Optimal Impulse Research Articles

Robust and Computationally Efficient Digital IIR Filter Synthesis and Stability Analysis Under Finite Precision Implementations

In this paper, an analytical synthesis method for obtaining an optimal infinite impulse response (IIR) state-space realization, say minimal pole-zero and pole-L2 sensitivity realizations, based on minimizing zero/L2 sensitivity measures subject to sparse normal-form state transition matrix is proposed. The proposed nth order realization possesses strong robustness and at most only 4n + 1 multiplications per output sample to prevent instability and output distortion, as well as to keep computational efficiency under finite word-length (FWL) effects. This is important for the IIR filter implemented in fixed-point and portable digital devices. In this paper, the proposed pole-L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> sensitivity minimization method, an alternative approach of pole-zero sensitivity minimization, may solve the issue of zero multiplicity. A normal-form realization has been proven that it can achieve a global minimum of un-weighted pole sensitivity measure as well as zero-input limit-cycle free property. The sparse normal-form realization can be synthesized from an arbitrary initial realization with distinct poles by using an analytical similarity transformation. Based on the derived fixed-point arithmetic model in state-space realizations, the Bellman-Gronwall Lemma, and normal-form transformation, a new word-length estimation to guarantee stability is derived. Finally, numerical simulations are performed to verify the correctness and the effectiveness of the theoretical results.

Recursive Least-Squares Lattice Algorithm Combined With Secondary-Path Innovation and Lattice-Order Decision Algorithms for Active Noise Control

This paper proposes a new active noise control (ANC) system based on a recursive least-squares lattice (RLSL) algorithm by designing secondary-path innovation (SPI) and lattice-order decision (LOD) algorithms. The SPI algorithm associated with the power spectral factorization of the secondary path is designed to apply the RLSL algorithm to the ANC system without the filtered-input structure. The SPI algorithm whitens the error microphone signals into the virtual error signals just ahead of the secondary path to construct the virtual desired signals corresponding to the outputs of the lattice filter. The LOD algorithm is designed to operate the ANC system without knowing the tap length of the optimal finite impulse response (FIR) filter. The decision algorithm using the initial and final estimation errors of the lattice filter estimates the tap length of the optimal FIR filter by increasing the lattice order one-by-one until the final estimation error reaches below a threshold value. Even in environments where the tap length of the optimal FIR filter is unknown, the proposed ANC system with low computational complexity shows almost the same performance as the ANC system based on a filtered-input recursive least squares algorithm.

Error Estimates of Penalty Schemes for Quasi-Variational Inequalities Arising from Impulse Control Problems

This paper proposes penalty schemes for a class of weakly coupled systems of Hamilton--Jacobi--Bellman quasi-variational inequalities (HJBQVIs) arising from stochastic hybrid control problems of regime-switching models with both continuous and impulse controls. We show that the solutions of the penalized equations converge monotonically to those of the HJBQVIs. We further establish that the scheme is half-order accurate for HJBQVIs with Lipschitz coefficients and first-order accurate for equations with more regular coefficients. Moreover, we construct the action regions and optimal impulse controls based on the error estimates and the penalized solutions. The penalty schemes and convergence results are then extended to HJBQVIs with possibly negative impulse costs. We also demonstrate the convergence of monotone discretizations of the penalized equations and establish that policy iteration applied to the discrete equation is monotonically convergent with an arbitrary initial guess in an infinite-dimensional setting. Numerical examples for infinite-horizon optimal switching problems are presented to illustrate the effectiveness of the penalty schemes over the conventional direct control scheme.

