Design of reduced-order functional observers for linear systems with unknown inputs

This brief paper presents new conditions for the existence and design of reduced-order linear functional state observers for linear systems with unknown inputs. Systematic procedures for the synthesis of reduced-order functional observers are given. Numerical examples are given to illustrate the attractiveness and simplicity of the new design procedures.

A new algorithm to design minimal multi-functional observers for linear systems

Designing minimum possible order (minimal) observers for Multi-Input Multi-Output (MIMO) linear systems have always been an interesting subject. In this paper, a new methodology to design minimal multi-functional observers for Linear Time-Invariant (LTI) systems is proposed. The approach is applicable, and it also helps in regulating the convergence rate of the observed functions. It is assumed that the system is functional observable or functional detectable, which is less conservative than assuming the observability or detectability of the system. To satisfy the minimality of the observer, a recursive algorithm is provided that increases the order of the observer by appending the minimum required auxiliary functions to the desired functions that are going to be estimated. The algorithm increases the number of functions such that the necessary and sufficient conditions for the existence of a functional observer are satisfied. Moreover, a new methodology to solve the observer design interconnected equations is elaborated. Our new algorithm has advantages with regard to the other available methods in designing minimal order functional observers. Specifically, it is compared with the most common schemes, which are transformation based. Using numerical examples it is shown that under special circumstances, the conventional methods have some drawbacks. The problem partly lies in the lack of sufficient numerical degrees of freedom proposed by the conventional methods. It is shown that our proposed algorithm can resolve this issue. A recursive algorithm is also proposed to summarize the observer design procedure. Several numerical examples and simulation results illustrate the efficacy, superiority and different aspects of the theoretical findings.

A delay-dependent functional observer for linear time-invariant systems with input delay

A delay-dependent functional observer is designed for linear time-invariant (LTI) systems with time-varying input delay. Compared to delay-free observers, delay-dependent functional observers are less conservative and cover more systems. The designed functional observer is with minimum possible order (minimal). Necessary and sufficient conditions of the existence of the observer and asymptomatic stability of it are illustrated. The proposed observer is extended to multiple input delayed systems with time-varying delays. An algorithm is developed for designing of the minimal order observer based on the methodology of this paper. Two numerical examples and simulations are used to support our proposed methodology.

Productive structure and the functional distribution of income: an application of the input-output model

Includes bibliography

Axotomized neonatal motoneurons overexpressing the bcl2 proto-oncogene retain functional electrophysiological properties.

Bcl2 overexpression prevents axotomy-induced neuronal death of neonatal facial motoneurons, as defined by morphological criteria. However, the functional properties of these surviving lesioned transgenic neurons are unknown. Using transgenic mice overexpressing the protein Bcl2, we have investigated the bioelectrical properties of transgenic facial motoneurons from 7 to 20 days after neonatal unilateral axotomy using brain-stem slices and whole cell patch-clamp recording. Nonaxotomized facial motoneurons from wild-type and transgenic mice had similar properties; they had an input resistance of 38 +/- 6 M omega and fired repetitively after injection of positive current pulses. When cells were voltage-clamped at or near their resting membrane potential, alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA), N-methyl-D-aspartic acid (NMDA), or vasopressin generated sustained inward currents. In transgenic axotomized mice, facial motoneurons could be found located ipsilaterally to the lesion; they had an input resistance of 150 +/- 30 M omega, indicating that they were smaller in size, fired repetitively, and were also responsive to AMPA, NMDA, and vasopressin. Morphological measurements achieved 1 week after the lesion have shown that application of brain-derived neurotrophic factor prevented the reduction in size of axotomized transgenic motoneurons. These data indicate that Bcl2 not only prevents morphological apoptotic death of axotomized neonatal transgenic motoneurons but also permits motoneurons to conserve functional electrophysiological properties.

Existence and Uniqueness of Solutions for Partial Differential-Functional Equations of the First Order with Deviating Argument of the Derivative of Unknown Function

We consider the existence and uniqueness problem for partial differential-functional equations of the first order with the initial condition for which the right-hand side depends on the derivative of unknown function with deviating argument.

