Continuous Static State Feedback Research Articles

Nonholonomic system control via particle swarm optimization of a neural‐aided direct gradient descent control

AbstractIt is well known that the class of nonholonomic systems cannot be asymptotically stabilized by continuous static state feedback controls. It has been reported that the so‐called direct gradient descent control (DGDC) is able to stabilize nonholonomic systems. This article attempts to improve the performance of the DGDC by using neural network (NN) and particle swarm optimization (PSO). A control method is proposed by embedding an NN into the control law derived by the original DGDC. PSO is employed in order to search globally the parameters of the controller without requiring a redesign process of the parameters. To verify the method, the control problems of two typical nonholonomic systems, one being a wheeled mobile robot and the other a rotary crane system, are considered under constraints applied to the systems. Comparative performance tests are carried out, showing that the proposed approach outperforms the original method and a neurocontroller. Also, simulations show that the proposed method is able to control the systems effectively under the given constraints without the need of the redesign process. © 2011 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Stabilizability and Motion Tracking Conditions for Mechanical Nonholonomic Control Systems

This paper addresses formulation of stabilizability and motion tracking conditions for mechanical systems from the point of view of constraints put on them. We present a new classification of constraints, which includes nonholonomic constraints that arise in both mechanics and control. Based on our classification we develop kinematic and dynamic control models of systems subjected to these constraints. We demonstrate that a property of being a “hard-to-control” nonholonomic system may not be related to the nature of the constraints. It may result from the formulation of control objectives for a system. We examine two control objectives which are stabilization to the target equilibrium by a continuous static state feedback control and motion tracking. Theory is illustrated with examples of control objective formulations for systems with constraints of various types.

Continuous stabilization controllers for singular bilinear systems: The state feedback case

Global asymptotic stabilization for a class of singular bilinear systems is first studied in this paper. New approaches are developed by means of the LaSalle invariant principle for nonlinear systems. A new set of sufficient condition is first derived via the continuous static state feedback, the feedback not only guarantees the existence of solution but also the global asymptotical stabilization for the closed loop system.

VSS-version of energy-based control for swinging up a pendulum

A new algorithm ensuring global attractivity of the upright (unstable) equilibrium of a pendulum, based on the variable structure system-version of the energy-speed-gradient method, is proposed. It is shown that global attractivity cannot be obtained with continuous static state feedback. A detailed global analysis of the transient behavior of the closed loop system is presented. In addition, it is shown that the global attractivity of the upright equilibrium can be achieved by applying a control of arbitrarily small magnitude.

Local stabilization and controllability of a class of non-triangular nonlinear systems

This paper considers the problems of local asymptotic stabilization using continuous static state feedback (LCFS) and small time local controllability (STLC) of single-input nonlinear systems. A specific class of nontriangular systems, called the essentially triangular form, is introduced. For this class of systems sufficient conditions for LCFS and necessary and sufficient conditions for STLC are obtained. In particular, it is shown that STLC implies LCFS. A motivating physical example of the ETF system is presented.

Design of Continuous Stabilizing Control Laws for Nonlinear Triangular Systems

For a class of systems that can not be smoothly stabilized, a constructive method for the design of continuous stabilizing control laws is proposed. Its theoretical justification is briefly discussed. Then, a set of worked examples is studied and simulated, to demonstrate the main features of the method. In particular, the model of an underactuated weakly coupled mechanical system is shown to be stabilizable by continuous static state feedback.

On the relation between local controllability and stabilizability for a class of nonlinear systems

The problem of local stabilizability of locally controllable nonlinear systems is considered. It is well known that, contrary to the linear case, local controllability does not necessarily imply stabilizability. A class of nonlinear systems for which local controllability implies local asymptotic stabilizability using continuous static-state feedback is described, as for this class of systems the well-known Hermes controllability condition is necessary and sufficient for local controllability.

Triangular Forms, Local Controllability and Stabilizability of Single-Input Nonlinear Systems

A rather complete treatment of the problem of the local state equivalence of single-input nonlinear system to several types of triangular form systems and its relation with local controllability and stabilizability is presented here. A set of necessary and sufficient condition for the small time local controllability and continuous static state feedback stabilizability of triangular form system is obtained. Geometric version of these results is provided as well. Various examples illustrate the results obtained.

Time-State Control Form and its Application to a Non-Holonomic Space Robot

Many non-holonomic systems, such as vehicles and space robots, are modeled in state equations which can not be stabilized with continuous static state feedback. Thus, we can not design stabilizing controllers for such systems using conventional methods.For vehicle control, feedback position controllers for multi-trailer systems were proposed by Sørdalen and Canudas de Wit (1992a),(1992b). But their works are restricted to systems which can be represented in the chained form. For space robots, a motion planning method using bidirectional search was proposed by Nakamura and Mukherjee (1991), but the feedback stabilizing controller for space robots has not been discussed yet.On the other hand, the authors proposed the time-state control form and used it for the position control of multi-trailer systems(Sampei, 1994). It was also shown that the proposed strategy can also be used for the system which can not be transformed into the chained form.In this paper, we will show that this control strategy can be applied to a space robot. We will show, in simulation, that our control strategy allows us to control the position of a space robot. This is the first feedback control strategy for space robots.