Singular controls for port-Hamiltonian systems (Theory of singularities of smooth mappings and around it)

"Theory of singularities of smooth mappings and around it". November 25～29, 2013. edited by Takashi Nishimura. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.The port-Hamiltonian system is a generalized Hamiltonian system and is regarded as an especial input-output control system. We see the port-Hamiltonian systems from the viewpoint of geometric control theory. Controllability and observability are basic concepts in control theory and important for system design. Singular controls play an important role in a control system, especially in the sense of optimal control problem. We see the following properties are equivalent for linear port-Hamiltonian systems: controllability, observability and nonexistence of singular control

A Satisfiability Modulo Theory Approach to Secure State Reconstruction in Differentially Flat Systems Under Sensor Attacks

We address the problem of estimating the state of a differentially flat system from measurements that may be corrupted by an adversarial attack. In cyber-physical systems, malicious attacks can directly compromise the system's sensors or manipulate the communication between sensors and controllers. We consider attacks that only corrupt a subset of sensor measurements. We show that the possibility of reconstructing the state under such attacks is characterized by a suitable generalization of the notion of s-sparse observability, previously introduced by some of the authors in the linear case. We also extend our previous work on the use of Satisfiability Modulo Theory solvers to estimate the state under sensor attacks to the context of differentially flat systems. The effectiveness of our approach is illustrated on the problem of controlling a quadrotor under sensor attacks.Comment: arXiv admin note: text overlap with arXiv:1412.432

A probabilistic algorithm to test local algebraic observability in polynomial time

The following questions are often encountered in system and control theory. Given an algebraic model of a physical process, which variables can be, in theory, deduced from the input-output behavior of an experiment? How many of the remaining variables should we assume to be known in order to determine all the others? These questions are parts of the \emph{local algebraic observability} problem which is concerned with the existence of a non trivial Lie subalgebra of the symmetries of the model letting the inputs and the outputs invariant. We present a \emph{probabilistic seminumerical} algorithm that proposes a solution to this problem in \emph{polynomial time}. A bound for the necessary number of arithmetic operations on the rational field is presented. This bound is polynomial in the \emph{complexity of evaluation} of the model and in the number of variables. Furthermore, we show that the \emph{size} of the integers involved in the computations is polynomial in the number of variables and in the degree of the differential system. Last, we estimate the probability of success of our algorithm and we present some benchmarks from our Maple implementation.Comment: 26 pages. A Maple implementation is availabl

Rational interpolation and state-variable realizations

AbstractThe problem is considered of passing from interpolation data for a real rational transfer-function matrix to a minimal state-variable realization of the transfer-function matrix. The tool is a Loewner matrix, which is a generalization of the Standard Hankel matrix of linear system realization theory, and which possesses a decomposition into a product of generalized observability and controllability matrices

State Observability in Presence of Disturbances: the Analytic Solution and its Application in Robotics

International audience— This paper presents the analytic solution of a fundamental open problem in the framework of state esti-mation/nonlinear observability, which is the Unknown Input Observability problem (UIO problem). The problem consists in deriving the analytic criterion that allows us to automatically obtain the state observability in presence of disturbances (or unknown inputs). In other words, the problem is to extend the well known observability rank condition to the case when the dynamics are also driven by unknown inputs. Enunciated in the seventies by the control theory community, this problem was only solved in the linear case. The solution here provided holds for nonlinear systems in presence of a single unknown input. The first part of the paper presents this analytic solution. Very surprisingly, the complexity of the overall analytic criterion is comparable to the complexity of the observability rank condition. The second part of the paper applies this analytic criterion to a robotics system when its dynamics are affected by an external disturbance (e.g., due to the presence of wind). To corroborate the results of our observability analysis we perform extensive simulations and we show that, a simple estimator based on an Extended Kalman Filter, provides results that agree with what we could expect from the observability analysis

Approximate Input-Output Linearization of Nonlinear Systems Using the Observability Normal Form

Abstract The problem of controlling nonlinear nonminimum-phase systems is considered, where standard input-output feedback linearization leads to unstable internal dynamics. This problem is handled here by using the observability normal form in conjunction with input-output linearization. The system is feedback linearized upon neglecting a part of the system dynamics, with the neglected part being considered as a perturbation. A linear controller is designed to accommodate the perturbation resulting from the approximation. Stability analysis is provided based on the vanishing perturbation theory