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This work proposes a control algorithm to stabilize a circular formation of AUVs tracking a time-varying center. We also consider the problem of uniform distribution of all the agents along the circle from two approaches: all-to-all and limited communication. We tackle with this communication constraint using a cooperative control strategy which includes the Laplacian matrix of the communication graph...
In the general framework of continuous-time linear systems with saturating actuators, this work is devoted to the characterization of the widest stability region of a planar unstable linear system for a fixed saturation level.
Variation paradigm is introduced for stability in terms of asymptotic gain of persistent dwell-time switched time-delay systems. The principle of small-variation small-state is conceived to formulate conditions on ultimate variations between end times of dwell-time switching intervals for convergence in these intervals. Trajectory convergence is then derived using evolutionary data in both retarded...
This paper proposes a method to estimate the region of attraction of nonlinear polynomial systems. Based on quadratic Lyapunov functions, stability analysis conditions in a ??quasi??-LMI form are stated in a regional (local) context. An LMI-based optimization problem is then derived for computing the Lyapunov matrix maximizing the estimate of the region of attraction of the origin.
This paper addresses the dynamic anti-windup synthesis problem for state delayed linear control systems subject to saturating inputs. Based on the Projection Lemma and on a modified sector condition, it is shown that the rational full-order compensator synthesis problem is convex. The computation of the anti-windup compensator aiming at ensuring both ??2 input-to-state stability and internal stability...
A new type of global stability is introduced and its equivalent Lyapunov characterization is presented. The problem of global stability of the compact set composed by all invariant solutions of a nonlinear system (several equilibriums, for instance) is analyzed. Consideration of such set allows us to present global stability properties for multi-stable systems.
This paper proposes a reactive motion controller for a humanoid robot to maintain balance against a large disturbance, by relatively stepping. A reactive step is performed by the robot, so that it reduces the disturbance force. Several problems are addressed: first the motion is designed to ensure the respect of stepping constraints such as a dynamical stability, motion feasibility of the swing leg...
Interconnection of several hybrid input-to-state stable (ISS) systems is considered in this paper. We ask under what condition is such an interconnection stable and how an ISS-Lyapunov function can be constructed for the whole interconnection. Small-gain condition to assure stability is given. A construction of an ISS-Lyapunov function for the whole system is provided under the small-gain condition.
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...
This paper deals with stabilization of networked control systems (NCS) affected by uncertain time-varying delays and data packet dropouts. We point out that such network effects are likely to render the classical control Lyapunov function (CLF) method unfeasible, mainly due to the monotonic decreasing condition. To solve this problem we make use of a discrete-time equivalent of a control Lyapunov-Razumikhin...
We consider networks of input-to-state dynamically stable (ISDS) systems and provide a small gain condition under which the entire network is again ISDS. A Lyapunov formulation of the nonlinear small gain theorem for two interconnected ISDS systems is proved. It provides a constructive method to find an ISDS Lyapunov function for such an interconnection.
This paper develops semistability analysis results for nonlinear switched systems. Semistability is the property whereby the solutions of a dynamical system converge to Lyapunov stable equilibrium points determined by the system initial conditions. The main results of the paper involve sufficient conditions for semistability using multiple Lyapunov functions and integral-type inequalities.
The presented work addresses the observation problem for a large class of nonlinear systems, including systems which are nonlinear in the unmeasured states. Assuming partial state measurements, the unmeasured states are reconstructed so that a prediction of the measured states converges to a neighborhood of the actual measurements. This prediction-based observer algorithm relies on carefully selected...
In this paper, we consider linear shift-invariant discrete n-dimensional systems over ??n in the behavioral context (nD behaviors) and investigate the regular implementation of autonomous behaviors with different degrees of autonomy. Taking into account that stable nD behaviors have the highest degree of autonomy, we apply the previous results to characterize all stabilizable behaviors.
In this paper we combine an invariant-set approach to fault detection and identification (FDI), recently proposed by the authors, with the virtual actuator approach to controller reconfiguration of Steffen, Lunze and co-authors. The FDI approach is based on the separation of invariant sets that characterise healthy system operation from invariant sets that characterise faulty operation. The derivation...
We propose an underactuated mechanical system named inverted pendulum on a cart beam system. The proposed system has three degrees-of-freedom and one control input. The mathematical model is derived using Lagrangian method and the stabilization is achieved with constraints using a linear controller designed based on linear matrix inequality approach. Simulation results are presented to validate the...
This paper addresses the problem of tracking periodic references for uncertain linear systems subject to control saturation. Accordingly to the internal model principle, a control loop containing the modes of both the references and additive disturbances is considered. From this structure, conditions in a ??quasi?? LMI form are proposed to simultaneously compute a stabilizing state feedback gain and...
In this work, we focus on the problem of stabilization of two constrained linear systems coupled through the inputs by two different agents which communicate in order to take a decision assuming that each agent only has partial information of the model and the state of the system. We extend previous results on distributed model predictive control and provide sufficient conditions that guarantee practical...
We consider a plant switching among a set of dynamic systems each associated with a single stable equilibrium point. We assume that a constraint region for the state is assigned. The main problem is that of finding suitable limitations on the commutation speed in order to avoid constraints violations, even in the absence of state measurements. We introduce the concepts of modal and transition dwell...
This paper is concerned with the theory of quasivelocities and its applications to control. The equations of motion of a mechanical system are derived using the Lagrange-d'Alembert principle written in an arbitrary configuration-dependent frame. The structure of the equations of motion written in quasivelocities is utilized in the design of a nonlinear feedback stabilizing controller for an example...
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