On nonlinear H∞ filtering for discrete-time stochastic systems with missing measurements

Copyright [2008] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, the H∞ filtering problem is investigated for a general class of nonlinear discrete-time stochastic systems with missing measurements. The system under study is not only corrupted by state-dependent white noises but also disturbed by exogenous inputs. The measurement output contains randomly missing data that is modeled by a Bernoulli distributed white sequence with a known conditional probability. A filter of very general form is first designed such that the filtering process is stochastically stable and the filtering error satisfies H infin performance constraint for all admissible missing observations and nonzero exogenous disturbances under the zero-initial condition. The existence conditions of the desired filter are described in terms of a second-order nonlinear inequality. Such an inequality can be decoupled into some auxiliary ones that can be solved independently by taking special form of the Lyapunov functionals. As a consequence, a linear time-invariant filter design problem is discussed for the benefit of practical applications, and some simplified conditions are obtained. Finally, two numerical simulation examples are given to illustrate the main results of this paper

Neural Dynamics of Motion Grouping: From Aperture Ambiguity to Object Speed and Direction

A neural network model of visual motion perception and speed discrimination is developed to simulate data concerning the conditions under which components of moving stimuli cohere or not into a global direction of motion, as in barberpole and plaid patterns (both Type 1 and Type 2). The model also simulates how the perceived speed of lines moving in a prescribed direction depends upon their orientation, length, duration, and contrast. Motion direction and speed both emerge as part of an interactive motion grouping or segmentation process. The model proposes a solution to the global aperture problem by showing how information from feature tracking points, namely locations from which unambiguous motion directions can be computed, can propagate to ambiguous motion direction points, and capture the motion signals there. The model does this without computing intersections of constraints or parallel Fourier and non-Fourier pathways. Instead, the model uses orientationally-unselective cell responses to activate directionally-tuned transient cells. These transient cells, in turn, activate spatially short-range filters and competitive mechanisms over multiple spatial scales to generate speed-tuned and directionally-tuned cells. Spatially long-range filters and top-down feedback from grouping cells are then used to track motion of featural points and to select and propagate correct motion directions to ambiguous motion points. Top-down grouping can also prime the system to attend a particular motion direction. The model hereby links low-level automatic motion processing with attention-based motion processing. Homologs of model mechanisms have been used in models of other brain systems to simulate data about visual grouping, figure-ground separation, and speech perception. Earlier versions of the model have simulated data about short-range and long-range apparent motion, second-order motion, and the effects of parvocellular and magnocellular LGN lesions on motion perception.Office of Naval Research (N00014-920J-4015, N00014-91-J-4100, N00014-95-1-0657, N00014-95-1-0409, N00014-91-J-0597); Air Force Office of Scientific Research (F4620-92-J-0225, F49620-92-J-0499); National Science Foundation (IRI-90-00530

Neural Dynamics of Motion Perception: Direction Fields, Apertures, and Resonant Grouping

A neural network model of global motion segmentation by visual cortex is described. Called the Motion Boundary Contour System (BCS), the model clarifies how ambiguous local movements on a complex moving shape are actively reorganized into a coherent global motion signal. Unlike many previous researchers, we analyse how a coherent motion signal is imparted to all regions of a moving figure, not only to regions at which unambiguous motion signals exist. The model hereby suggests a solution to the global aperture problem. The Motion BCS describes how preprocessing of motion signals by a Motion Oriented Contrast Filter (MOC Filter) is joined to long-range cooperative grouping mechanisms in a Motion Cooperative-Competitive Loop (MOCC Loop) to control phenomena such as motion capture. The Motion BCS is computed in parallel with the Static BCS of Grossberg and Mingolla (1985a, 1985b, 1987). Homologous properties of the Motion BCS and the Static BCS, specialized to process movement directions and static orientations, respectively, support a unified explanation of many data about static form perception and motion form perception that have heretofore been unexplained or treated separately. Predictions about microscopic computational differences of the parallel cortical streams V1 --> MT and V1 --> V2 --> MT are made, notably the magnocellular thick stripe and parvocellular interstripe streams. It is shown how the Motion BCS can compute motion directions that may be synthesized from multiple orientations with opposite directions-of-contrast. Interactions of model simple cells, complex cells, hypercomplex cells, and bipole cells are described, with special emphasis given to new functional roles in direction disambiguation for endstopping at multiple processing stages and to the dynamic interplay of spatially short-range and long-range interactions.Air Force Office of Scientific Research (90-0175); Defense Advanced Research Projects Agency (90-0083); Office of Naval Research (N00014-91-J-4100

A Neural Model of First-order and Second-order Motion Perception and Magnocellular Dynamics

