Positive-realness analysis of sampled-data systems and its applications

In this paper, we first study strong positive-realness of sampled-data systems and introduce a measure called positive-realness gap index. We show that this index can be computed efficiently with a bisection method, and provide state space formulas for its computation. The importance of this index lies in that it is useful for robust stability analysis of sampled-data systems. An iterative procedure for computing an exact robust stability margin is given and illustrated through a numerical example.     

Ellipsoidal parameter or state estimation under model uncertainty

Ellipsoidal outer-bounding of the set of all feasible state vectors under model uncertainty is a natural extension of state estimation for deterministic models with unknown-but-bounded state perturbations and measurement noise. The technique described in this paper applies to linear discrete-time dynamic systems; it can also be applied to weakly non-linear systems if non-linearity is replaced by uncertainty. Many difficulties arise because of the non-convexity of feasible sets. Combined quadratic constraints on model uncertainty and additive disturbances are considered in order to simplify the analysis. Analytical optimal or suboptimal solutions of the basic problems involved in parameter or state estimation are presented, which are counterparts in this context of uncertain models to classical approximations of the sum and intersection of ellipsoids. The results obtained for combined quadratic constraints are extended to other types of model uncertainty.     

Decentralized overlapping control of a formation of unmanned aerial vehicles

Decentralized overlapping feedback laws are designed for a formation of unmanned aerial vehicles. The dynamic model of the formation with an information structure constraint in which each vehicle, except the leader, only detects the vehicle directly in front of it, is treated as an interconnected system with overlapping subsystems. Using the mathematical framework of the inclusion principle, the interconnected system is expanded into a higher dimensional space in which the subsystems appear to be disjoint. Then, at each subsystem, a static state feedback controller is designed to robustly stabilize the perturbed nominal dynamics of the subsystem. The design procedure is based on the application of convex optimization tools involving linear matrix inequalities. As a final step, the decentralized controllers are contracted back to the original interconnected system for implementation.     

Nonlinear system fault diagnosis based on adaptive estimation

An approach to fault diagnosis for a class of nonlinear systems is proposed in this paper. It is based on a new adaptive estimation algorithm for recursive estimation of the parameters related to faults. This algorithm is designed in a constructive manner through a nontrivial combination of a high gain observer and a recently developed linear adaptive observer, without resort to any linearization. Its global exponential convergence is ensured by an easy-to-check persistent excitation condition. A numerical example is presented for illustration.     

Nonlinear adaptive control for bioreactors with unknown kinetics

We consider a control problem for a single bioreaction occurring in a continuous and well-mixed bioreactor, assuming that the bioreaction's kinetics is not represented by a validated model. We develop a nonlinear controller and prove the global asymptotic stability of the closed-loop system towards the equilibrium corresponding to the set point. Since this control law needs the knowledge of some parameters, we derive an adaptive version of the nonlinear controller and prove again the global asymptotic stability of the closed-loop system. Finally, we show the relevance of our approach on a real-life wastewater treatment plant.     

Iterative learning control design based on composite energy function with input saturation

In this work, an iterative learning control scheme is designed for a class of nonlinear uncertain systems with input saturation. The analysis of convergence in the iteration domain is based on composite energy function, which consists of both input and state information along the time and iteration axes. Through rigorous analysis, the learning convergence in the iteration domain can be guaranteed under the input saturation, provided the desired trajectory is realizable within the saturation bound.     

Assessing the quality of identified models through the asymptotic theory—when is the result reliable?

In this paper, the problem of estimating uncertainty regions for identified models is considered. A typical approach in this context is to resort to the asymptotic theory of Prediction Error Methods for system identification, by means of which ellipsoidal uncertainty regions can be constructed for the uncertain parameters.We show that the uncertainty regions worked out through the asymptotic theory can be unreliable in certain situations, precisely characterized in the paper.Then, we critically analyze the theoretical conditions for the validity of the asymptotic theory, and prove that the asymptotic theory also applies under new assumptions which are less restrictive than the usually required ones. Thanks to this result, we single out the classes of models among standard ones (ARX, ARMAX, Box-Jenkins, etc.) where the asymptotic theory can be safely used in practical applications to assess the quality of the identified model.These results are of interest in many applications, including iterative controller design schemes.     

Feedback passivity of nonlinear discrete-time systems with direct input-output link

This paper is devoted to the study of the feedback passivity property in nonlinear discrete-time systems. The relative degree and zero dynamics of the non-passive system are related to the feedback passivity of the system. Two main results are presented. First, some relative degree-related properties of passive systems in general form are stated. Second, sufficient conditions in order to render a multiple-input multiple-output (MIMO) system passive by means of a static state feedback control law are obtained.     

Nonlinear optimal tracking control with application to super-tankers for autopilot design

A new method is introduced to design optimal tracking controllers for a general class of nonlinear systems. A recently developed recursive approximation theory is applied to solve the nonlinear optimal tracking control problem explicitly by classical means. This reduces the nonlinear problem to a sequence of linear-quadratic and time-varying approximating problems which, under very mild conditions, globally converge in the limit to the nonlinear systems considered. The converged control input from the approximating sequence is then applied to the nonlinear system. The method is used to design an autopilot for the ESSO 190,000-dwt oil tanker. This multi-input-multi-output nonlinear super-tanker model is well established in the literature and represents a challenging problem for control design, where the design requirement is to follow a commanded maneuver at a desired speed. The performance index is selected so as to minimize: (a) the tracking error for a desired course heading, and (b) the rudder deflection angle to ensure that actuators operate within their operating limits. This will present a trade-off between accurate tracking and reduced actuator usage (fuel consumption) as they are both mutually dependent on each other. Simulations of the nonlinear super-tanker control model are conducted to illustrate the effectiveness of the nonlinear tracking controller.     

CAD modeling for the components made of multi heterogeneous materials and smart materials

There appear more critical requirements for special functions of components/products in various areas, which can be satisfied only by using heterogeneous materials and/or smart materials. The heterogeneous materials include composite materials, functionally graded materials, and heterogeneous materials with a periodic microstructure. To design and manufacture the components made of these materials, the computer models for representing them need first to be built so that further analysis, optimization and manufacturing can be implemented based on the models. This paper develops such a modeling method, which can be implemented by employing the functions of current CAD graphic software and obtain the model that includes all the material information (about periodic microstructures, constituent composition, inclusions, and embedded parts) along with geometry information in 3D solid modeling without the problem arising from too much data.