A game theory approach to mixed H2/H∞ control for a class of stochastic time-varying systems with randomly occurring nonlinearities

Copyright @ 2011 Elsevier B.V. This is the author’s version of a work that was accepted for publication in Systems and Control Letters. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published and may be accessed at the link below.This paper is concerned with the mixed H2/H∞ control problem for a class of stochastic time-varying systems with nonlinearities. The nonlinearities are described by statistical means and could cover several kinds of well-studied nonlinearities as special cases. The occurrence of the addressed nonlinearities is governed by two sequences of Bernoulli distributed white sequences with known probabilities. Such nonlinearities are named as randomly occurring nonlinearities (RONs) as they appear in a probabilistic way. The purpose of the problem under investigation is to design a controller such that the closed-loop system achieves the expected H2 performance requirements with a guaranteed H∞ disturbance attenuation level. A sufficient condition is given for the existence of the desired controller by means of solvability of certain coupled matrix equations. By resorting to the game theory approach, an algorithm is developed to obtain the controller gain at each sampling instant. A numerical example is presented to show the effectiveness and applicability of the proposed method

Robust H∞ control of time-varying systems with stochastic non-linearities: the finite-horizon case

The official published version can be obtained from the link below.This paper is concerned with the robust H∞ control problem for the class of uncertain non-linear discrete time-varying stochastic systems with a covariance constraint. All the system parameters are time-varying and the uncertainties enter into the state matrix. The non-linearities under consideration are described by statistical means and they cover several classes of well-studied non-linearities. The purpose of the addressed problem is to design a dynamic output-feedback controller such that, the H∞ disturbance rejection attenuation level is achieved in the finite-horizon case while the state covariance is not more than an individual upper bound at each time point. An algorithm is developed to deal with the addressed problem by means of recursive linear matrix inequalities (RLMIs). It is shown that the robust H∞ control problem is solvable if the series of RLMIs is feasible. An illustrative simulation example is given to show the applicability and effectiveness of the proposed algorithm.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under grant GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Robust H-infinity sliding mode control for nonlinear stochastic systems with multiple data packet losses

This is the post-print version of this Article. The official published version can be accessed from the link below - Copyright @ 2012 John Wiley & SonsIn this paper, an ∞ sliding mode control (SMC) problem is studied for a class of discrete-time nonlinear stochastic systems with multiple data packet losses. The phenomenon of data packet losses, which is assumed to occur in a random way, is taken into consideration in the process of data transmission through both the state-feedback loop and the measurement output. The probability for the data packet loss for each individual state variable is governed by a corresponding individual random variable satisfying a certain probabilistic distribution over the interval [0 1]. The discrete-time system considered is also subject to norm-bounded parameter uncertainties and external nonlinear disturbances, which enter the system state equation in both matched and unmatched ways. A novel stochastic discrete-time switching function is proposed to facilitate the sliding mode controller design. Sufficient conditions are derived by means of the linear matrix inequality (LMI) approach. It is shown that the system dynamics in the specified sliding surface is exponentially stable in the mean square with a prescribed ∞ noise attenuation level if an LMI with an equality constraint is feasible. A discrete-time SMC controller is designed capable of guaranteeing the discrete-time sliding mode reaching condition of the specified sliding surface with probability 1. Finally, a simulation example is given to show the effectiveness of the proposed method.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., the National Natural Science Foundation of China under Grant 61028008 and the Alexander von Humboldt Foundation of German

Robust variance-constrained filtering for a class of nonlinear stochastic systems with missing measurements

The official published version of the article can be found at the link below.This paper is concerned with the robust filtering problem for a class of nonlinear stochastic systems with missing measurements and parameter uncertainties. The missing measurements are described by a binary switching sequence satisfying a conditional probability distribution, and the nonlinearities are expressed by the statistical means. The purpose of the filtering problem is to design a filter such that, for all admissible uncertainties and possible measurements missing, the dynamics of the filtering error is exponentially mean-square stable, and the individual steady-state error variance is not more than prescribed upper bound. A sufficient condition for the exponential mean-square stability of the filtering error system is first derived and an upper bound of the state estimation error variance is then obtained. In terms of certain linear matrix inequalities (LMIs), the solvability of the addressed problem is discussed and the explicit expression of the desired filters is also parameterized. Finally, a simulation example is provided to demonstrate the effectiveness and applicability of the proposed design approach.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK and the Alexander von Humboldt Foundation of Germany

The Gardener Site (41CP55): A Late Caddo Settlement on Big Cypress Creek in East Texas

