constraints

This paper presents a new approach to finite-horizon guaranteed state prediction for discrete-time systems affected by bounded noise and unknown-but-bounded parameter uncertainty. Our framework handles possibly nonlinear dependence of the state-space matrices on the uncertain parameters. The main result is that a minimal confidence ellipsoid for the state, consistent with the measured output and the uncertainty description, may be recursively computed in polynomial time, using interior-point methods for convex optimization. With n states, l uncertain parameters appearing linearly in the state-space matrices, with rank-one matrix coefficients, the worst-case complexity grows as O(l(n + l) 3:5 ). With unstructured uncertainty in all system matrices, the worst-case complexity reduces to O(n 3:5 ).

This paper develops a framework for state-space estimation when the parameters of the underlying linear model are subject to uncertainties. Compared with existing robust filters, the proposed filters perform regularization rather than de-regularization. It is shown that, under certain stabilizability and detectability conditions, the steady-state filters are stable and that, for quadratically-stable models, the filters guarantee a bounded error variance. Moreover, the resulting filter structures are similar to various (time- and measurement-update, prediction, and information) forms of the Kalman filter, albeit ones that operate on corrected parameters rather than on the given nominal parameters. Simulation results and comparisons with H1 , guaranteed-cost, and set-valued state estimation filters are provided.

This thesis examines the problem of localising an Autonomous Guided Vehicle (AGV) travelling in an unknown environment. In this problem, the AGV faces the dual task of modeling the environment and simultaneously localising its position within it. The Simultaneous Localisation and Map Building (SLAM) problem is currently one of the most important goals of AGV research. Solving this problem would allow anAGV to be deployed easily, with very little initial preparation. The AGV would also be exible and able to cope with modi cations in the environment. A solution to the SLAM problem would enable an AGV to would be truly \autonomous." The thesis examines the SLAM problem from an estimation theoretic point ofview. The estimation approach provides a rigorous framework for the analysis and has also proven to be successful in actual applications. The most signi cant contribution of this thesis is to provide, for the rst time, a detailed development of the theory of the SLAM problem. It is shown that correlations arise between errors in the vehicle and the map estimates, and these correlations are identi ed as fundamentally important to the solution of the SLAM problem. It is demonstrated that ignoring these correlations results in the loss of the fundamental structure of the SLAM problem and leads to inconsistency in map

In this paper we consider the problem of worst-case simulation for a discrete-time system with structured uncertainty. The approach is based on the recursive computation of ellipsoids of condence for the system state, based on semidefinite programming.

For a class of dynamical systems, with uncertain nonlinear terms considered as "unknown inputs", we give sufficient conditions for observability. We show also that there does not exist any exact observer independent of the unknown inputs. Under the additional assumption that the uncertainty is bounded, we build practical observers whose error converges exponentially towards an arbitrarily small neighborhood of the origin. Under the hypothesis that bounds are available for the uncertain terms, we build parallelotopic observers providing time-varying bounds for the state variables, even when the system is not observable for unknown inputs These results are illustrated on a biological model of a structured population.

This paper analyzes the performance of an optimal bounding ellipsoid (OBE) algorithm for tracking time-varying parameters with incrementally bounded time variations. A linear state-space model is used, with the time-varying parameters represented by the state vector. The OBE algorithm exhibits a selective update property for the time and observation-update equations, and necessary and sufficient conditions for state tracking are derived. The interpretability of the optimization criterion is also investigated along with simulation results. 1 Introduction Tracking of time varying parameters is an important problem, both from theoretical as well as practical viewpoints, in adaptive signal processing, communication and control systems. An elegant, convenient and general framework for formulating the problem is provided by linear state-space equations. In this paper, we use the discrete-time state equation framework and present an optimal bounding ellipsoid (OBE) algorithm for tracking tim...

Set membership H1 identification is investigated using time-domain data and mixed parametric and nonparametric models as well as supposing power bounded measurement errors. The problem of optimally estimating the unknown parameters and evaluating the minimal worst case identification error, called radius of information, is solved. For classes of models affine in the parameters, the radius of information is obtained as function of the H1 norm of the unmodeled dynamics. A method is given for estimating this norm from the available data and some general a priori information on the unmodeled dynamics, thus allowing the actual evaluation of the radius of information. The radius represents a measure of the "predictive ability" of the considered class of models, and it is then used for comparing the quality of different classes of models and for the order selection of their parametric part. The effectiveness of the proposed procedure is tested on some numerical examples and compared with stan...

We compare the theoretical and practical considerations of two common sensor data fusion methodologies: set-based and statistically based parameter estimation. We first examine their convergence behavior for a variety of simulated problems. We then describe robot localization systems implemented using both methods and compare their performance. Our conclusion is that set-based methods have performance that sometimes exceeds that of statistical methods, although this result is highly problem dependent. We then characterize these problem dependencies. 1 Introduction Recently, it has become common to express sensor data fusion problems in terms of parameter estimation or hypothesis testing, and to solve these problems using statistical estimation methods [6]. Practically without exception, solutions apply variations of classical mean-square estimation techniques [9]. However, the efficacy of these techniques depends greatly on the character and fidelity of mathematical sensor models [12,...

: The problem considered here is state estimation in the presence of bounded process and measurement noise. A new nonlinear state estimator, based on interval analysis and the notion of set inversion, is applied to robot localization and tracking. This estimator evaluates a set guaranteed to contain all values of the state that are consistent with the available observations, given the noise bounds and some possibly very large set containing the initial value of the state. Three situations are considered to illustrate the properties of the estimator. Keywords: Bounded-error estimation, Interval analysis, Robot localization, Robot tracking, State estimation. 1 Introduction Much of recent research in robotics has been devoted to increasing autonomy, e.g., by adding sensors, mobility and decision capability. To be autonomous, robots must be able to estimate their present state from available prior information and measurements. The problem to be considered here is the autonomous localizati...