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In this paper, a control algorithm based on Backstepping technique for differential drive mobile robot path tracking is developed. The use of backstepping theory to solve the problem of path tracking is relatively new in the field of mobile robots control. Numerical simulations were conducted to show the effectiveness of the proposed algorithms to solve the nonholonomic constraints of the mobile robot,...
Control design methods for the control of the reaction wheel pendulum using a single actuator are presented in this paper. The control algorithms are based on the energy of the system and its passivity properties.
LgV controllers are well known continuous-time Lyapunov design tools. The object of this work is to discuss their sampled-data versions. Piecewise constant controllers are described in order to provide asymptotic stability and damping at the sampling instants. These sampled-data controllers are tested on a synchronous machine model and their performances are compared through simulations to those obtained...
A succinct survey of theoretical results for LPV systems is presented in this paper. From modeling to synthesis of LPV controllers, details are given about some techniques and several references are laid for the different aspects of the procedure. Classical Lyapunov-based results are presented, as well as a recent approach for LPV closed-loop systems. Performance norm-based results are presented,...
This paper presents the synthesis of a control law which guarantees asymptotic stability for a wheeled mobile robot under slip conditions subject to both constraints and system dynamics. This control law is obtained using Linear Matrix Inequalities. The improvements provided by the pro- posed adaptive control are compared with other control laws, dealing with slip effect, through simulation.
In this paper we consider several interconnected ISS systems supplied with ISS Lyapunov functions defined in the dissipative form. Our aim is to construct an ISS Lyapunov function for the interconnection. We provide a condition of a small gain type under which this construction is possible and describe a method of an explicit construction of such an ISS Lyapunov function.
An optimal tracking controller design approach for non-linear non minimum-phase systems based on the concept of modified optimal control is presented. We extend the existing design strategy of modified optimal control to non-linear time-variant systems, since tracking a desired trajectory results in a time-variant non-linear system for the tracking error. We obtain an optimal control law which achieves...
This paper examines the capturability of a guidance law that provides a desired angular acceleration of the heading angle to a pursuer. The guidance law has originally been proposed by Fajen and Warren[13], in order to explain the behavior of walking humans. It is shown that the relative rotational motion between a pursuer and an evader can be represented by an equation similar to the equation of...
This paper presents a constructive methodology to design sliding mode surfaces for a class of underactuated mechanical systems. The surfaces are designed taking advantage of a fictitious output and the Lyapunov theory. The fictitious output is chosen in such a way that the system is minimum-phase. The technique is developed for a class of underactuated mechanical systems with uncertainty in their...
In this paper we develop an entirely new constructive global analysis methodology for a class of hybrid systems known as Piecewise Linear Systems (PLS). This methodology consists in inferring global properties of PLS solely by studying their behavior at switching surfaces associated with PLS. The main idea is to analyze impact maps, i.e., maps from one switching surface to the next switching surface,...
This paper investigates the problem of practical finite-time trajectory tracking and practical finite-time stabilization of two important classes of dynamical systems by means of C(∞) feedbacks. It is shown that Hamiltonian mechanical systems and systems in strict feedback form can be made globally finite-time stable by smooth parameterized feedbacks. We show that we could bring all the trajectories...
For a parameterized family of homogeneous sliding mode based controllers under the influence of bounded perturbation, a strong Lyapunov function is presented for the first time. The family of controllers range from twisting algorithm, the linear PD control law, to the uniformly stable control law. The strict homogeneous Lyapunov function proposed here allows the estimation of the ultimate bound of...
In this paper a strong Lyapunov function is proposed, for the first time, for a parameterized family of homogeneous sliding mode based controllers. Indeed, from twisting algorithm, to the linear PD control law, to the uniformly stable control law, a general homogeneous family of control algorithms are considered. The strict locally Lipschitz homogeneous Lyapunov function allows the possibility to...
In this paper, we analyze a formation control problem of two disk-shaped holonomic mobile robots without collision each other. We show that the tracking control problem can be reduced to sample stabilization of the origin of the nonlinear system defined on noncontractible manifold by exact linearization via coordinate transformation. We propose a tracking control method which is applying the Rifford-Sontag...
Wake homing guidance is the tracking guidance method that enables an underwater vehicle to follow the wake trajectory which a target ship remains. Because wake detection region by a wake sensor is not wide enough, wake is detected only when the vehicle get to near the wake. It cannot be known real wake trajectory, existing well-developed guidance method is not applicable, so it is needed to guidance...
This paper considers the problem of computing a Lyapunov function for nonlinear discrete-time systems. The proposed solution is systematic and consists of two steps. First, a pseudo-Lyapunov function, called finite-step Lyapunov function, is computed by solving a finite dimensional nonlinear optimization problem. Then, a recent converse theorem is employed, which gives an explicit construction of...
In this paper, we address the problem of controlled output synchronization of uncertain, nonlinear agents with relative degree one. Under the additional assumption that all agents are weakly minimum phase, it is well known that the agents are then feedback equivalent to a passive system. This feedback equivalence has been exploited by [1] to deal with output synchronization on strongly connected graphs,...
In this paper, a two-degree-of-freedom-control concept for a flexible single-link robot is considered offering trajectory tracking as well as vibration damping. The robot — a flexible link with tip mass attached to a moving cart — is modeled as distributed parameter system including structural damping. The proposed forward controller is designed based on the exact modal approximation of the system...
This paper studies global synchronization between a heterogeneous dynamical network and a known target trajectory via distributed impulsive control. Synchronization with an error level, called quasi-synchronization, is analyzed by utilizing the time-varying Lyapunov function. Some sufficient quasi-synchronization conditions are presented and explicit expressions of error levels are derived. Furthermore,...
This paper concerns the trajectory tracking control for AGV. Considering the differences between the simulation and the practical situation and to improve the performance of AGV, this paper proposes a novel tracking control method for AGV. After presenting the kinematical model of AGV, the method proposed is explicated. In minimizing the time spent, the method, which is applicable for any given tracking...
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