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In order to reduce communication in network control systems, it is of great interest to be able to synthesize event-triggered control laws from continuous-time controls. This work proposes a new rule to design event-based stabilizing controllers for linear systems. More precisely, based on a given reference system, a state observer, and a quadratic Lyapunov-like function, an event-based sampling algorithm...
This article describes the approach to control of human leg dynamical model as a switched linear system. The control scheme consists of fractional and integral order PID controllers. In the paper we analyze the responses of the system depending on the above-mentioned controllers. We focus our attention on angular displacements only. The angular velocity maybe arbitrary. Additionally, we present the...
In this paper we propose a linear time-invariant (LTI) state feedback operator for nonholonomic mobile robots to track a pre-defined trajectory on a 2D planar region. Designing an on-line smooth state feedback control law is still among the major challenges for solving the trajectory tracking problem of nonholonomic systems including differential drive mobile robots. To address this problem, numerous...
In this work, we propose a method to compute the poles of the linear approximation to a nonlinear system, locally around a stable equilibrium point. The method uses periodic inputs, just like hermonic identification of linear systems. We show in passing that the class of Wiener-Hammerstein systems is but a small subset of the collection of all nonlinear control systems, locally around a hyperbolic...
The RRT* algorithm has efficiently extended Rapidly-exploring Random Trees (RRTs) to endow it with asymptotic optimality. We propose Goal-Rooted Feedback Motion Trees (GR-FMTs) that honor state/input constraints and generate collision-free feedback policies. Given analytic solutions for optimal local steering, GR-FMTs obtain and realize safe, dynamically feasible, and asymptotically optimal trajectories...
Stability condition is considered for a class of second-order piecewise linear systems. The state space of the system is divided by partitions into some subsystems. The state trajectory evolves along with the dynamics of the subsystem in which the state exists. A necessary and sufficient condition for the system to be stable is derived. The condition is expressed via the eigenvalues of the matrices...
In this paper, we discuss event-triggering scheme with sliding mode control where sensors are distributed over network. Here, a decentralized event-triggering mechanism is proposed where event is observed at each sensor nodes with local information for possible triggering and control update is done whenever a centralized event is triggered. In order to achieve this, the states are sampled at any one...
Switched linear systems exhibit a continuous state evolving along the continuous flow of time according to linear time invariant differential equations. Furthermore, a discrete interface to the environment is provided, acting on input signals by switching between a finite number of differential equations and generating output signals when the continuous state crosses certain boundaries. We suggest...
This paper considers a problem of optimal model approximation in a behavioral framework. For the class of linear time-invariant ℓ2-systems, an angle criterion is introduced to define the distance measure between two systems in this class. Given a system of degree n, a characterization of all optimal approximants of degree n − 1 is given. The result is derived using the notion of canonical past-future...
The main goal of the paper is to investigate well-posedness issue for a class of piecewise linear systems within the framework of complementarity systems. The class of piecewise linear systems to be considered includes for instance electrical network with piecewise linear resistors, mechanical systems with Coulomb friction. After giving a definition of solution for this class of systems, we present...
A novel formulation of linear model-based predictive control is presented. Predicted flat output trajectories and stabilization around these trajectories constitute the main components of our predictive control approach. A simple dc motor and a cement mill model illustrate the principal features of the method.
This paper presents a simple adaptive controller which universally achieves so-called X-tracking for linear systems where only little structural information about the system to be controlled is needed. The paper extends previous results to the case of systems with higher relative degree. Stability and convergence of the adaptation is proven for tracking arbitrary but sufficiently smooth reference...
The determination of the reachable states for a class of infinite-dimensional nonlinear systems with control constraints is investigated. The main results reduce this problem to the determination of the reachable states, by means of admissible controls, for the approximate linear systems. The approach is developed using a state space system framework and is based on the application of a result from...
Given an interval matrix system with discrete- or continuous-time dynamics, the flow-invariance of an arbitrarily time-dependent rectangular set with respect to this system is introduced as a concept of geometric nature. The case of rectangular sets with exponential time-dependence is separately explored. If there exist flow-invariant rectangular sets approaching the state space origin for an infinite...
In this paper we discuss the concept of compatible behavior interconnections. We distinguish the case where all variables are available for interconnection (total interconnection) from the case where only a part of them are (partial interconnection). The main idea behind the notion of compatibility for total interconnection is causality of (the effect of) the interconnection. We also show that state...
A stochastic linear hybrid system is said to be observable if the hybrid state of the system can be uniquely determined from its output. In this paper, we derive conditions for the observability of stochastic linear hybrid systems by exploiting the information obtained from system noise characteristics. Having established the necessary criteria for observability, we study the effect of these conditions...
This contribution presents a flatness based approach for disturbance decoupling and asymptotic disturbance rejection for linear and nonlinear systems with measurable disturbances. Different from previous flatness based approaches the disturbance input is regarded as an additional fictitious input. This on the one hand enlarges the class of systems, where flatness based disturbance decoupling and asymptotic...
A relay feedback linear system with the transfer function of the pole excess equal to two can have a sliding mode in the set of co-dimension two and chattering mode around it. The chattering can be a part of a limit cycle in the relay feedback system and this limit cycle can be unique and globally stable. It was shown before that a limit cycle exists for a special class of systems with stable denominator...
An extension of the structural conditions for non-interacting controls is considered for linear discrete time-invariant systems. The approach is strictly geometric and exploits the basic properties of the minimum conditioned invariant containing a given subspace. The investigation is motivated by the impact of this extension on the dual setting of fault detection and identification.
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