Robust State Space Filtering under Incremental Model Perturbations Subject to a Relative Entropy Tolerance

This paper considers robust filtering for a nominal Gaussian state-space model, when a relative entropy tolerance is applied to each time increment of a dynamical model. The problem is formulated as a dynamic minimax game where the maximizer adopts a myopic strategy. This game is shown to admit a saddle point whose structure is characterized by applying and extending results presented earlier in [1] for static least-squares estimation. The resulting minimax filter takes the form of a risk-sensitive filter with a time varying risk sensitivity parameter, which depends on the tolerance bound applied to the model dynamics and observations at the corresponding time index. The least-favorable model is constructed and used to evaluate the performance of alternative filters. Simulations comparing the proposed risk-sensitive filter to a standard Kalman filter show a significant performance advantage when applied to the least-favorable model, and only a small performance loss for the nominal model

A novel code generation methodology for block diagram modeler and simulators Scicos and VSS

Block operations during simulation in Scicos and VSS environments can naturally be described as Nsp functions. But the direct use of Nsp functions for simulation leads to poor performance since the Nsp language is interpreted, not compiled. The methodology presented in this paper is used to develop a tool for generating efficient compilable code, such as C and ADA, for Scicos and VSS models from these block Nsp functions. Operator overloading and partial evaluation are the key elements of this novel approach. This methodology may be used in other simulation environments such as Matlab/Simulink

Teaching Introductory Differential Equations with ScicosLab

Perhaps the largest and most capable open source software for doing applied mathematics is the open source package Scicoslab. Widely used in Europe and Asia it is less well known in the United States. In this article we will explain how ScicosLab can be easily used to help teach differential equations and to also introduce students to a software package that they can take with them for the rest of their careers

Innovation generation in the presence of unknown inputs : application to robust failure detection

Projet META2The first step in innovations-based failure detection is the construction of an innovations generator, i.e., a filter which, in the absence of failures, from the inputs and the outputs of the system, generates a zero-mean white process with known covariance called innovations. Decision on whether a failure has occurred is then made by monitoring and applying statistical tests to this innovations process. In this paper, we present a method for constructing innovations in the case where the model contains unknown inputs and disturbances. Our solution is complete in the sense that it covers all "singular" cases

A New Methodology for Observer Design and Implementation

Projet META2Observers are usually formulated as explicit systems of differential equations and implemented using standard ODE solvers. In this paper, we show that there can be advantages in formulating the observer as a DAE (Differential-Algebraic Equation). A canonical DAE observer is proposed and it is shown that it can be implemented using standard DAE solvers. The DAE implementation of the observer can be considered regardless of the design philosophy used (extended linearization, Lyapunov based, Lie algebraic, ...). We present a simple design strategy for this canonical DAE observer based on the extended-linearization method

A realization theory for autonomous boundary-value linear systems

A frequency-domain realization theory is developed for the class of autonomous- , but not necessarily stationary, boundary-value linear systems. It is shown that this realization problem, which consists of constructing autonomous boundary-value linear systems from prescribed weighting patterns, reduces to the factorization of several rational matrices in two variables having separable denominators. This factorization problem is examined and a method is given for constructing minimal factorizations for such rational matrices. The special case of stationary systems is also considered

State-space representation of rational matrices in psi lab

Projet META2Statepace descriptions have been proven to be effective means for manipulating proper rational matrices. In many systems and control applications, however, rational matrices representing system transfer functions are not necessarily proper. ylab uses a state-space description for both proper and improper rational matrices. In this report, we describe this state-space description and the corresponding basic algebraic manipulations

Normalizing compensators for general H standard problems

In practical applications of H control theory, one often encounters standard problems that do not satisfy the assumptions on their pole-zero structure at infinity required for the application of Riccati-based solution methods. In this paper, we present a method based on the idea of pre-and post-compensation for transforming these H standard problems into problems that do satisfy these assumptions. These transformations are very important, because, solutions to compensated standard problems can be used to construct solutions to the original standard problems very easily. The method presented is very systematic and can easily by implemented

A Mixed symbolic-numeric software environmenrnt and its application to control systems engineering

Projet META2A high-level interactive symbolic-numeric software environment based on the symbolic computer algebra system Maple, its extension Macrofort and the high performance scientific software package y lab. is presented. This general purpose software environment can be used both for solving specific problems and for developing specialized software packages. We shall illustrate this latter application by developing a simple software package for the simulation and control of multibody mechanical systems. As an example, simulation and control of a bicycle are presented

SCICOS A Dynamic System Builder and Simulator User's Guide - Version 1.0

Projet META2Scicos (Scilab Connected Object Simulator) is a Scilab package for modeling and simulation of hybrid dynamical systems. More specifically, Scicos is intended to be a simulation environment in which both continuous systems and discrete systems co-exist. Unlike many other existing hybrid system simulation softwares, Scicos has not been constructed by extension of a continuous simulator or of a discrete simulator; Scicos has been developed based on a formalism that considers both aspects from the beginning. Scicos includes a graphical editor which can be used to build complex models by interconnecting blocks which represent either predefined basic functions defined in Scicos libraries (palettes), or user defined functions. A large class of hybrid systems can be modeled and simulated this way