Liu Hsu

Variable structure model reference adaptive control using only input and output measurements

Abstract A variable structure model reference adaptive controller (VS-MRAC) using only the input and output measurements of the plant is proposed. Stability and transient properties are analysed and discussed. Remarkable transient behaviour is revealed, in particular, model following can be perfectly achieved in a finite time. The effect of plant input disturbance is investigated and the performance of the VS controller is also shown to be qualitatively superior to that obtained with (conventional) integral adaptation algorithms. A link between the VS-MRAC and the conventional MRAC is suggested. Simulations are presented to highlight the theoretical results.

LMI characterization of structural and robust stability

Abstract This paper introduces several stability conditions for a given class of matrices expressed in terms of Linear Matrix Inequalities (LMI), being thus simply and efficiently computable. Diagonal and simultaneous stability, both characterized by polytopes of matrices, are addressed. Using this approach a method particularly attractive to test a given matrix for D-stability is proposed. Lyapunov parameter dependent functions are built in order to reduce conservativeness of the stability conditions. The key idea is to relate Hurwitz stability with a positive realness condition.

Analysis and design of I/O based variable structure adaptive control

This paper presents an overview of a technique for the design of variable structure model reference adaptive control (VS-MRAC) systems, using only input-output data. The main ideas underlying the design and the analysis, as well as the main properties of the controller, are described having as point of departure a well known parameter adaptive MRAC scheme. Then, asymptotic properties of the VS-MRAC system are established taking into account the effect of the averaging filters necessary to implement some equivalent control signals. In particular, global exponential stability of the associated error system with respect to a small residual set is demonstrated. The effect of linear zones in the relay functions is assessed showing that they can alleviate the chattering phenomena. This is related with the fact that the VS-MRAC has a high-gain stability property. A procedure for noise sensitivity reduction is also proposed. Simulations illustrate the very satisfactory performance of the VS-MRAC in adverse operating conditions. >

LMI characterization of structural and robust stability: the discrete-time case☆

Abstract This paper extends to the discrete-time case some robust stability conditions, recently obtained for continuous-time systems. Those conditions are expressed in terms of Linear Matrix Inequalities (LMI), being thus simply and efficiently computable. As in the continuous-time case, parameter-dependent Lyapunov functions can be constructed and, consequently, the new approach can yield much sharper and less conservative results than the simultaneous stability approach. In particular, well-known stability problems, namely, D-stability and robust stability in the presence of diagonally structured uncertainty can be more efficiently addressed. Numerical examples are included to illustrate the advantages of the new stability conditions.

Two solutions to the adaptive visual servoing problem

We present two globally convergent vision-based position controllers for a planar two-links manipulator in the so-called fixed-camera configuration, where the camera orientation and scale factor are considered unknown. This is a basic adaptive visual servoing problem whose solution was hampered by the nonlinear dependence of the system dynamics on the unknown parameters. The controller design techniques of immersion and invariance and nonlinear proportional integral (PI) are used to derive the smooth adaptive schemes that ensure global asymptotic regulation without overparameterization, projections, or persistency of excitation assumptions. In the case of tracking, we establish error bounds that are reduced, eventually to zero, as the speed of the reference trajectory decreases, and with improved prior knowledge on the camera scale factor, for the immersion and invariance controller, or increasing a tuning gain for the nonlinear PI. The efficacy of the approaches is shown through simulations.

Output-feedback model-reference sliding mode control of uncertain multivariable systems

This note considers the robust output tracking problem using a model-reference sliding mode controller for linear multivariable systems of relative degree one. It is shown that the closed loop system is globally exponentially stable and the performance is insensitive to bounded input disturbances and parameter uncertainties. The strategy is based on output-feedback unit vector control to generate sliding mode. The only required a priori information about the plant high frequency gain matrix K/sub p/ is the knowledge of a matrix S/sub p/ such that -K/sub p/S/sub p/ is Hurwitz which relaxes the positive definiteness requirement usually needed by other methods.

Adaptive visual tracking with uncertain manipulator dynamics and uncalibrated camera

A control-theoretic solution is proposed for designing a stable visual servoing adaptive controller for a planar robot manipulator based on a monocular and fixed camera. The controller should allow tracking of a moving target, under uncertain knowledge of the robot/camera parameters. In order to solve the direct parameter adaptive problem related with the camera calibration uncertainty, a novel stable adaptation scheme is introduced. The scheme is then combined with a robust or adaptive controller for the manipulator, taking into account its nonlinear dynamics, leading to an overall stable adaptive system.

Variable structure adaptive cascade control of rigid-link electrically-driven robot manipulators

This paper addresses the design of adaptive tracking control of rigid-link electrically-driven robot manipulators, in the case of arbitrary uncertain mechanical and electrical parameters of the robot model. A strategy based on cascade central is presented combining an adaptive scheme for rigid-link robot control with a variable-structure control law for actuator control. Global asymptotic stability is ensured and the very satisfactory performance achieved is illustrated by a simulation example.<<ETX>>

Achieving global convergence to an equilibrium population in predator–prey systems by the use of a discontinuous harvesting policy

Abstract This paper analyses the dynamics of two predator–prey models, namely, Lotka–Volterra and Leslie–Gower, when submitted to a specific harvesting schedule known as the weighted escapement policy. The main goal is to show that global stability of a desired equilibrium population can be achieved by the application of simple switching controls, chosen in accordance with variable structure system theory. A qualitative analysis shows that the global stability depends on the existence of virtual equilibrium points which in turn is ensured by a suitable choice of the control parameters.

Bursting phenomena in continuous-time adaptive systems with a &#963; -modification

Recently, the introduction of a kind of forgetting factor, called σ-modification, in the adaptation law for continuous-time systems was proposed to improve the adaptive system robustness. However, this paper shows that, similarly to the diserete-time case, bursting phenomena may occur solely due to the forgetting factor.