A neural model of motion perception simulates psychophysical data. concerning first-order and second-order motion stimuli, including the reversal of perceived motion direction with distance from the stimulus (I display), and data about directional judgments as a function of relative spatial phase or spatial and temporal frequency. Many other second-order motion percepts that have been ascribed to a second non-Fourier processing stream can also be explained in the model by interactions between ON and OFF cells within a single, neurobiologically interpreted magnocellular processing stream. Yet other percepts may be traced to interactions between form and motion processing streams, rather than to processing within multiple motion processing strea.ms. The model hereby explains why monkeys with lesions of the parvocellular layers, but not the magnocellular layers, of the lateral geniculate nucleus (LGN) are capable of detecting the correct direction of second-order motion, why most cells in area MT are sensitive to both first-order and second-order motion, and why after APB injection selectively blocks retinal ON bipolar cells, cortical cells are sensitive only to the motion of a moving bright bar's trailing edge. Magnoccllular LGN cells show relatively transient responses while parvoccllular LGN cells show relatively sustained responses. Correspondingly, the model bases its directional estimates on the outputs of model ON and OFF transient cells that are organized in opponent circuits wherein antagonistic rebounds occur in response to stimmulus offset. Center-surround interactions convert these ON and OFF outpr1ts into responses of lightening and darkening cells that are sensitive both to direct inputs and to rebound responses in their receptive field centers and surrounds. The total pattern of activity increments and decrements is used by subsequent processing stages (spatially short-range filters, competitive interactions, spatially long-range filters, and directional grouping cells) to dntermine the perceived direction of motion

On design of quantized fault detection filters with randomly occurring nonlinearities and mixed time-delays

This paper is concerned with the fault detection problem for a class of discrete-time systems with randomly occurring nonlinearities, mixed stochastic time-delays as well as measurement quantizations. The nonlinearities are assumed to occur in a random way. The mixed time-delays comprise both the multiple discrete time-delays and the infinite distributed delays that occur in a random way as well. A sequence of stochastic variables is introduced to govern the random occurrences of the nonlinearities, discrete time-delays and distributed time-delays, where all the stochastic variables are mutually independent but obey the Bernoulli distribution. The main purpose of this paper is to design a fault detection filter such that, in the presence of measurement quantization, the overall fault detection dynamics is exponentially stable in the mean square and, at the same time, the error between the residual signal and the fault signal is made as small as possible. Sufficient conditions are first established via intensive stochastic analysis for the existence of the desired fault detection filters, and then the explicit expression of the desired filter gains is derived by means of the feasibility of certain matrix inequalities. Also, the optimal performance index for the addressed fault detection problem can be obtained by solving an auxiliary convex optimization problem. A practical example is provided to show the usefulness and effectiveness of the proposed design method

Analysis and design of space vehicle flight control systems. Volume XIII - Adaptive control

Mathematical models used for space vehicle flight adaptive control system

Nonlinear Attitude and Pose Filters with Superior Convergence Properties

In this thesis, several deterministic and stochastic attitude filtering solutions on the special orthogonal group SO(3) are proposed. Firstly, the attitude estimation problem is approached on the basis of nonlinear deterministic filters on SO(3) with guaranteed transient and steady-state measures. The second solution to the attitude estimation problem considers nonlinear stochastic filters on SO(3) with superior convergence properties with two filters being developed in the sense of Ito, and one in the sense of Stratonovich. This thesis also presents several deterministic and stochastic pose filtering solutions developed on the special Euclidean group SE(3). The first solution includes two nonlinear deterministic pose filters on SE(3) with predefined transient as well as steady-state performance, while the second one involves a nonlinear stochastic filter on SE(3) in the sense of Stratonovich. The proposed nonlinear deterministic filters on SO(3) and SE(3) guarantee that attitude and pose error are trapped to initially start within a known large set and converge systematically and asymptotically to the equilibrium point from almost any initial condition, respectively. The proposed stochastic filters ensure that errors of the estimates and attitude or errors of the estimates and pose are semi-globally uniformly ultimately bounded in mean square, and they converge to a small neighborhood of the origin from almost any initial condition. The output performance of the proposed filters is examined and simulated considering high level of uncertainties in the measurements and large error in initialization. The above-mentioned consideration makes the proposed filters a good fit for measurements obtained from low-cost inertial measurement units or low-cost inertial vision systems

Intelligent Autonomous Decision-Making and Cooperative Control Technology of High-Speed Vehicle Swarms

This book is a reprint of the Special Issue “Intelligent Autonomous Decision-Making and Cooperative Control Technology of High-Speed Vehicle Swarms”,which was published in Applied Sciences