Integral sliding mode design for robust filtering and control of linear stochastic time‐delay systems

This paper presents an integral sliding mode technique robustifying the optimal controller for linear stochastic systems with input and observation delays, which is based on integral sliding mode compen‐sation of disturbances. The general principles of the integral sliding mode compensator design are modified to yield the basic control algorithm oriented to time‐delay systems, which is then applied to robustify the optimal controller. As a result, two integral sliding mode control compensators are designed to suppress disturbances in state and observation equations, respectively, from the initial time moment. Moreover, it is shown that if certain matching conditions hold, the designed compensator in the state equation can simultaneously suppress observation disturbances, as well as the designed compensator in the observation equation can simultaneously suppress state disturbances. The obtained robust control algorithm is verified by simulations in the illustrative example, where the compensator in the observation equation provides simultaneous suppression of state and observation disturbances. Copyright © 2005 John Wiley & Sons, Ltd.     

Optimal linear filtering over observations with multiple delays

In this paper, the optimal filtering problem for a linear system over observations with multiple delays is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate and its variance. As a result, the optimal filtering equations similar to the traditional Kalman–Bucy ones are obtained in the form dual to the Smith predictor, commonly used for robust control design in time‐delay systems. In the example, the obtained optimal filter over observations with multiple delays is verified for a sample system and compared with the best Kalman–Bucy filter available for delayed measurements. Copyright © 2004 John Wiley & Sons, Ltd.     

Metareasoning about Security Protocols using Distributed Temporal Logic

We introduce a version of distributed temporal logic for rigorously formalizing and proving metalevel properties of different protocol models, and establishing relationships between models. The resulting logic is quite expressive and provides a natural, intuitive language for formalizing both local (agent specific) and global properties of distributed communicating processes. Through a sequence of examples, we show how this logic may be applied to formalize and establish the correctness of different modeling and simplification techniques, which play a role in building effective protocol tools.     

Verifying a signature architecture: a comparative case study

We report on a case study in applying different formal methods to model and verify an architecture for administrating digital signatures. The architecture comprises several concurrently executing systems that authenticate users and generate and store digital signatures by passing security relevant data through a tightly controlled interface. The architecture is interesting from a formal-methods perspective as it involves complex operations on data as well as process coordination and hence is a candidate for both data-oriented and process-oriented formal methods. We have built and verified two models of the signature architecture using two representative formal methods. In the first, we specify a data model of the architecture in Z that we extend to a trace model and interactively verify by theorem proving. In the second, we model the architecture as a system of communicating processes that we verify by finite-state model checking. We provide a detailed comparison of these two different approaches to formalization (infinite state with rich data types versus finite state) and verification (theorem proving versus model checking). Contrary to common belief, our case study suggests that Z is well suited for temporal reasoning about process models with complex operations on data. Moreover, our comparison highlights the advantages of proving theorems about such models and provides evidence that, in the hands of an experienced user, theorem proving may be neither substantially more time-consuming nor more complex than model checking.     

Parametric method of calculating a transient laminar boundary layer

A universal equation is derived for a transient laminar boundary layer in an incompressible fluid and is solved by numerical integration for certain values of the chosen parameters.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 22, No. 2, pp. 282–292, February, 1972.     

An attachment for mechanizing linear measurements

Summary The optimum method of mechanizing production measurements of dimensional parameters in engineering, especially under conditions of small-scale mass production in small establishments, consists in the use of universal checking devices which comprise a set of independent compound units, whose production must be undertaken by our instrument-making industry. This solution of the problem frees the customer plants from the necessity of producing special equipment, since they will only have to choose the measuring arrangement and a set of units whose various combinations can be used for checking details of any given type. This method will raise the quality of the control gear and lower its cost, will reduce to a minimum the time required for its assembly and familiarization with its measurement techniques; it will simplify the organization of inspection and speed the measuring.     

Differential equations determining the function that describes precatastrophic behavior of a system

Based on an analysis of the experimental data obtained for various catastrophic phenomena, Malinetskii et al. [1] considered the main parameters of a process preceding the catastrophe and proposed the following function of time that describes this process: I(t) = A + B(t _c ? t)^α[1 + Ccos(θ log(t _c ? t) ? ?)]. The passage to complex quantities and substitution of variables reveal a power-law character of this approximation. Using this approach, differential equations determining the function that describes the precatastrophic behavior are obtained.     

Adaptive event-triggered consensus control of multi-agent systems with prescribed performance and input quantization

This paper focuses on the adaptive fuzzy event-triggered consensus control problem for multi-agent systems (MAS) with prescribed performance and input quantization. Based on a prescribed performance function and an input quantization decomposition method, a new adaptive fuzzy event-triggered consensus protocol is presented. The instances in the event-triggered mechanism are triggered only when the event-triggered error exceeds a specified threshold, which can save limited communication resources. It is demonstrated that the event-triggered control protocol ensures that all signals in the MAS are semi-globally uniformly ultimately bounded. As a result, the consensus tracking errors converge to prescribed limits. Finally, simulation examples are provided to validate effectiveness of the proposed event-triggered control methods.     

Optimal Controller for Stochastic Polynomial Systems with State-Dependent Polynomial Input

This paper presents an optimal quadratic-Gaussian controller for stochastic polynomial systems with a state-dependent polynomial control input and a quadratic criterion over linear observations. The optimal closed-form controller equations are obtained using the separation principle, whose applicability to the considered problem is substantiated. As an intermediate result, the paper gives a closed-form solution of the optimal regulator (control) problem for polynomial systems with a state-dependent polynomial control input and a quadratic criterion. Performance of the obtained optimal controller is verified in an illustrative example against a conventional linear-quadratic-Gaussian (LQG) controller that is optimal for linearized systems. Simulation graphs demonstrating overall performance and computational accuracy of the designed optimal controller are included.     

Editorial

Higher-Order and Symbolic Computation -