Asymptotic Impulse Control of Mean-Reverting Interest Rates with a Slowly Varying Stochastic Volatility

This paper studies the optimal central bank intervention of interest rate problem, where the interest rate process is modelled by an Ornstein—Uhlenbeck (mean-reverting) process with a slowly varying stochastic volatility. The objective of the central bank is to maintain the interest rate close to a target level, subject to fixed and proportional costs of interventions. The problem is formulated as an impulse control problem, which is being converted to a free boundary problem by adopting an ansatz of a band policy. Due to the complexity introduced by the stochastic volatility, there is no analytical solution to the free boundary value problem in the literature. This paper applies a regular perturbation approach to derive an asymptotic solution to the value function and the optimal impulse control (intervention). We rigorously prove that the zeroth-order approximation of the optimal impulse control is associated with the first-order approximation of the value function. Moreover, we show that this zeroth-order suboptimal impulse control is asymptotically optimal in a specific family of impulse controls.

Qualification status of high power ion thruster and flow control unit

Using high power space transportation systems equipped with electric propulsion requires development and qualification of electric thrusters with power equal to tens of kW. The optimal specific impulse of such systems designed for deep space missions should be very high (6000 … 8000 s). Elements for electric propulsion systems are developing at Keldysh Research Center (KeRC). This paper presents qualification status of IT-500 35-kW ion thruster and FCU-500 flow control unit. 2000-hours lifetime test of the IT-500 and FCU-500 was performed as a part of qualification. The ion thruster accomplished 2018 h of operation for the most part at input power of 17,8 kW, utilized 40 kg of xenon. Magnetic field and ion optics improvement and graphite grids development status are also described in this paper.

Optimal impulse control of a SIR epidemic

SummaryBased on our recent results on the optimal impulse control, we solve explicitly an optimal isolation problem for a specific SIR (susceptible‐infective‐removed) epidemic model describing, eg, the spread of AIDS.

Sparse Finite Impulse Response Low Pass Filter Design using Improved Firefly Algorithm

In this work, optimal sparse linear phase Finite impulse response filters are designed using swarm intelligence-based Firefly optimization algorithm. Filters are designed to meet the desired specification with fixed and variable sparsity. The objective function is formulated consisting of three parameters, i. e., maximum passband ripple, maximum stopband ripple and stopband attenuation. The effectiveness of the proposed method is evaluated in two stages. In first stage, the designed filters have been compared with non- sparse in terms of deviation in their specification. The Comparative analysis depicts that the proposed approach of sparse linear phase FIR filter design method performs better than the conventional methods without significantly deviating from the desired specification. The proposed designed filter is then implemented on xilinx ISE14.7(Vertex7) design environment and their performance is compared in terms of time delay, resource utilizaion and frequency of operation. In the second stage, designed sparse FIR filters are compared with earlier state of art sparse FIR filters design techniques.

The effectiveness of expert decision-making on the connection of myofibrosis with the profession using modern x-ray methods

Introduction. About 40% of all occupational diseases of the musculoskeletal system is degenerative muscle disease from overstrain — myofibrosis. Currently, the diagnosis is already established in the presence of obvious signs of disability, when the patient cannot continue his work in the previous profession.The aim of the study was to assess the informativeness of MRI in the early revealing of the disease. To develop the technique of MRI and detect changes in striated muscles of the upper extremities 50 patients with previously established diagnosis of myofibrosis were examined and 10 with suspicion on it. The analysis of the obtained image showed the most informative pulse sequences for revealing muscle changes. The optimal impulse sequence for the evaluation of muscle structures is IDEAL, for the determination of muscle edema — diffuse-weighted image and post-contrast T1-weighted image to visualize the disturbance of the histo-hematic barrier penetration. The presence of brachioradialis muscle edema on a diffusely weighted image served as an objective basis to regard these changes as the initial stage of myofibrosis and allowed to transfer patients from the group with suspected myofibrosis to the group with the initial stage of the disease, thus increasing the effectiveness of expert decisions on the connection of this disease with the profession.

