Suboptimal control law for a near-space hypersonic vehicle based on Koopman operator and algebraic Riccati equation

This paper presents a novel suboptimal attitude tracking controller based on the algebraic Riccati equation for a near-space hypersonic vehicle (NSHV). Since the NSHV’s attitude dynamics is complexly nonlinear, it is hard to directly construct an appropriate algebraic Riccati equation. We design the construction based on the Chebyshev series and the Koopman operator theory, which includes three steps. First, the Chebyshev series are considered to transform the error dynamics of the NSHV’s attitude into a polynomial system. Second, the Koopman operator is used to obtain a series of high-dimensional linear dynamics to approximate each of the polynomial system’s vector fields. In this step, our contribution is to determine a well-posed linear dynamics with the minimal dimension to approximate the original nonlinear vector field, which helps to design the control law and analyze the control performance. Third, based on the high-dimensional dynamics, the NSHV’s attitude error dynamics is separated into the linear part and the nonlinear part, such that the algebraic Riccati equation can be constructed according to the linear part. Then, the suboptimal error feedback control law is derived from the algebraic Riccati equation. The closed-loop control system is proved to be locally exponentially stable. Finally, the numerical simulation demonstrates the effectiveness of the suboptimal control law.

Suboptimal control synthesis for state and input delayed quadratic systems

In this article a suboptimal linear-state feedback controller for multi-delay quadratic system is investigated. Optimal state and input coefficients resulting from the expansion over a hybrid basis of block pulse and Legendre polynomials are first obtained by formulating a nonlinear programming problem. Afterwards, suboptimal control gains are found by solving a least square problem constructed with optimal coefficients of the open loop study. A sufficient condition for the exponential stability of the closed loop is obtained from generalized Grönwall–Bellman lemma. The Van de Vusse chemical reactor case is handled allowing to validate the proposed technique.

Nonlinear suboptimal attitude control law for near-space hypersonic vehicle: Eigenvalue analysis and weight matrices design

This paper considers a nonlinear suboptimal control problem for a near-space hypersonic vehicle's (NSHV's) attitude dynamics. The least-square and stable manifold methods first solve an unconstrained approximately optimal control law corresponding to the nonlinear attitude model. Then, to further meet the dynamic performance requirement of the attitude control system, a novel strategy based on the Koopman operator, symplectic geometric theory, and the stable manifold theorem is proposed to approximate the eigenvalues of the closed-loop nonlinear unconstrained approximated optimal control system. The weight matrices in the optimal performance index, which directly determine the output responses of the nonlinear attitude dynamics, can be appropriately designed according to the eigenvalues. The final control law considers the actuator constraints. The NSHV's closed-loop attitude control system is proved to be locally exponentially stable, and the suboptimality of the control law is analyzed. Numerical simulation demonstrates the effectiveness of the proposed scheme.

Prevalence, Awareness, Treatment, and Control of Hypertension in the United Arab Emirates: A Systematic Review and Meta-Analysis

Background: Evidence for the prevalence, awareness, treatment, and control of hypertension in the United Arab Emirates (UAE) is limited. A systematic review and meta-analysis were conducted to summarize the existing knowledge regarding the prevalence, awareness, treatment, and control of hypertension in the UAE. Methods: We searched PubMed/MEDLINE, Embase, Scopus, and Google Scholar using prespecified medical subject handling (MeSH) terms and text words to identify the relevant published articles from 1 January 1995 to 31 August 2021. Population-based prospective observational studies conducted among healthy adult subjects living in the UAE and that defined hypertension using the guidelines-recommended blood pressure (BP) cut-offs ≥ 130/80 mmHg or ≥ 140/90 mmHg were considered. Results: Of 1038 studies, fifteen cross-sectional studies were included for data extraction involving 139,907 adults with a sample size ranging from 74 to 50,138 and with cases defined as blood pressure ≥ 140/90 mmHg. The pooled prevalence of hypertension was 31% (95% confidence interval (CI): 27–36), and a higher prevalence was observed in Dubai (37%, 95% CI: 28–45) than in the Abu Dhabi region (29%, 95% CI: 24–35) and in multicenter studies (24%, 95% CI: 14–33). The level of awareness was only 29% (95% CI: 17–42), 31% (95% CI: 18–44) for treatment, and 38% (95% CI: 19–57) had controlled BP (< 140/90 mmHg). Conclusion: This study revealed a high prevalence of hypertension with low awareness and suboptimal control of hypertension. Multifaceted approaches that include the systematic measurement of BP, raising awareness, and improving hypertension diagnoses and treatments are needed.

Nonlinear suboptimal attitude control law for near-space hypersonic vehicle: Eigenvalue analysis and weight matrices design

This paper considers a nonlinear suboptimal control problem for a near-space hypersonic vehicle's (NSHV's) attitude dynamics. The least-square and stable manifold methods first solve an unconstrained approximately optimal control law corresponding to the nonlinear attitude model. Then, to further meet the dynamic performance requirement of the attitude control system, a novel strategy based on the Koopman operator, symplectic geometric theory, and the stable manifold theorem is proposed to approximate the eigenvalues of the closed-loop nonlinear unconstrained approximated optimal control system. The weight matrices in the optimal performance index, which directly determine the output responses of the nonlinear attitude dynamics, can be appropriately designed according to the eigenvalues. The final control law considers the actuator constraints. The NSHV's closed-loop attitude control system is proved to be locally exponentially stable, and the suboptimality of the control law is analyzed. Numerical simulation demonstrates the effectiveness of the proposed scheme.

