Difference algebra and system identification

The framework of differential algebra, especially Ritt’s algorithm, has turned out to be a useful tool when analyzing the identifiability of certain nonlinear continuous-time model structures. This framework provides conceptually interesting means to analyze complex nonlinear model structures via the much simpler linear regression models. One difficulty when working with continuous-time signals is dealing with white noise in nonlinear systems. In this paper, difference algebraic techniques, which mimic the differential-algebraic techniques, are presented. Besides making it possible to analyze discrete-time model structures, this opens up the possibility of dealing with noise. Unfortunately, the corresponding discrete-time identifiability results are not as conclusive as in continuous time. In addition, an alternative elimination scheme to Ritt’s algorithm will be formalized and the resulting algorithm is analyzed when applied to a special form of the nfir model structure.     

Reachability determination in acyclic Petri nets by cell enumeration approach

Reachability is one of the most important behavioral properties of Petri nets. We propose in this paper a novel approach for solving the fundamental equation in the reachability analysis of acyclic Petri nets, which has been known to be NP-complete. More specifically, by adopting a revised version of the cell enumeration method for an arrangement of hyperplanes in discrete geometry, we develop an efficient solution scheme to identify firing count vector solution(s) to the fundamental equation on a bounded integer set, with a complexity bound of O((nu)^n−m), where n is the number of transitions, m is the number of places and u is the upper bound of the number of firings for all individual transitions.     

Vision-based control for rigid body stabilization

This paper addresses the problem of stabilizing to a desired equilibrium point an eye-in-hand system, which consists of a single camera mounted on a rigid body free to move on . It is assumed that there is a collection of landmarks fixed in the environment and that the image coordinates of those landmarks are provided to the system by an on-board CCD camera. The proposed method addresses not only the problem of stabilization but also that of maintaining feature visibility along the system’s trajectory. The resulting solution consists of a feedback control law based on the current and desired image coordinates and reconstructed attitude and depth ratio information, which guarantees that (i) the desired equilibrium point is an almost global attractor; (ii) a set of necessary conditions for feature visibility holds throughout the system’s trajectories; and (iii) the image of a predefined feature point is kept inside the camera’s field of view.     

Feedback stabilization for high order feedforward nonlinear time-delay systems

This paper investigates the problem of global strong stabilization by state feedback, for a family of high order feedforward nonlinear time-delay systems. The uncertain nonlinearities are assumed to satisfy a polynomial growth assumption with an input or delayed input dependent rate. With the help of the appropriate Lyapunov–Krasovskii functionals, and a rescaling transformation with a gain to be tuned online by a dynamic equation, we propose a dynamic low gain state feedback control scheme. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.     

Identification and data-driven model reduction of state-space representations of lossless and dissipative systems from noise-free data

We illustrate procedures to identify a state-space representation of a lossless or dissipative system from a given noise-free trajectory; important special cases are passive systems and bounded-real systems. Computing a rank-revealing factorization of a Gramian-like matrix constructed from the data, a state sequence can be obtained; the state-space equations are then computed by solving a system of linear equations. This idea is also applied to perform model reduction by obtaining a balanced realization directly from data and truncating it to obtain a reduced-order model.     

Position USBL/DVL sensor-based navigation filter in the presence of unknown ocean currents

This paper presents a novel approach to the design of globally asymptotically stable (GAS) position and velocity filters for Autonomous Underwater Vehicles (AUVs) based directly on the sensor readings of an Ultra-short Baseline (USBL) acoustic array system and a Doppler Velocity Log (DVL). The proposed methodology is based on an equivalent linear time-varying (LTV) system that fully captures the dynamics of the nonlinear system, allowing for the use of powerful linear system analysis and filtering design tools that yield GAS filter error dynamics. Numerical results using Monte Carlo simulations and comparison to the Bayesian Cramér Rao Bound (BCRB) reveal that the performance of the proposed filter is tight to this theoretical estimation error lower bound. In comparison with other approaches, the present solution achieves the same level of performance of the Extended Kalman Filter (EKF), which does not offer GAS guarantees, and outperforms other classical filtering approaches designed in inertial coordinates instead of the body-fixed coordinate frame.     

Active fault tolerant control of discrete event systems using online diagnostics

The aim of this paper is to deal with the problem of fault tolerant control in the framework of discrete event systems modeled as automata. A fault tolerant controller is a controller able to satisfy control specifications both in nominal operation and after the occurrence of a fault. This task is solved by means of a parameterized controller that is suitably updated on the basis of the information provided by online diagnostics: the supervisor actively reacts to the detection of a malfunctioning component in order to eventually meet degraded control specifications. Starting from an appropriate model of the system, we recall the notion of safe diagnosability as a necessary step in order to achieve fault tolerant control. We then introduce two new notions: (i) “safe controllability”, which represents the capability, after the occurrence of a fault, of steering the system away from forbidden zones and (ii) “active fault tolerant system”, which is the property of safely continuing operation after faults. Finally, we show how the problem can be solved using a general control architecture based on the use of special kind of diagnoser, called “diagnosing controller”, which is used to safely detect faults and to switch between the nominal control policy and a bank of reconfigured control policies. A simple example is used to illustrate the new notions and the control architecture introduced in the paper.     

Stabilization of linear systems over networks with bounded packet loss and its use in model predictive control

This paper considers stabilization of discrete-time linear systems, where network exists for transmitting the sensor and controller information, and arbitrary bounded packet loss occurs in the sensor–controller link and the controller–actuator link. The stabilization of this system is transformed into the robust stabilization of a set of systems. The stability result for this system is specially applied on model predictive control (MPC) that explicitly considers the satisfaction of input and state constraints. Two synthesis approaches of MPC are presented, one parameterizing the infinite horizon control moves into a single state feedback law, the other into a free control move followed by the single state feedback law. Two simulation examples are given to illustrate the effectiveness of the proposed techniques.     

Using hash tables to manage the time-storage complexity in a point location problem: Application to explicit model predictive control

The online computational burden of linear model predictive control (MPC) can be moved offline by using multi-parametric programming, so-called explicit MPC. The solution to the explicit MPC problem is a piecewise affine (PWA) state feedback function defined over a polyhedral subdivision of the set of feasible states. The online evaluation of such a control law needs to determine the polyhedral region in which the current state lies. This procedure is called point location; its computational complexity is challenging, and determines the minimum possible sampling time of the system. A new flexible algorithm is proposed which enables the designer to trade off between time and storage complexities. Utilizing the concept of hash tables and the associated hash functions, the proposed method solves an aggregated point location problem that overcomes prohibitive complexity growth with the number of polyhedral regions, while the storage–processing trade-off can be optimized via scaling parameters. The flexibility and power of this approach is supported by several numerical examples.