Optimal True Time Delay Filter With Application to FPGA Firmware‐Based Phased Array Radar Signal Processing

AbstractThe European Incoherent Scatter‐3D phased array radar system will be largely based on field‐programmable gate array (FPGA) firmware electronics that carry out the signal processing by using different digital filters. In this paper we have presented a method of designing an optimal true time delay finite impulse response filter with applications to an FPGA firmware‐based multichannel signal processing system. The method provides an optimal true time delay finite impulse response filter with the desired responses at both band pass and stopband. This is possible by finding a mathematical minimization solution for the total power of all filter coefficients longer than a prespecified half‐length. The analysis is based on freely choosing the responses in the transition band until user‐specified desired responses are achieved. We have investigated the performance of these optimal digital filters in terms of the required digital signal processing (DSP) resources in GMACs (giga multiply accumulates per second) by considering both all‐in‐one stage filtering and cascaded solutions for ion and plasma line incoherent scatter radar measurements. We have shown that the cascaded solution provides more efficient utilization of DSP resources and hence represents the optimal choice for processing the proposed European Incoherent Scatter‐3D phased array radar signals. An example is demonstrated in which 906.88 GMACs are required to process 208 ion line beams with 2×4‐bit resolution in all‐in‐one stage processing, as compared to the 79.16 GMACs needed for a similar task in a cascaded solution.

Minimal Time Impulse Control of an Evolution Equation

This paper is concerned with a kind of minimal time control problem for a linear evolution equation with impulse controls. Each problem depends on two parameters: the upper bound of the control constraint and the moment of impulse time. The purpose of such a problem is to find an optimal impulse control (among certain control constraint set), which steers the solution of the evolution equation from a given initial state to a given target set as soon as possible. In this paper, we study the existence of optimal control for this problem; by the geometric version of the Hahn–Banach theorem, we show the bang–bang property of optimal control, which leads to the uniqueness of the optimal control; we also establish the continuity of the minimal time function of this problem with respect to the above mentioned two parameters, and discuss the convergence of the optimal control when the two parameters converge.

Optimal Impulse Vaccination Approach for an SIR Control Model with Short-Term Immunity

Vaccines are not administered on a continuous basis, but injections are practically introduced at discrete times often separated by an important number of time units, and this differs depending on the nature of the epidemic and its associated vaccine. In addition, especially when it comes to vaccination, most optimization approaches in the literature and those that have been subject to epidemic models have focused on treating problems that led to continuous vaccination schedules but their applicability remains debatable. In search of a more realistic methodology to resolve this issue, a control modeling design, where the control can be characterized analytically and then optimized, can definitely help to find an optimal regimen of pulsed vaccinations. Therefore, we propose a susceptible-infected-removed (SIR) hybrid epidemic model with impulse vaccination control and a compartment that represents the number of vaccinated individuals supposed to not acquire sufficient immunity to become permanently recovered due to the short-term effect of vaccines. A basic reproduction number, when the control is defined as a constant parameter, is calculated. Since we also need to find the optimal values of this impulse control when it is defined as a function of time, we start by stating a general form of an impulse version of Pontryagin’s maximum principle that can be adapted to our case, and then we apply it to our model. Finally, we provide our numerical simulations that are obtained via an impulse progressive-regressive iterative scheme with fixed intervals between impulse times (theoretical example of an impulse at each week), and we conclude with a discussion of our results.

Variant of the charged system search algorithm for the design of optimal linear phase finite impulse response filters

ABSTRACT Digital signal filtering is one of the prime area which is frequently used in practical applications. In the class of digital filters, the prominent filters include – filters with finite impulse response (FIR) and filters with infinite impulse response (IIR). Low pass, high pass, band pass and band stop filters are the different types of filters that are currently employed for carrying out filtering actions. Filters are used for practical applications to reduce the noise incurred while processing the signals received, whether it may be an audio signal, video signal, bio-medical signal and so on. The key features for the design of filters include the optimization of coefficients and in turn the design of coefficients is based on attaining maximum stop band attenuation with less ripple rates. This paper proposes the soft computing based wavelet concept being introduced in the charged system search algorithm at the updation process. The scaling factor in the updation equation is implemented with a wavelet introduced to improve the exploration and exploitation capability of the algorithm. This introduction of wavelet into the algorithm results in faster convergence of the algorithm and proves its effectiveness in comparison with that of the other approaches as available in the literature.

