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Necessary and sufficient stability conditions are given for the existence of a continuous Lyapunov function for a semicontinuous, stochastic discrete-time system. The continuity of the Lyapunov function is linked to robustness of the stability property, which reduces to classical stability plus convergence for deterministic systems. The nature of the Lyapunov results are inspired by Lyapunov results...
We consider control systems of the type x?? = Ax+??(t)ub, where u ?? R, (A; b) is a controllable pair and ?? is an unknown time-varying signal with values in [0; 1] satisfying a permanent excitation condition of the kind ??t+Tt ?? ?? ??for 0 < ?? ?? T independent on t. We prove that such a system is stabilizable with a linear feedback depending only on the pair (T; ??) if the real part of the...
In this paper we give conditions that a discrete time switched linear systems must satisfy if it is stable. We do this by calculating the mean and covariance of the set of matrices obtained by using all possible switches. The theory of switched linear systems has received considerable attention in the systems theory literature in the last two decades. However, for discrete time switched systems the...
In this article we extend previous results for back-stepping and passivity-based design of cooperative control laws to a class of chained form systems that includes certain drift-free nonholonomic systems. We exploit the cascaded structure and feedback equivalence to passive systems to derive suitable control laws using a modified backstepping methodology. A virtual output is obtained and shared within...
By making discrete filtration, we study a sort of discrete backward stochastic differential equations (BSDEs) with Duffie & Epstein's type. Based on the properties of those filtrations, we prove the existence and uniqueness of the solutions. Finally, we discuss the numerical stability and convergence of the discrete BSDEs.
A central tool in systems theory for synthesizing control laws that achieve stability are control Lyapunov functions (CLFs). Classically, a CLF enforces that the resulting closed-loop state trajectory is contained within a cone with a fixed, predefined shape, and which is centered at and converges to a desired converging point. However, such a requirement often proves to be overconservative. In this...
We introduce an approach for stable deployment of agents into planar curves (1-D formations in 2-D space) parameterized by the agent index. Stability is ensured by leader feedback, which is designed in a manner similar to boundary control of PDEs. By discretizing the model and the PDE controllers with respect to the continuous agent index, we obtain control laws for the discrete follower agents and...
This paper concerns the problem of state-derivative feedback with exponential convergence rate for a linear system with a constant time-delay. This is promising for better applicability in practical systems where the state-derivative signals are easier to obtain than the state ones. Based on a system state transformation and appropriate Lyapunov functions, a sufficient condition for the design of...
This paper proposes a novel general Lyapunov-based line-of-sight (LOS) controller design for rigid spacecraft by means of two torques. Then, the approach is developed in order to simultaneously stabilize the angular velocity and LOS, while the LOS axis is unactuated. As a feature of the introduced controller, it is shown that the total closed loop system's stability is robust against any unpredefined...
This paper considers the global output feedback stabilization of a class of upper-triangular nonlinear systems with a single input and multiple output. It is shown that under a structural condition, the output feedback stabilization problem can be solved for this class of systems by coupling with a finite-time convergent observer and a saturated homogeneous stabilizer. More general results are also...
In this paper, periodic learning control is presented for deterministic periodic auto-regressive exogenous systems. The control problem is approached in a certainty equivalence framework, of which a periodic learning identification algorithm is formed to estimate the periodic time-varying parameters, and the only prior knowledge is the periodicity. The learning algorithm updates the estimates periodically,...
Over the years, we have been applying multi- objective evolutionary algorithms (MOEAs) to a number of real- world problems, solving multi-objective optimization problems (MOPs) in the real world faces a number of challenges including when to terminate the algorithm. This paper addresses this challenge by introducing what we call a "stability measure". We use this measure to estimate when...
In the Immune Neural Network (INN), the key point is stability and convergence. The existing INN has shortages in the control of local optimization, so the paper bring forward INN algorithm which is based on extension theory. With the concepts of dependent function and matter-element, the improved algorithm firstly can optimize architecture and rule extraction of INN. And then, the new algorithm is...
This paper addresses the problem of coordination path following control of multiple autonomous vehicles. Stated briefly, the problem consists in steering a group of vehicles along a specified paths, while holding a desired inter-ship formation pattern. Path-following for each vehicle amounts to reducing an appropriately defined geometric error to zero. We first show a passivity property for the path...
We consider a discrete time stochastic queueing system where a controller makes a 2-stage decision every slot. The decision at the first stage reveals a hidden source of randomness with a control-dependent (but unknown) probability distribution. The decision at the second stage incurs a penalty vector that depends on this revealed randomness. The goal is to stabilize all queues and minimize a convex...
The double inverted pendulum system is a less-driven, multi-parameter, highly nonlinear system. The sliding mode controller is designed to make the double pendulum stable at the upright equilibrium position. But, it is difficult to determine the sliding surface in design, which is the key to the performance of the control system. The improved genetic strategy is applied to search the optimal sliding...
The traditional model reference adaptive system (MRAS) is of parallel configuration. By representing the reference model as an equivalent closed-loop subsystem, these two subsystems can share a controller virtually. An embedded structure of MRAS is thereby presented. In this paper, two approaches are developed for designing the adaptive laws. The adaptive law based on Lyapunov stability theory is...
In this paper, a Dmeyer wavelet function is utilized to decompose the mixed load current waveforms and extract the parameter values which represent the nonlinear loads. A three layer BP neural network model is established, which is trained using Levenberg-Marquardt (LM) algorithm which shows fast convergence and strong stability. The results indicate that the proposed method of the wavelet BP neural...
This paper is concerned with simultaneous stability of a collection of continuous-time linear plants whose feedback control loops are closed via a shared digital communication network. Because of the limitation of communication capacity, only a limited number of controller-plant connections can be accommodated at any time instant. Therefore, it is necessary to carefully design the scheduling policy...
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