Security through Obscurity: Layout Obfuscation of Digital Integrated Circuits using Don't Care Conditions

Contemporary integrated circuits are designed and manufactured in a globalized environment leading to concerns of piracy, overproduction and counterfeiting. One class of techniques to combat these threats is circuit obfuscation which seeks to modify the gate-level (or structural) description of a circuit without affecting its functionality in order to increase the complexity and cost of reverse engineering. Most of the existing circuit obfuscation methods are based on the insertion of additional logic (called “key gates”) or camouflaging existing gates in order to make it difficult for a malicious user to get the complete layout information without extensive computations to determine key-gate values. However, when the netlist or the circuit layout, although camouflaged, is available to the attacker, he/she can use advanced logic analysis and circuit simulation tools and Boolean SAT solvers to reveal the unknown gate-level information without exhaustively trying all the input vectors, thus bringing down the complexity of reverse engineering. To counter this problem, some ‘provably secure’ logic encryption algorithms that emphasize methodical selection of camouflaged gates have been proposed previously in literature [1,2,3]. The contribution of this paper is the creation and simulation of a new layout obfuscation method that uses don't care conditions. We also present proof-of-concept of a new functional or logic obfuscation technique that not only conceals, but modifies the circuit functionality in addition to the gate-level description, and can be implemented automatically during the design process. Our layout obfuscation technique utilizes don’t care conditions (namely, Observability and Satisfiability Don’t Cares) inherent in the circuit to camouflage selected gates and modify sub-circuit functionality while meeting the overall circuit specification. Here, camouflaging or obfuscating a gate means replacing the candidate gate by a 4X1 Multiplexer which can be configured to perform all possible 2-input/ 1-output functions as proposed by Bao et al. [4]. It is important to emphasize that our approach not only obfuscates but alters sub-circuit level functionality in an attempt to make IP piracy difficult. The choice of gates to obfuscate determines the effort required to reverse engineer or brute force the design. As such, we propose a method of camouflaged gate selection based on the intersection of output logic cones. By choosing these candidate gates methodically, the complexity of reverse engineering can be made exponential, thus making it computationally very expensive to determine the true circuit functionality. We propose several heuristic algorithms to maximize the RE complexity based on don’t care based obfuscation and methodical gate selection. Thus, the goal of protecting the design IP from malicious end-users is achieved. It also makes it significantly harder for rogue elements in the supply chain to use, copy or replicate the same design with a different logic. We analyze the reverse engineering complexity by applying our obfuscation algorithm on ISCAS-85 benchmarks. Our experimental results indicate that significant reverse engineering complexity can be achieved at minimal design overhead (average area overhead for the proposed layout obfuscation methods is 5.51% and average delay overhead is about 7.732%). We discuss the strengths and limitations of our approach and suggest directions that may lead to improved logic encryption algorithms in the future. References: [1] R. Chakraborty and S. Bhunia, “HARPOON: An Obfuscation-Based SoC Design Methodology for Hardware Protection,” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 28, no. 10, pp. 1493–1502, 2009. [2] J. A. Roy, F. Koushanfar, and I. L. Markov, “EPIC: Ending Piracy of Integrated Circuits,” in 2008 Design, Automation and Test in Europe, 2008, pp. 1069–1074. [3] J. Rajendran, M. Sam, O. Sinanoglu, and R. Karri, “Security Analysis of Integrated Circuit Camouflaging,” ACM Conference on Computer Communications and Security, 2013. [4] Bao Liu, Wang, B., "Embedded reconfigurable logic for ASIC design obfuscation against supply chain attacks,"Design, Automation and Test in Europe Conference and Exhibition (DATE), 2014 , vol., no., pp.1,6, 24-28 March 2014.

Minimal-order functional observer-based residual generators for fault detection and isolation of dynamical systems

This paper examines the design of minimal-order residual generators for the purpose of detecting and isolating actuator and/or component faults in dynamical systems. We first derive existence conditions and design residual generators using only first-order observers to detect and identify the faults. When the first-order functional observers do not exist, then based on a parametric approach to the solution of a generalized Sylvester matrix equation, we develop systematic procedures for designing residual generators utilizing minimal-order functional observers. Our design approach gives lower-order residual generators than existing results in the literature. The advantages for having such lower-order residual generators are obvious from the economical and practical points of view as cost saving and simplicity in implementation can be achieved, particularly when dealing with high-order complex systems. Numerical examples are given to illustrate the proposed fault detection and isolation schemes. In all of the numerical examples, we design minimum-order residual generators to effectively detect and isolate actuator and/or component faults in the system.

A common functional observer scheme for three systems with unknown inputs

This paper presents a novel common functional observer scheme for three systems with unknown inputs. The scheme uses three observers in cascade with two logic switches. The existence conditions of the scheme are investigated and presented in terms of the original system matrices. Significantly, the conditions allow the observers to be designed independently of each other which greatly simplify the design process, and also serve as a basis of comparison for future development of common functional observer schemes. A numerical example is given to illustrate the effectiveness of the proposed scheme.

