Fractional Order Version of the HJB Equation

We consider an extension of the well-known Hamilton-Jacobi-Bellman (HJB) equation for fractional order dynamical systems in which a generalized performance index is considered for the related optimal control problem. Owing to the nonlocality of the fractional order operators, the classical HJB equation, in the usual form, does not hold true for fractional problems. Effectiveness of the proposed technique is illustrated through a numerical example.Comment: This is a preprint of a paper whose final and definite form is with 'Journal of Computational and Nonlinear Dynamics', ISSN 1555-1415, eISSN 1555-1423, CODEN: JCNDDM. Submitted 28-June-2018; Revised 15-Sept-2018; Accepted 28-Oct-201

A numerical approach for solving fractional optimal control problems using modified hat functions

We introduce a numerical method, based on modified hat functions, for solving a class of fractional optimal control problems. In our scheme, the control and the fractional derivative of the state function are considered as linear combinations of the modified hat functions. The fractional derivative is considered in the Caputo sense while the Riemann-Liouville integral operator is used to give approximations for the state function and some of its derivatives. To this aim, we use the fractional order integration operational matrix of the modified hat functions and some properties of the Caputo derivative and Riemann-Liouville integral operators. Using results of the considered basis functions, solving the fractional optimal control problem is reduced to the solution of a system of nonlinear algebraic equations. An error bound is proved for the approximate optimal value of the performance index obtained by the proposed method. The method is then generalized for solving a class of fractional optimal control problems with inequality constraints. The most important advantages of our method are easy implementation, simple operations, and elimination of numerical integration. Some illustrative examples are considered to demonstrate the effectiveness and accuracy of the proposed technique.publishe

Designing a New Digital Modulator for Chaotic Secure Communication Systems Using Total

This paper addresses a new method for decreasing error in secure chaotic communication which utilizes an adaptive law in demodulator part. The basic tools in this process are the Total Least Square as the fundamental technique in demodulating section and a chaotic signal as the carrier one which impose some complexities on the overall system. This algorithm may be used in digital filter for estimating parameters with lower error. Using this approach an improvement can be achieved in estimating the desired signal in comparison with two famous methods, namely, ordinary Least Mean Square (LMS) and Constrained-Stability LMS (CS-LMS). An illustrative example has been used to verify the presented technique through numerical simulation

Utilising electroanatomic mapping during ablation in patients with CHD to reduce radiation exposure

Background: Patients with CHD can be exposed to high levels of cumulative ionising radiation. Utilisation of electroanatomic mapping during catheter ablation leads to reduced radiation exposure in the general population but has not been well studied in patients with CHD. This study evaluated the radiation sparing benefit of using three-dimensional mapping in patients with CHD. Methods: Data were retrospectively collected from the Catheter Ablation with Reduction or Elimination of Fluoroscopy multi-institutional registry. Patients with CHD were selected. Those with previous ablations, concurrent diagnostic or interventional catheterisation and unknown arrhythmogenic foci were excluded. The control cohort was matched for operating physician, arrhythmia mechanism, arrhythmia location, weight and age. The procedure time, rate of fluoroscopy use, fluoroscopy time, procedural success, complications, and distribution of procedures per year were compared between the two groups. Results: Fifty-six patients with congenital heart disease and 56 matched patients without CHD were included. The mean total procedure time was significantly higher in patients with CHD (212.6 versus 169.5 minutes, p = 0.003). Their median total fluoroscopy time was 4.4 minutes (compared to 1.8 minutes), and their rate of fluoroscopy use was 23% (compared to 13%). The acute success and minor complication rates were similar and no major complications occurred. Conclusions: With the use of electroanatomic mapping during catheter ablation, fluoroscopy use can be reduced in patients with CHD. The majority of patients with CHD received zero fluoroscopy

Utilising electroanatomic mapping during ablation in patients with CHD to reduce radiation exposure.

BACKGROUND: Patients with CHD can be exposed to high levels of cumulative ionising radiation. Utilisation of electroanatomic mapping during catheter ablation leads to reduced radiation exposure in the general population but has not been well studied in patients with CHD. This study evaluated the radiation sparing benefit of using three-dimensional mapping in patients with CHD. METHODS: Data were retrospectively collected from the Catheter Ablation with Reduction or Elimination of Fluoroscopy multi-institutional registry. Patients with CHD were selected. Those with previous ablations, concurrent diagnostic or interventional catheterisation and unknown arrhythmogenic foci were excluded. The control cohort was matched for operating physician, arrhythmia mechanism, arrhythmia location, weight and age. The procedure time, rate of fluoroscopy use, fluoroscopy time, procedural success, complications, and distribution of procedures per year were compared between the two groups. RESULTS: Fifty-six patients with congenital heart disease and 56 matched patients without CHD were included. The mean total procedure time was significantly higher in patients with CHD (212.6 versus 169.5 minutes, p = 0.003). Their median total fluoroscopy time was 4.4 minutes (compared to 1.8 minutes), and their rate of fluoroscopy use was 23% (compared to 13%). The acute success and minor complication rates were similar and no major complications occurred. CONCLUSIONS: With the use of electroanatomic mapping during catheter ablation, fluoroscopy use can be reduced in patients with CHD. The majority of patients with CHD received zero fluoroscopy

Acute outcomes of three-dimensional mapping for fluoroscopy reduction in paediatric catheter ablation for supraventricular tachycardia.

BACKGROUND: Catheter ablation is a safe and effective therapy for the treatment of supraventricular tachycardia in children. Current improvements in technology have allowed progressive reduction in radiation exposure associated with the procedure. To assess the impact of three-dimensional mapping, we compared acute procedural results collected from the Catheter Ablation with Reduction or Elimination of Fluoroscopy registry to published results from the Prospective Assessment after Pediatric Cardiac Ablation study. METHODS: Inclusion and exclusion criteria from the Prospective Assessment after Pediatric Cardiac Ablation study were used as guidelines to select patient data from the Catheter Ablation with Reduction or Elimination of Fluoroscopy registry to compare acute procedural outcomes between cohorts. Outcomes assessed include procedural and fluoroscopy exposure times, success rates of procedure, and complications. RESULTS: In 786 ablation procedures, targeting 498 accessory pathways and 288 atrioventricular nodal reentrant tachycardia substrates, average procedural time (156.5 versus 206.7 minutes, p \u3c 0.01), and fluoroscopy time (1.2 versus 38.3 minutes, p \u3c 0.01) were significantly shorter in the study group. Success rates for the various substrates were similar except for manifest accessory pathways which had a significantly higher success rate in the study group (96.4% versus 93.0%, p \u3c 0.01). Major complication rates were significantly lower in the study group (0.3% versus 1.6%, p \u3c 0.01). CONCLUSIONS: In a large, multicentre study, three-dimensional systems show favourable improvements in clinical outcomes in children undergoing catheter ablation of supraventricular tachycardia compared to the traditional fluoroscopic approach. Further improvements are anticipated as technology advances