103 Coronary plaque healing and diabetes: insights from optical coherence tomography imaging

Aims Atherosclerotic plaque healing is a dynamic process developing after plaque rupture or erosion, which aims to prevent lasting occlusive thrombus formation and to promote plaque repair. We hypothesized that diabetes mellitus, one of the major conventional cardiovascular risk factors, may influence the healing capacity after plaque destabilization. Methods and results In this single-centre observational cohort study, patients with acute coronary syndrome (ACS) or chronic coronary syndrome (CCS) who underwent optical coherence tomography (OCT) imaging at Fondazione Policlinico A. Gemelli–IRCCS, Rome, were included. Patients were divided into two groups (i.e. diabetes vs. no diabetes), and stratified based on diabetes medications (i.e. insulin, vs. oral antidiabetic drugs). OCT analysis of non-culprit coronary segments was performed. 105 patients were included (44 diabetes, 61 no diabetes). Prevalence of HCPs was not significantly different between patients with and without diabetes (3.6% vs. 3.8%, P = 0.854). However, patients with diabetes on insulin showed a lower prevalence of HCPs both at patient-based (7.1% vs. 26.4%, P = 0.116) and at segment-based analysis (1.2% vs. 4.2%, P = 0.020). When comparing HbA1c levels based on the presence or absence of healed plaque at the non-culprit lesions, patients with healed plaque showed significantly lower levels of HbA1c compared to patients without healed plaques (43.5 ± 12.1% vs. 61.2 ± 10.4%, P &lt; 0.001). At segment-based analysis, normal vessel structure, pathological intimal thickening (PIT), and spotty calcifications were significantly less prevalent in diabetic patients (2.1% vs. 5.1%, P = 0.001; 7.2% vs. 9.5%, P = 0.05; 9.9% vs. 13.6%, P = 0.02, respectively), whereas neovascularization was significantly higher (19.2% vs. 15.6%, P = 0.035). Conclusions Patients with diabetes have a distinct coronary non-culprit plaque phenotype. Healing capacity may be impaired in patients with advanced diabetes on insulin therapy and in those with a suboptimal control of the disease. Further prospective, larger scale studies are warranted to confirm these findings.

Ivabradine–Flecainide as Breakthrough Drug Combination for Congenital Junctional Ectopic Tachycardia: A Case Report and Literature Review

Congenital junctional ectopic tachycardia (CJET) is a rare tachyarrhythmia that remains difficult to manage, with suboptimal control in most cases. Here, we report literature research on the use of ivabradine in the treatment of pediatric junctional ectopic tachycardia (JET), both congenital and postoperative, and describe the successful use of ivabradine–flecainide association for CJET therapy resistant to other antiarrhythmic agents. This new drug combination was effective in completely suppressing JET. Ivabradine–flecainide combination may be considered a new therapeutic strategy of CJET with a satisfactory efficacy/tolerability ratio in patients resistant to conventional drug combinations.

Modified Infinite-Time State-Dependent Riccati Equation Method for Nonlinear Affine Systems: Quadrotor Control

This paper presents modeling and infinite-time suboptimal control of a quadcopter device using the state-dependent Riccati equation (SDRE) method. It establishes a solution to the control problem using SDRE and proposes a new procedure for solving the problem. As a new contribution, the paper proposes a modified SDRE-based suboptimal control technique for affine nonlinear systems. The method uses a pseudolinearization of the closed-loop system employing Moore–Penrose pseudoinverse. Then, the algebraic Riccati equation (ARE), related to the feedback compensator gain, is reduced to state-independent form, and the solution can be computed only once in the whole control process. The ARE equation is applied to the problem reported in this study that provides general formulation and stability analysis. The effectiveness of the proposed control technique is demonstrated through the use of simulation results for a quadrotor device.

Dual Quaternion Based Close Proximity Operation for In-Orbit Assembly via Model Predictive Control

This paper studies the problem of guidance and control for autonomous in-orbit assembly. A six-degree-of-freedom (6-DOF) motion control for in-orbit assembly close proximity operation between a service satellite and a target satellite is addressed in detail. The dynamics based on dual quaternion are introduced to dispose the coupling effect between translation and rotation in a succinct frame, in which relevant perturbation and disturbance are involved. With the consideration of economical principle for fuel consume, a generic control system based on model predictive control (MPC) is then designed to generate a suboptimal control sequence for rendezvous trajectory considering actuator output saturation. The stability and robustness issues of the MPC-based control system are analyzed and proved. Numerical simulations are presented to demonstrate the effectiveness and robustness of the proposed control scheme, while additional comparisons for diverse horizons of the MPC are further conducted.