Evaluation of functional performance in commercial buildings

This report fully summarises a project designed to enhance commercial real estate performance within both operational and investment contexts through the development of a model aimed at supporting improved decision-making. The model is based on a risk adjusted discounted cash flow, providing a valuable toolkit for building managers, owners, and potential investors for evaluating individual building performance in terms of financial, social and environmental criteria over the complete life-cycle of the asset. The ‘triple bottom line’ approach to the evaluation of commercial property has much significance for the administrators of public property portfolios in particular. It also has applications more generally for the wider real estate industry given that the advent of ‘green’ construction requires new methods for evaluating both new and existing building stocks. The research is unique in that it focuses on the accuracy of the input variables required for the model. These key variables were largely determined by market-based research and an extensive literature review, and have been fine-tuned with extensive testing. In essence, the project has considered probability-based risk analysis techniques that required market-based assessment. The projections listed in the partner engineers’ building audit reports of the four case study buildings were fed into the property evaluation model developed by the research team. The results are strongly consistent with previously existing, less robust evaluation techniques. And importantly, this model pioneers an approach for taking full account of the triple bottom line, establishing a benchmark for related research to follow. The project’s industry partners expressed a high degree of satisfaction with the project outcomes at a recent demonstration seminar. The project in its existing form has not been geared towards commercial applications but it is anticipated that QDPW and other industry partners will benefit greatly by using this tool for the performance evaluation of property assets. The project met the objectives of the original proposal as well as all the specified milestones. The project has been completed within budget and on time. This research project has achieved the objective by establishing research foci on the model structure, the key input variable identification, the drivers of the relevant property markets, the determinants of the key variables (Research Engine no.1), the examination of risk measurement, the incorporation of risk simulation exercises (Research Engine no.2), the importance of both environmental and social factors and, finally the impact of the triple bottom line measures on the asset (Research Engine no. 3).

Vision, functional and cognitive determinants of motor vehicle incidents in older drivers

Background: The proportion of older individuals in the driving population is predicted to increase in the next 50 years. This has important implications for driving safety as abilities which are important for safe driving, such as vision (which accounts for the majority of the sensory input required for driving), processing ability and cognition have been shown to decline with age. The current methods employed for screening older drivers upon re-licensure are also vision based. This study, which investigated social, behavioural and professional aspects involved with older drivers, aimed to determine: (i) if the current visual standards in place for testing upon re-licensure are effective in reducing the older driver fatality rate in Australia; (ii) if the recommended visual standards are actually implemented as part of the testing procedures by Australian optometrists; and (iii) if there are other non-standardised tests which may be better at predicting the on-road incident-risk (including near misses and minor incidents) in older drivers than those tests recommended in the standards. Methods: For the first phase of the study, state-based age- and gender-stratified numbers of older driver fatalities for 2000-2003 were obtained from the Australian Transportation Safety Bureau database. Poisson regression analyses of fatality rates were considered by renewal frequency and jurisdiction (as separate models), adjusting for possible confounding variables of age, gender and year. For the second phase, all practising optometrists in Australia were surveyed on the vision tests they conduct in consultations relating to driving and their knowledge of vision requirements for older drivers. Finally, for the third phase of the study to investigate determinants of on-road incident risk, a stratified random sample of 600 Brisbane residents aged 60 years and were selected and invited to participate using an introductory letter explaining the project requirements. In order to capture the number and type of road incidents which occurred for each participant over 12 months (including near misses and minor incidents), an important component of the prospective research study was the development and validation of a driving diary. The diary was a tool in which incidents that occurred could be logged at that time (or very close in time to which they occurred) and thus, in comparison with relying on participant memory over time, recall bias of incident occurrence was minimised. Association between all visual tests, cognition and scores obtained for non-standard functional tests with retrospective and prospective incident occurrence was investigated. Results: In the first phase,rivers aged 60-69 years had a 33% lower fatality risk (Rate Ratio [RR] = 0.75, 95% CI 0.32-1.77) in states with vision testing upon re-licensure compared with states with no vision testing upon re-licensure, however, because the CIs are wide, crossing 1.00, this result should be regarded with caution. However, overall fatality rates and fatality rates for those aged 70 years and older (RR=1.17, CI 0.64-2.13) did not differ between states with and without license renewal procedures, indicating no apparent benefit in vision testing legislation. For the second phase of the study, nearly all optometrists measured visual acuity (VA) as part of a vision assessment for re-licensing, however, 20% of optometrists did not perform any visual field (VF) testing and only 20% routinely performed automated VF on older drivers, despite the standards for licensing advocating automated VF as part of the vision standard. This demonstrates the need for more effective communication between the policy makers and those responsible for carrying out the standards. It may also indicate that the overall higher driver fatality rate in jurisdictions with vision testing requirements is resultant as the tests recommended by the standards are only partially being conducted by optometrists. Hence a standardised protocol for the screening of older drivers for re-licensure across the nation must be established. The opinions of Australian optometrists with regard to the responsibility of reporting older drivers who fail to meet the licensing standards highlighted the conflict between maintaining patient confidentiality or upholding public safety. Mandatory reporting requirements of those drivers who fail to reach the standards necessary for driving would minimise potential conflict between the patient and their practitioner, and help maintain patient trust and goodwill. The final phase of the PhD program investigated the efficacy of vision, functional and cognitive tests to discriminate between at-risk and safe older drivers. Nearly 80% of the participants experienced an incident of some form over the prospective 12 months, with the total incident rate being 4.65/10 000 km. Sixty-three percent reported having a near miss and 28% had a minor incident. The results from the prospective diary study indicate that the current vision screening tests (VA and VF) used for re-licensure do not accurately predict older drivers who are at increased odds of having an on-road incident. However, the variation in visual measurements of the cohort was narrow, also affecting the results seen with the visual functon questionnaires. Hence a larger cohort with greater variability should be considered for a future study. A slightly lower cognitive level (as measured with the Mini-Mental State Examination [MMSE]) did show an association with incident involvement as did slower reaction time (RT), however the Useful-Field-of-View (UFOV) provided the most compelling results of the study. Cut-off values of UFOV processing (>23.3ms), divided attention (>113ms), selective attention (>258ms) and overall score (moderate/ high/ very high risk) were effective in determining older drivers at increased odds of having any on-road incident and the occurrence of minor incidents. Discussion: The results have shown that for the 60-69 year age-group, there is a potential benefit in testing vision upon licence renewal. However, overall fatality rates and fatality rates for those aged 70 years and older indicated no benefit in vision testing legislation and suggests a need for inclusion of screening tests which better predict on-road incidents. Although VA is routinely performed by Australian optometrists on older drivers renewing their licence, VF is not. Therefore there is a need for a protocol to be developed and administered which would result in standardised methods conducted throughout the nation for the screening of older drivers upon re-licensure. Communication between the community, policy makers and those conducting the protocol should be maximised. By implementing a standardised screening protocol which incorporates a level of mandatory reporting by the practitioner, the ethical dilemma of breaching patient confidentiality would also be resolved. The tests which should be included in this screening protocol, however, cannot solely be ones which have been implemented in the past. In this investigation, RT, MMSE and UFOV were shown to be better determinants of on-road incidents in older drivers than VA and VF, however, as previously mentioned, there was a lack of variability in visual status within the cohort. Nevertheless, it is the recommendation from this investigation, that subject to appropriate sensitivity and specificity being demonstrated in the future using a cohort with wider variation in vision, functional performance and cognition, these tests of cognition and information processing should be added to the current protocol for the screening of older drivers which may be conducted at licensing centres across the nation.

