaptive control design scheme is proposed, in which a dynamic high gain and a high gain function are jointly introduced to compensate the serious system uncertainties. Under the designed controller, all the signals of the resulting closed‐loop system are bounded and furthermore the tracking error remains any prescribed small after a finite time. [ABSTRACT FROM AUTHOR]

Summary: This article is devoted to global adaptive stabilization for a class of uncertain nonlinear systems. Notably, the systems under investigation admit unknown control directions and unknown input powers, and particularly the latter, which are a new type of system uncertainties, largely challenge the feasibility of continuous feedbacks. This spurs us to pursue a switching adaptive feedback which is actual a discontinuous one with high feedback capability. To solve the control problem, a parameterized controller in a specified form is first introduced, which can globally stabilize the system once the design parameter involved belongs to a certain set. However, the controller cannot directly be implemented since the set depends heavily on the unknown input powers. To make the parameterized controller implementable, a new switching strategy is delicately proposed, which can instantly update the parameters of the controller to compensate the serious system uncertainties. It turns out that the parameterized controller with switching updating mechanism guarantees that all the signals of the closed‐loop system are globally bounded and ultimately converge to zero. Simulation examples demonstrate the effectiveness of the proposed design scheme. [ABSTRACT FROM AUTHOR]

This paper considers the global stabilization for a class of uncertain nonlinear systems with unknown powers, unknown control directions, and unknown nonlinearities. Mainly due to the presence of the unknown powers which have not known upper bound, no existing methods are applicable to the control problem to be solved. In this paper, to compensate the serious system uncertainties and particularly to overcome the major obstruction from unknown powers, we appeal to the mechanism of switching adaptive feedback. By flexibly combining the domination and the method of adding a power integrator, we propose a new adaptive controller design, whose design parameters are tuned online based on a switching logic. The designed controller will become operative as long as finite switchings happen and will not lead to Zeno phenomenon, and can guarantee the global boundedness as well as ultimate convergence of the resulting closed-loop system. Two numerical examples are given to demonstrate the effectiveness of the developed design scheme. [ABSTRACT FROM AUTHOR]

This paper is devoted to the global output-feedback stabilisation for a class of nonlinear systems with inherent nonlinearities and coarse disturbance. Remarkably, the disturbance may be non-periodic, non-differentiable and/or of unknown magnitude, and hence some critical requirements on the disturbance in the existing related literature are successfully removed. Recognising that the strategies of disturbance compensation, such as internal model principle, sliding mode control method, learning method and active disturbance rejection control method, are quite hard or even impossible to apply, a time-varying design scheme is developed in the paper. Moreover, the serious unknowns and time-variations reflected in the growth rate of the system are also dealt with by the proposed scheme. By designing a time-varying output-feedback controller, all the signals of the resulting closed-loop system are globally bounded, and the original system state and the observer state ultimately converge to zero. [ABSTRACT FROM AUTHOR]

This paper investigates the global output-feedback stabilization for a class of stochastic nonlinear systems with function control coefficients. Notably, the systems in question possess control coefficients that are functions of output, rather than constants; hence, they are different from the existing literature on stochastic stabilization. To solve the control problem, an appropriate reduced-order observer is introduced to reconstruct the unmeasured system states before a smooth output-feedback controller is designed using the backstepping method, which guarantees that the closed-loop system is globally asymptotically stable in probability. This paper combines the related results in the deterministic and stochastic setting and gives the first treatment on the global output-feedback stabilization for the stochastic nonlinear systems with function control coefficients. A simulation example is given also to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper addresses the global adaptive stabilisation via switching and learning strategies for a class of uncertain nonlinear systems. Remarkably, the systems in question simultaneously have unknown control directions, unknown input disturbance and unknown growth rate, which makes the problem in question challenging to solve and essentially different from those in the existing literature. To solve the problem, an adaptive scheme via switching and learning is proposed by skilfully integrating the techniques of backstepping design, adaptive learning and adaptive switching. One key point in the design scheme is the introduction of the learning mechanism, in order to compensate the unknown input disturbance, and the other one is the design of the switching mechanism, through tuning the design parameters online to deal with the unknown control directions, unknown bound and period of input disturbance and unknown growth rate. The designed controller guarantees that all the signals of the resulting closed-loop systems are bounded, and furthermore, the closed-loop system states globally converge to zero. [ABSTRACT FROM AUTHOR]