Costanzo Manes

A new approach to state observation of nonlinear systems with delayed output

The article presents a new approach for the construction of a state observer for nonlinear systems when the output measurements are available for computations after a nonnegligible time delay. The proposed observer consists of a chain of observation algorithms reconstructing the system state at different delayed time instants (chain observer). Conditions are given for ensuring global exponential convergence to zero of the observation error for any given delay in the measurements. The implementation of the observer is simple and computer simulations demonstrate its effectiveness.

An observer for a class of nonlinear systems with time varying observation delay

Abstract This paper presents a state observer for drift observable nonlinear systems when output measurements are affected by a known and bounded time varying delay. The structure of the proposed observer is very simple and it is a generalization of an existing observer for undelayed systems. The observer exhibits good performance in estimating the system state also in the presence of significant measurement delays. The technique used to prove the asymptotical convergence to zero of the observation error, based on the Lyapunov–Razumikhin approach, does not require any assumption about the dependence of the delay on the time.

Polynomial extended Kalman filter

This work presents a polynomial version of the well-known extended Kalman filter (EKF) for the state estimation of nonlinear discrete-time stochastic systems. The proposed filter, denoted polynomial EKF (PEKF), consists in the application of the optimal polynomial filter of a chosen degree /spl mu/ to the Carleman approximation of a nonlinear system. When /spl mu/=1 the PEKF algorithm coincides with the standard EKF. For the filter implementation the moments of the state and output noises up to order 2/spl mu/ are required. Numerical simulations compare the performances of the PEKF with those of some other existing filters, showing significant improvements.

Design of state observers from a drift-observability property

In this paper, the problem of state observation with exponential error decay for nonlinear systems affine in the input is considered and an observer is proposed. For such an observer, the drift-observability property of the system (i.e., observability for zero input), together with an assumption on the input amplitude or on the observation relative degree, are sufficient conditions for exponential convergence of the observation error. The existence of an exponential observer is correlated to the existence of a solution for an H/sub /spl infin// Riccati-like inequality. Global and semiglobal convergence results are presented.

Local asymptotic stability for nonlinear state feedback delay systems

In previous papers the authors presented an elementary theory for feedback control of nonlinear delay systems, in which methods of standard nonlinear analysis were used to solve control problems such as output regulation and tracking, disturbance decoupling and model matching for a class of nonlinear delay systems. Output control was obtained by means of state feedback control laws, but nothing was said about the behavior of the system state. In this paper some results have been obtained about this problem. It is proved that if the output and its derivatives up to a given order are driven to zero, and if the system owns a certain Lipschitz property in a suitable neighborhood of the origin, and the initial state is inside such neighborhood, then the system state asymptotically goes to zero. Simulations on nonlinear delay systems unstable in open loop match the theoretical results.

A state observer for nonlinear dynamical systems

The problem of state observation for nonlinear systems is of main importance in automatic control. In recent years many contributions have been presented in literature that solve the design problem for classes of nonlinear systems. Most works can be roughly classi ed into two categories. In one the geometrical properties of vector elds de ning the system are exploited, and therefore mathematical tools of the di®erential geometry are extensively employed. In the other one the functional properties of the input-state and state-output maps which de ne the system are mainly used. While the geometrical methods often provide a general solution of the problem for systems that belong to restricted classes, characterized by geometrical properties [1,2,3,4,5,6,7,13,14,17,18,19], the second approach gives solutions for classes of nonlinear systems whose geometrical nature is not investigated and only macroscopic parameters (norms, gains, Lipschitz constants and so on) are involved in the design procedure [8,9,11,12,21]. One main problem in state observation for nonlinear systems is that the property of driftobservability does not imply observability for any input function, as shown in [16,19]. Thus it is interesting to investigate when the drift-observability property allows the solution of the state observation problem, nding conditions that restricts the class of input functions. Due to the mathematical tools employed, this work may be considered as belonging to both the categories above mentioned. In this paper nonlinear systems of the form

Filtering of Stochastic Nonlinear Differential Systems via a Carleman Approximation Approach

This paper deals with the state estimation problem for stochastic nonlinear differential systems, driven by standard Wiener processes, and presents a filter that is a generalization of the classical extended kalman-bucy filter (EKBF). While the EKBF is designed on the basis of a first order approximation of the system around the current estimate, the proposed filter exploits a Carleman-like approximation of a chosen degree v ges 1. The approximation procedure, applied to both the state and the measurement equations, allows to define an approximate representation of the system by means of a bilinear system, for which a filtering algorithm is available from the literature. Numerical simulations on an example show the improvement, in terms of sample error covariance, of the filter based on the first-order, second-order and third-order system approximations (v = 1,2,3).

A CHAIN OBSERVER FOR NONLINEAR SYSTEMS WITH MULTIPLE TIME-VARYING MEASUREMENT DELAYS ∗

This paper presents a method for designing state observers with exponential error decay for nonlinear systems whose output measurements are affected by known time-varying delays. A modular approach is followed, where subobservers are connected in cascade to achieve a desired exponential convergence rate (chain observer). When the delay is small, a single-step observer is sufficient to carry out the goal. Two or more subobservers are needed in the the presence of large delays. The observer employs delay-dependent time-varying gains to achieve the desired exponential error decay. The proposed approach allows to deal with vector output measurements, where each output component can be affected by a different delay. Relationships among the error decay rate, the bound on the measurement delays, the observer gains, and the Lipschitz constants of the system are presented. The method is illustrated on the synchronization problem of continuous-time hyperchaotic systems with buffered measurements.

Hybrid Force-Position Control for Robots in Contact with Dynamic Environments

Abstract A generalization of the hybrid force-position approach for controlling robots in contact with dynamic environments is presented. Classical hybrid control applies only when the environment is supposed to be stiff, acting as a kinematic constraint on the robot end-effector, and relies on the orthogonality of admissible end-effector velocities with respect to reaction forces. When considering dynamic environments, this orthogonality does not hold anymore. In order to extend the hybrid strategy to cases when the environment, besides possibly imposing kinematic constraints on the end-effector, exhibits also a dynamic behavior, a suitable description of the robot-environment interaction is introduced. In this setting, the design of a hybrid controller can be carried out so to independently handle quantities in complementary subspaces. As an interesting result, two alternative hybrid schemes arise, since either forces or positions can be controlled along properly defined dynamic directions. Issues related to planning of nominal trajectories and filtering of actual measures so to fit them with the available interaction model are also discussed.

A Twofold Spline Approximation for Finite Horizon LQG Control of Hereditary Systems

In this paper an approximation scheme is developed for the solution of the linear quadratic Gaussian (LQG) control on a finite time interval for hereditary systems with multiple noncommensurate delays and distributed delay. The solution here proposed is achieved by means of two approximating subspaces: the first one to approximate the Riccati equation for control and the second one to approximate the filtering equations. Since the approximating subspaces have finite dimension, the resulting equations can be implemented. The convergence of the approximated control law to the optimal one is proved. Simulation results are reported on a wind tunnel model, showing the high performance of the method.