Functional outcome of transfemoral amputees fitted with an osseointegrated fixation : temporal gait characteristics

The purpose of this study was to characterise the functional outcome of 12 transfemoral amputees fitted with osseointegrated fixation using temporal gait characteristics. The objectives were (A) to present the cadence, duration of gait cycle, support and swing phases with an emphasis on the stride-to-stride and participant-to-participant variability, and (B) to compare these temporal variables with normative data extracted from the literature focusing on transfemoral amputees fitted with a socket and able-bodied participants. The temporal variables were extracted from the load applied on the residuum during straight level walking, which was collected at 200 Hz by a transducer. A total of 613 strides were assessed. The cadence (46±4 strides/min), the duration of the gait cycle (1.29±0.11 s), support (0.73±0.07 s, 57±3% of CG) and swing (0.56±0.07 s, 43±3% of GC) phases of the participants were 2% quicker, 3%, 6% shorter and 1% longer than transfemoral amputees using a socket as well as 11% slower, 9%, 6% and 13% longer than able-bodied, respectively. All combined, the results indicated that the fitting of an osseointegrated fixation has enabled this group of amputees to restore their locomotion with a highly functional level. Further longitudinal and cross-sectional studies would be required to confirm these outcomes. Nonetheless, the data presented can be used as benchmark for future comparisons. It can also be used as input in generic algorithms using templates of patterns of loading to recognise activities of daily living and to detect falls.

Investigating functional thinking in the elementary classroom : foundations of early algebraic reasoning

This paper examines the development of student functional thinking during a teaching experiment that was conducted in two classrooms with a total of 45 children whose average age was nine years and six months. The teaching comprised four lessons taught by a researcher, with a second researcher and classroom teacher acting as participant observers. These lessons were designed to enable students to build mental representations in order to explore the use of function tables by focusing on the relationship between input and output numbers with the intention of extracting the algebraic nature of the arithmetic involved. All lessons were videotaped. The results indicate that elementary students are not only capable of developing functional thinking but also of communicating their thinking both verbally and symbolically.