Irreversible investment with fixed adjustment costs: a stochastic impulse control approach

We consider an optimal stochastic impulse control problem over an infinite time horizon motivated by a model of irreversible investment choices with fixed adjustment costs. By employing techniques of viscosity solutions and relying on semiconvexity arguments, we prove that the value function is a classical solution to the associated quasi-variational inequality. This enables us to characterize the structure of the continuation and action regions and construct an optimal control. Finally, we focus on the linear case, discussing, by a numerical analysis, the sensitivity of the solution with respect to the relevant parameters of the problem.

Nonsingular Dual–Primal Algorithm for Fuel-Optimal Impulsive Rendezvous

This paper addresses a fuel-optimal impulsive rendezvous problem for minimizing the total characteristic velocity. In previous research, the authors proposed an efficient dual–primal optimization algorithm for this problem, taking advantage of the primal and dual formulations at once. Although the dual–primal optimization algorithm is capable of computing the accurate global-optimal trajectory for most cases, it cannot solve the nontrivial primer vector cases in which the optimal impulse timings (that is, the time points at which the optimality conditions are satisfied) are not identical to the time points of the optimal impulses (that is, the time points at which the impulses are applied in the optimal trajectory). The main contributions of this paper are 1) development of a novel strategy resolving the nontrivial primer vectors for general dual-first approaches, and 2) development of a new nonsingular dual–primal optimization algorithm adopting the strategy. The new algorithm generates an impulse sequence set including the possible combinations of time points of impulses, and then it searches through the impulse sequence set to find the primal root. To demonstrate its nontriviality resolution capability, the rendezvous problems near circular and elliptical orbits are solved for five test cases, and the newly developed algorithm succeeds in resolving nontrivial primer vectors.

Optimal Impulse Control of Dynamical Systems

Using the tools of the Markov Decision Processes, we justify the dynamic programming approach to the optimal impulse control of deterministic dynamical systems. We prove the equivalence of the integral and differential forms of the optimality equation. The theory is illustrated by an example from mathematical epidemiology. The developed methods can be also useful for the study of piecewise deterministic Markov processes.

Bias-Constrained Optimal Fusion Filtering for Decentralized WSN With Correlated Noise Sources

We propose and investigate a robust fusion optimal unbiased finite impulse response (FOUFIR) algorithm, which is composed of robust UFIR filters implemented in smart sensors and a bias-constrained optimal fusion filter (FF) implemented in a local node of a decentralized wireless sensor network (WSN). The algorithm is designed in discrete time-invariant state space for correlated sensor and node noise sources. To convert the model with correlated noise sources to that without the correlation, the method of indefinite coefficient is used. Assuming that the estimates are delivered to a node with no delay and missing data, a bias-constrained optimal FF is designed employing the linear unbiased minimum variance approach. Simulations are provided for a node operating with 12 smart sensors. Experimental verification is given for a WSN composed with 8 sensors of temperature and humidity. It is shown that the FOUFIR algorithm has better robustness against errors in the noise statistics and model uncertainties than the existing fusion and decentralized Kalman filtering algorithms.

