E.B. Castelan

Control design for linear systems with saturating actuators and /spl Lscr//sub 2/-bounded disturbances

This paper addresses the problem of synthesis of state feedback control laws for systems subject to /spl Lscr//sub 2/-bounded disturbances in presence of saturating actuators. Conditions that allow to guarantee both the internal and external stability of the closed-loop system are proposed. They are formulated from the use of the Finslers lemma and a generalized sector non-linearity description. This approach allows to introduce new variables (multipliers) in the problem which increase the degrees of freedom in the synthesis problem. Based on the stability conditions, a multiobjective problem is addressed: the synthesis of a state feedback gain that simultaneously maximizes the magnitude of the admissible /spl Lscr//sub 2/-disturbance and the size of the domain of stability of the closed-loop system.

Stability and stabilization of a class of nonlinear systems with saturating actuators

Abstract This paper addresses the problem of controlling a certain class of continuous-time nonlinear systems subject to actuator saturations. The design of state feedback gains is done by considering a modelling of the nonlinear saturated system through deadzone nonlinearities satisfying a modified sector condition , which encompasses the classical sector-nonlinearity condition considered in previous works.

Absolute stabilization of discrete-time systems with a sector bounded nonlinearity under control saturations

This paper presents some results on absolute stabilization of nonlinear discrete-time systems under control saturations. The studied control law consists of the feedback of both the states and of the nonlinearity present in the dynamics of the controlled system. Saturations are taken into account by modelling the nonlinear saturated system through deadzone nonlinearities satisfying a modified sector condition. Thus, as for continuous-time systems, LMI absolute stabilization conditions are proposed for the design of the feedback gains, both in the local and global stability contexts. Some relations of the proposed results with the dissipativity and passivity theory are included and a numerical example is reported

Friction Compensation in Flexible Joints Robot with GMS Model: Identification, Control and Experimental Results

Abstract In this paper the position control of robot manipulators considering joint flexibilities and friction compensation is presented. For the control purposes a cascade control strategy is presented and the friction compensation is described using the Generalized Maxwell-Slip (GMS) model. The GMS parameters are identified and a friction observer based on this model is proposed and incorporated to the cascade strategy so that the stability and performance can be improved. An experimental setup was constructed to validate the proposed control and friction compensation strategy: a planar two degrees of freedom robot with joint flexibilities prototype. The behavior of the cascade control with GMS model was tested in simulation and it was validated in the experimental setup.

Delay-independent robust stability conditions of neutral linear time-delay systems #

Abstract. Although published in the first part of the twentieth century, Finslers Lemma has shown to be a very attractive mathematical tool to treat stability of linear systems only recently. It is shown in this paper how this tool may be used to reformulate delay-independent stability conditions for neutral linear time-delay systems. The conditions allow, in particular, to construct parameter-dependent Lyapunov-Krasovskii functions for uncertain polytopic neutral systems. Extensions to stabilization problems can also be derived.

Neural Dynamic Control of a Nonholonomic Mobile Robot Incorporating the Actuator Dynamics

In this paper, a trajectory tracking control for a nonholonomic mobile robot by the integration of a kinematic controller and neural dynamic controller is investigated, where the wheel actuator (e.g., dc motor) dynamics is integrated with mobile robot dynamics and kinematics so that the actuator input voltages are the control inputs. The proposed neural dynamic controller (PNDC), based on the sliding mode theory, is applied to compensate the mobile robot dynamics, bounded unknown disturbances, and influence of payload. This controller is obtained by modeling the Radial Basis Functions Neural Networks (RBFNNs) of the centripetal and Coriolis matrix through of the inertia matrix of the mobile robot dynamics. Thus, PNDC is constituted of static RBFNNs only, what makes possible the reduction of the size of the RBFNNs, of the computational load and the implementation in real time. Stability analysis and numerical simulations are provided to show the effectiveness of the PNDC.

Stabilization of Discrete-Time Nonlinear Systems Subject to Input Saturations: A New Lyapunov Function Class

Abstract This paper addresses the problem of stabilization of discrete-time systems including a cone-bounded nonlinearity and a saturating actuator. In the sense of Lyapunov stability, we introduce a new candidate Lyapunov function which takes nonlinearity behavior into account. The local stability criterion is formulated as a set of Bilinear Matrix Inequalities (BMI) conditions. We present an optimization problem in order to guarantee the closed-loop stability aiming the largest basin of attraction, which may be nonconvex, and/or, nonconnected. Furthermore, a simple iterative algorithm is proposed in order to solve our BMI problem. Some numerical examples are presented to highlight the relevance of the new Lyapunov function in regard to the classical quadratic function.

LMI approach for L2-Control of linear systems with saturating actuators

Abstract This paper addresses the problem of controlling a continuous-time linear system subject to actuator saturations and to L 2 -bounded disturbances. We propose LMI conditions that allow to design a state feedback saturating control law in order to satisfy the closed-loop Input-to-State stability (ISS). By considering a quadratic candidate Lyapunov function, two particular tools are used to derive the LMI conditions: a modified sector condition , which encompasses the classical sector-nonlinearity condition considered in previous works, and Finsler’s Lemma , which allows to derive stabilization conditions which are potentially adapted to be cast into multiple objective control optimization problems. Relative to a previous work which proposed BMI conditions for treating a similar problem, the given LMI conditions allow to propose a more efficient convex programming design technique.

Pole assignment in a disk for linear systems by static output feedback

A systematic approach for pole assignment in a disk for continuous or discrete-time linear systems using a static output control law is proposed. It is shown that if the open-loop system satisfies certain structural conditions, a static output feedback gain can be easily computed, using a formula that simply involves the original system matrices and the parameters that define the disk. Among the conditions the system has to satisfy, the key one relies on a minimum phase argument. Square and non-square, proper and non-proper systems are considered. The main results are derived invoking the limiting behaviour of the optimal linear quadratic regulator for discrete-time systems. Some other implications are also presented.

NASH STRATEGY PARAMETER DEPENDENT CONTROL FOR POLYTOPIC SYSTEMS

Abstract This paper deals with designing Linear-Parameter Varying state feedback controls for systems including structured uncertainties described by a poly-tope, in the multiobjective framework. These controls are obtained by noncon-vex coupled Semi-Definite Programs for linear-quadratic nonzero-sum differential games on infinite time horizon. An example illustrates the proposed generic algorithm.