The Gardener site (41CP55) in Camp County, Texas, was first recorded by Sullivan prior to construction of Lake Bob Sandlin on Big Cypress Creek. A surface collection of sherds and daub suggested that the site was the locus of a Late Caddo period (ca. A.D. 1450-1680) settlement and burned house. However, no further archaeological work was done at the site before it was inundated by Lake Bob Sandlin in the late 1970s. Recently, because of lower flood pool levels at Lake Bob Sandlin due to East Texas drought conditions, archaeological materials from the Gardener site have been exposed along the shoreline of the lake. This article concerns the documentation of a substantial aboriginal artifact assemblage collected from the shoreline surface of the site. The Gardener site is located along an upland slope (330 ft. amsl) on the west side of Picket Spring Branch, a small and northward-flowing tributary to Big Cypress Creek, in the Post Oak Savanna. The old channel of Big Cypress Creek lies approximately 1.8 km north of the site. The overall extent of the site is not known, although Thurmond suggests it is relatively small

Documentation of Ceramic Vessels and Projectile Points from the C. D. Marsh Site (41HS269) in the Sabine River Basin

A total of at least eight Caddo burials were excavated at the C. D. Marsh site on Eight Mile Creek, a southward-flowing tributary to the Sabine River, by Buddy C. Jones in 1959-1960. This includes Burial 1, an historic (dating after ca. A.D. 1685) Nadaco Caddo burial; European trade goods found with this burial include two small silver disks. The other burials (Burials 2-8) are part of an earlier Caddo cemetery that is thought to be associated with the ca. A.D. 1350-17th century Pine Tree Mound community along the Sabine River and its tributaries. Jones suggests that these latter burials are from a ca. A.D. 1200-1500 Caddo cemetery. According to Jones and notes on file at the museum, Burials 2-8 are located ca. 120 m east-southeast from the one Historic Caddo burial at the site. The burials were placed in extended supine position in north-south oriented pits in rows, with the head of the deceased at the southern end of the burial and facing north. Funerary offerings included ceramic vessels and mussel shells. In this article, we describe eight ceramic vessels in the Gregg County Historical Museum collections from Burials 1, 4, and 7, as well as projectile points from habitation contexts at the C. D. Marsh site; the location of Burial 7 relative to Burial 4 is not known. There are also six other ceramic vessels from the ca. A.D. 1200-1500 burials at the site that are unassociated funerary objects in the Gregg County Historical Museum collections. This includes one vessel each from Burials 5 and 8; the provenience of the other vessels at the site is unknown. One of the unassociated funerary object ceramic vessels at the C. D. Marsh site is a Ripley Engraved, var. McKinney carinated bowl. Such vessels would not be expected in a ca. A.D. 1200-1500 Caddo cemetery, and although this type of fine ware is commonly seen on post-A.D. 1600 Titus phase sites in the region, it is rarely found in association with European trade goods. Therefore, it may represent a burial from a third temporal component (ca. A.D. 1600-1685) at the site

Archaeological Investigations at the Wade (GC-38) and Estes (GC-49) Sites in the Sabine River Basin, Gregg County, Texas

Buddy C. Jones conducted extensive archaeological investigations in the 1950s and 1960s at many sites in the mid-Sabine River basin of East Texas, especially on Caddo sites of various ages in Gregg, Harrison, and Rusk counties. However, that work has not illuminated our understanding of the archaeology of the Caddo Indian peoples that lived along this stretch of the Sabine River as much as it could have, primarily because little of the work completed by Jones was ever published, or the results and findings shared with professional and avocational archaeological colleagues working in the region. The Caddo archaeology of the Gregg County stretch of the Sabine River, in particular, is poorly known by comparison with the archaeological record in the upper Sabine River or to the archaeological studies recently completed downstream in Harrison County at sites such as Pine Tree Mound (41HS15). To begin to develop a better appreciation of the Caddo archaeology in the mid-Sabine River basin, we have made a concerted effort to analyze and document collections obtained by Jones from Caddo sites in Gregg County and the surrounding region. In this article, we discuss the archaeological findings from the Wade and Estes sites discovered and investigated by Jones in the late 1950s and early 1960s. The sites are near each other in the southeastern part of Gregg County. The Wade site is on a landform near the confluence of Peatown Creek and Dutchman Creek, northern-flowing tributaries to the Sabine River. The Estes site is on a large alluvial terrace on the north side of the Sabine River, across from the confluence of Dutchman Creek and the Sabine River This article focuses particularly on the excavations of portions of an ancestral Caddo house structure at the Wade site and the analysis of the substantial decorated sherd assemblages at both the Wade and Estes sites