Antonio Loria

Relaxed persistency of excitation for uniform asymptotic stability

The persistency of excitation property is crucial for the stability analysis of parameter identification algorithms and adaptive control loops. We propose a relaxed definition of persistency of excitation and we use it to establish uniform global asymptotic stability (UGAS) for a large class of nonlinear, time-varying systems. Our relaxed definition is conceptually equivalent to the definition introduced in Loria et al. (1999), but is easier to verify. It is useful for stability analysis of nonlinear systems that arise, for example, in nonlinear adaptive control, stabilization of nonholonomic systems, and tracking control. Our proof of UGAS relies on some integral characterizations of UGAS established in Teel et al. (2000). These characterizations also streamline the proof of UGAS in the presence of (uniform) classical persistency of excitation.

Uniform exponential stability of linear time-varying systems: revisited

Abstract Some classical results known in the adaptive control literature are often used as analysis tools for nonlinear systems by evaluating the nonlinear differential equations along trajectories. While this technique is widely used, as we remark through examples, one must take special care in the consideration of the initial conditions in order to conclude uniform convergence. One way of taking care explicitly of the initial conditions is to study parameterized linear time-varying systems. This paper re-establishes known results for linear time-varying systems via new techniques while stressing the importance of imposing that the formulated sufficient and necessary conditions must hold uniformly in the parameter. Our proofs are based on modern tools which can be interpreted as an “integral” version of Lyapunov theorems; rather than on the concept of uniform complete observability which is most common in the literature.

A separation principle for dynamic positioning of ships: theoretical and experimental results

Presents a globally asymptotically stabilizing (GAS) controller for regulation and dynamic positioning of ships, using only position measurements. It is assumed that these are corrupted with white noise hence a passive observer which reconstructs the rest of the states is applied. The observer produces noise-free estimates of the position, the slowly varying environmental disturbances and the velocity which are used in a proportional-derivative (PD)-type control law. The stability proof is based on a separation principle which holds for the nonlinear ship model. This separation principle is theoretically supported by results on cascaded nonlinear systems and standard Lyapunov theory, and it is validated in practice by experimentation with a model ship scale 1:70.

Brief Growth rate conditions for uniform asymptotic stability of cascaded time-varying systems

In the last decade several results on cascaded autonomous systems have appeared in the literature. The sufficient conditions for the stability and stabilizability of these systems are often related to certain growth rate conditions on the functions which define the dynamics of the system. In this paper we analyze three complementary classes of nonlinear time-varying systems according to these growth rates. For each case, we give further results to guarantee uniform global asymptotic stability of the cascade and relate our contributions to input-to-state stability and other growth rate conditions previously reported. The advantage of this type of analysis is that it is often easier to verify such conditions than to find a Lyapunov function with a negative-definite derivative.

Exponential tracking control of a mobile car using a cascaded approach

Abstract In this paper we address the problem of designing simple global tracking controllers for a kinematic model of a mobile robot and a simple dynamic model of a mobile robot. For this we use a cascaded systems approach, resulting into linear controllers that yield global K-exponential stability of the closed loop system.

Integral Characterizations of Uniform Asymptotic and Exponential Stability with Applications

Abstract. We present integral characterizations of uniform asymptotic stability and uniform exponential stability for differential equations and inclusions. These characterizations are used to establish new results on concluding uniform global asymptotic stability when uniform global stability is already known and uniform convergence must be established by additional arguments. In one case we generalize Matrosovs theorem on the use of a differentiable auxiliary function. In another case we draw conclusions from a system related to the original by suitable output injection.

Global Tracking Control of One Degree of Freedom Euler-Lagrange Systems without Velocity Measurements

The problem of global outputfeedback tracking control of robot manipulators has been open for several years. In this short note we propose a computed torque plus (nonlinear) PD-like controller to solve the output feedback tracking control problem ofone degree of freedom (dof) Euler-Lagrange (EL) systems. We prove in this case global asymptotic stability. Our approach is the extension ofour previous semi-global result (Loria and Ortega, Appl Math Comp Sci 1995; 5:2, 101–113 [1]). Even though we can not claim the same result for systems of more than one dol, as far as we know, none of the semi-global solutions present in the literature has been proved to be global even for one dof systems.

Brief paper: Spacecraft relative rotation tracking without angular velocity measurements

We present a solution to the problem of tracking relative rotation in a leader-follower spacecraft formation using feedback from relative attitude only. The controller incorporates an approximate-differentiation filter to account for the unmeasured angular velocity. We show uniform practical asymptotic stability (UPAS) of the closed-loop system. For simplicity, we assume that the leader is controlled and that we know orbital perturbations; however, this assumption can be easily relaxed to boundedness without degrading the stability property. We also assume that angular velocities of spacecraft relative to an inertial frame are bounded. Simulation results of a leader-follower spacecraft formation using the proposed controller structure are also presented.

/spl delta/-persistency of excitation: a necessary and sufficient condition for uniform attractivity

In previous papers we have introduced a sufficient condition for uniform attractivity of the origin of a class of nonlinear time-varying systems which is stated in terms of persistency of excitation (PE), a concept well known in the adaptive control and systems identification literature. The novelty of our condition, called uniform /spl delta/-PE, is that it is tailored for nonlinear functions of time and state and it allows us to prove uniform asymptotic stability. In this paper we present a new definition of u/spl delta/-PE which is conceptually equivalent to but technically different from its predecessors. We make connections between this property and similar properties previously used in the literature. We also show when this condition is necessary and sufficient for uniform (global) asymptotic stability for a large class of nonlinear time-varying systems.

Adaptive Tracking Control of Chaotic Systems With Applications to Synchronization

We address the problem of controlled synchronization of a class of uncertain chaotic systems. Our approach follows techniques of adaptive tracking control and identification of dynamic systems from recent developments of control theory. In particular, we use new notions of the so-called property of persistency of excitation - known to be sufficient and necessary for parameter estimation - to construct adaptive algorithms that ensure perfect tracking/synchronization and parameter estimation of chaotic systems with parameter uncertainty. Our theoretical findings are supported by particular examples and simulation studies on systems such as the Lorenz and Rossler oscillators and the Duffing equation.