Search results for "Uniform boundedness"
showing 10 items of 25 documents
Adaptive Asymptotically Tracking Control for Uncertain Strict-Feedback Nonlinear Systems with Input Quantization
2018
In this paper, we investigate the output tracking control problem for a class of uncertain nonlinear systems in parametric strict feedback form with quantized input. A novel backstepping based adaptive quantized control scheme is proposed. Different from the existing results, the true quantization parameters are allowed to be unknown in the design of adaptive controller. It is shown that with the proposed control scheme, the system output can track the desired trajectory asymptotically and all the closed-loop signals are globally uniformly bounded.
Distributed Adaptive Consensus Tracking Control of Uncertain High-order Nonlinear Systems under Directed Graph Condition
2018
In this paper, we investigate the output consensus tracking problem for a class of high-order nonlinear systems subjected to unknown parameters and uncertain external disturbances. A novel backstepping based distributed adaptive control scheme is presented under the directed communication status. For the subsystems without direct access to time-varying desired trajectory, local estimators are introduced and the corresponding adaptive laws are designed in a totally distributed fashion. With the presented scheme, the assumption on linearly parameterized reference signal and the information exchange operation of subsystem inputs in the existing results are no longer needed. It is shown that al…
Distributed adaptive leader–follower and leaderless consensus control of a class of strict-feedback nonlinear systems : a unified approach
2020
In this paper, distributed adaptive consensus for a class of strict-feedback nonlinear systems under directed topology condition is investigated. Both leader–follower and leaderless cases are considered in a unified framework. To design distributed controller for each subsystem, a local compensatory variable is generated based on the signals collected from its neighbors. Such a technique enables us to solve the leader–follower consensus and leaderless consensus problems in a unified framework. And it further allows us to treat the leaderless consensus as a special case of the leader–follower consensus. For leader–follower consensus, the assumption that the leader trajectory is linearly para…
Adaptive consensus of uncertain nonlinear systems with event triggered communication and intermittent actuator faults
2019
This paper investigates distributed consensus tracking problem for uncertain nonlinear systems with event-triggered communication. The common desired trajectory information and each subsystem's state will be broadcast to their linked subsystems only when predefined triggering conditions are satisfied. Compared with the existing related literature, the main features of the results presented in this paper include four folds. (i) A totally distributed adaptive control scheme is developed for multiple nonlinear systems without Lipschitz condition, while with parametric uncertainties. (ii) The derivative of desired trajectory function is allowed unknown by all subsystems and directed communicati…
Dissipativity-Based Small-Gain Theorems for Stochastic Network Systems
2016
In this paper, some small-gain theorems are proposed for stochastic network systems which describe large-scale systems with interconnections, uncertainties and random disturbances. By the aid of conditional dissipativity and showing times of stochastic interval, small-gain conditions proposed for the deterministic case are extended to the stochastic case. When some design parameters are tunable in practice, we invaginate a simpler method to verify small-gain condition by selecting one subsystem as a monitor. Compared with the existing results, the existence-and-uniqueness of solution and ultimate uniform boundedness of input are removed from requirements of input-to-state stability and smal…
Distributed Adaptive Control for Asymptotically Consensus Tracking of Uncertain Nonlinear Systems With Intermittent Actuator Faults and Directed Comm…
2019
In this article, we investigate the output consensus tracking problem for a class of high-order nonlinear systems with unknown parameters, uncertain external disturbances, and intermittent actuator faults. Under the directed topology conditions, a novel distributed adaptive controller is proposed. The common time-varying trajectory is allowed to be totally unknown by part of subsystems. Therefore, the assumption on the linearly parameterized trajectory signal in most literature is no longer needed. To achieve the relaxation, extra distributed parameter estimators are introduced in all subsystems. Besides, to handle the actuator faults occurring at possibly infinite times, a new adaptive com…
Singularity formation for Prandtl’s equations
2009
Abstract We consider Prandtl’s equations for an impulsively started disk and follow the process of the formation of the singularity in the complex plane using the singularity tracking method. We classify Van Dommelen and Shen’s singularity as a cubic root singularity. We introduce a class of initial data, uniformly bounded in H 1 , which have a dipole singularity in the complex plane. These data lead to a solution blow-up whose time can be made arbitrarily short within the class. This is numerical evidence of the ill-posedness of the Prandtl equations in H 1 . The presence of a small viscosity in the streamwise direction changes the behavior of the singularities. They stabilize at a distanc…
Approximating the solutions of differential inclusions driven by measures
2019
The matter of approximating the solutions of a differential problem driven by a rough measure by solutions of similar problems driven by “smoother” measures is considered under very general assumptions on the multifunction on the right-hand side. The key tool in our investigation is the notion of uniformly bounded $$\varepsilon $$-variations, which mixes the supremum norm with the uniformly bounded variation condition. Several examples to motivate the generality of our outcomes are included.
Holomorphic Mappings of Bounded Type on (DF)-Spaces
1992
We study the holomorphic functions of bounded type defined on (DF)-spaces. We prove that they are of uniformly bounded type. The space of all these functions is a Frechet space with its natural topology. Some consequences and related results are obtained.
Restricted Uniform Boundedness in Banach Spaces
2009
Precise conditions for a subset A of a Banach space X are known in order that pointwise bounded on A sequences of bounded linear functionals on X are uniformly bounded. In this paper, we study such conditions under the extra assumption that the functionals belong to a given linear subspace Γ of X *. When Γ = X *, these conditions are known to be the same ones assuring a bounded linear operator into X , having A in its image, to be onto. We prove that, for A , deciding uniform boundedness of sequences in Γ is the same property as deciding surjectivity for certain classes of operators. Keywords: Uniform boundedness; thick set; boundedness deciding set Quaestiones Mathematicae 32(2…