시변 최적 유한 임펄스 응답 필터 기반 전력 신호 고조파 검출

본 논문에서는 시변 최적 FIR 필터를 이용한 전력 신호의 고조파 검출 방법을 제안한다. 잡음이 고려된 전력 신호에 대해 고조파의 진폭과 위상각의 변화량이 확률적 정보로 고려된 시변 상태 방정식 모델에 대해 시변 최적 FIR 필터를 설계하여 고조파 성분을 검출한다. 제안한 검출 방법에 사용된 시변 FIR 필터는 유한 구간의 정보만을 사용하고 어떠한 초기 조건도 사용하지 않도록 설계되어 칼만 필터 기반의 검출 방법의 오차 누적에 따른 검출 성능 저하나 발산 문제를 해결할 수 있다. 또한 FIR 구조의 필터 사용을 통해 칼만 필터 대비 불확실성에 대해 보다 강인한 검출이 가능하다. 시변 최적 FIR 필터의 사용을 통해 시불변 최적 FIR 필터 기반 고조파 검출 방법 대비 보다 일반적인 해를 제공한다. 제안하는 검출 방법의 우수성을 검증하기 위해 시변 칼만 필터 및 적응 칼만 필터 기반 고조파 검출 방법과의 비교 시뮬레이션을 수행한다.

Analysis of the Requested Perfection of a Nuclear Electric Propulsion System for a Mars Mission with a 2-Year Duration

Abstract—The results of the design and ballistic analysis of a 2-year manned mission to Mars are presented. Dependences of the maximum permissible specific mass of the electric power and propulsion system on the spacecraft (SC) mass in the initial earth orbit are obtained. It is shown that, for the analyzed set of characteristics of SC systems with the SC mass in the initial orbit of 200 t, to implement a Mars mission with a 2-year duration, the required perfection of the electric power and propulsion system should be ideally high (the specific mass of the electric power and propulsion system should be no more than 3.26 kg/kW). Increasing the mass in the initial orbit leads to a relaxation of the requirements for the perfection of a transport system. If the mass in the initial orbit is increased to 475 t, then the maximum possible specific mass of the electric power and propulsion system grows to 11 kg/kW. The optimal electric power of the nuclear power plant with a change in the initial mass within the mentioned range (from 200 to 475 t) increases from 7.7 to 11.7 MW. The optimal specific impulse of the electric propulsion falls from 9000 s (this value is accepted as the maximum permissible) to 6880 s. It is shown that, if the specific mass of the electric power and propulsion system is 5, 7.5, and 10 kg/kW, then, to implement the mission, the SC mass in the initial orbit should be no less than 234.1, 305.4, and 415.5 t, respectively.

Optimal exchange rates management using stochastic impulse control for geometric Lévy processes

In this paper, we consider the optimal impulse control problem of a currency with exchange rate dynamics whose state follows a geometric Levy process. The objective of the Central Bank is to keep the exchange rate as close as possible to a given target. Running costs associating with the difference between the actual exchange rate and the target are continuously incurred to the system. We suppose that, when the Central Bank intervenes in the system, it requires the fixed and proportional costs. Applying the theory of stochastic impulse controls, we find the optimal exchange rate at which interventions should be performed and the optimal sizes of the interventions, so as to minimize the expected total discounted sum of the intervention costs and running costs incurred over the infinite time horizon. Furthermore, numerical comparisons for the optimal intervention strategy between the geometric Levy process model and the geometric Brownian motion model are investigated in details.

Optimal design of IIR filters based on least ℓp‐norm using a novel meta‐heuristic algorithm

AbstractIn this work, an optimal infinite impulse response (IIR) filter is designed using least Pth norm and new meta‐heuristic optimization algorithm called Crow Search Algorithm (CSA). The two approaches try to get a resolution to the specified problem but use unlike approaches to perform so. Furthermore, the ℓp‐norm is used to design optimum IIR filters. The main motivation of using CSA is its user‐friendly optimization tool for both beginner and professional users. This Algorithm provides a good stability between variety and strength which are mainly controlled by the parameter of awareness probability. Some examples of IIR filter design cases are treated, and a comparison is done. It is revealed that the design objective is successfully attained, and the resultant filter parameters are better using the ℓp‐norm combined with the proposed CSA meta‐heuristic optimization algorithms compared with IIR filter designed using butter synthesis approach in terms of accuracy and robustness. Classical approaches are largely outperformed by CSA for the same filter order.