Constrained optimal control theory for differential linear repetitive processes

Differential repetitive processes are a distinct class of continuous-discrete two-dimensional linear systems of both systems theoretic and applications interest. These processes complete a series of sweeps termed passes through a set of dynamics defined over a finite duration known as the pass length, and once the end is reached the process is reset to its starting position before the next pass begins. Moreover the output or pass profile produced on each pass explicitly contributes to the dynamics of the next one. Applications areas include iterative learning control and iterative solution algorithms, for classes of dynamic nonlinear optimal control problems based on the maximum principle, and the modeling of numerous industrial processes such as metal rolling, long-wall cutting, etc. In this paper we develop substantial new results on optimal control of these processes in the presence of constraints where the cost function and constraints are motivated by practical application of iterative learning control to robotic manipulators and other electromechanical systems. The analysis is based on generalizing the well-known maximum and $\epsilon$-maximum principles to the

Об управляемости, наблюдаемости и оптимизации дискретных нестационарных линейных систем Вольтерра

   Исследуются дискретные нестационарные линейные системы уравнений типа Вольтерра, существенной особенностью которых является зависимость каждого последующего состояния от всей предыстории процесса. Получено представление решений таких систем в форме Коши с учетом управляющих воздействий. Установлены необходимые и достаточные условия точечной управляемости, точечной управляемости по выходу и наблюдаемости, а также исследована линейно-квадратичная задача оптимизации рассматриваемых систем уравнений Вольтерра.   In this article, we study discrete nonstationary linear dynamic systems of Volterra type. An essential feature of such kind of systems is that their current states depend on the previous states of this system. The formula Cauchy, which gives us the solution of linear Volterra systems with the control inputs, is obtained. The necessary and sufficient conditions of the pointwise controllability, pointwise output controllability, and observability are proven. Also the linear-quadratic optimization problem for the nonstationary Volterra control systems is studied.   Исследуются дискретные нестационарные линейные системы уравнений типа Вольтерра, существенной особенностью которых является зависимость каждого последующего состояния от всей предыстории процесса. Получено представление решений таких систем в форме Коши с учетом управляющих воздействий. Установлены необходимые и достаточные условия точечной управляемости, точечной управляемости по выходу и наблюдаемости, а также исследована линейно-квадратичная задача оптимизации рассматриваемых систем уравнений Вольтерра

LAPAROSCOPIC THROMBECTOMY WITH RADICAL NEPHRECTOMY FOR RENAL CELL CARCINOMA WITH INFERIOR VENA CAVA THROMBUS

Laparoscopic radical nephrectomy (LRN) is presently viewed as the standard treatment for localized renal cancer. However, 5–10% of renal cell carcinoma is associated with the development of the tumor thrombus. The works of few authors have demonstrated the feasibility of laparoscopic radical nephrectomy in patients with tumor thrombus in renal vein. We describe the method and report our own experience of LRN with thrombectomy from the inferior vena cava. Two patients with renal masses with infrahepatic tumor thrombus underwent right-sided radical nephrectomy and thrombectomy. After clipping the right renal artery, we dissected the IVC above and below the level of the thrombus and introduced the vessel loops. In addition to that we mobilized the left renal vein and clipped the right gonadal vein. After occluding the IVC and the left renal vein with a vessel loops or a laparoscopic Satinsky vascular clamp, we made an incision the IVC wall, extracted the thrombus and excised the ostium of right renal vein. The defect in the IVC was closed with running sutures. Laparoscopic RN and thrombectomy were successfully performed in all the patients without conversion to open surgery. With a mean follow-up 8–20 months all patients have no signs of local recurrences or distant metastases. Laparoscopic RN with IVC thrombectomy in selected RCC-patients with differential extensions of tumor thrombus is a safe and feasible procedure. Additional studies are needed to examine the advantages of this approach