The book focuses on symplectic pseudospectral methods for nonlinear optimal control problems and their applications. Both the fundamental principles and engineering practice are addressed. Symplectic pseudospectral methods for nonlinear optimal control problems with complicated factors (i.e., inequality constraints, state-delay, unspecific terminal time, etc.) are solved under the framework of indirect methods. The methods developed here offer a high degree of computational efficiency and accuracy when compared with popular direct pseudospectral methods. The methods are applied to solve optimal control problems arising in various engineering fields, particularly in path planning problems for autonomous vehicles. Given its scope, the book will benefit researchers, engineers and graduate students in the fields of automatic control, path planning, ordinary differential equations, etc.

Primary liver cancer is the third most deadly and fifth most common cancer worldwide (approximately 500,000 deaths annually), with a sharp increase of incidence in the United States in recent years. Hepatocellular carcinoma (HCC) and cholangiocarcinoma (CC) are the major types of primary liver cancer. Risk factors include gender, hepatitis B virus (HBV), hepatitis C virus (HCV), cirrhosis, metabolism diseases, diabetes, obesity, toxins, excess alcohol consumption and smoking. Liver cancer arises most frequently in inflammatory livers with extensive oxidative stress due to viral hepatitis which causes over 80 per cent of HCC cases worldwide. Currently, survival remains dismal for most HCC and CC patients, largely due to the tumor's aggressiveness at the time of diagnosis and the lack of effective therapy.

Differential Quadrature and Differential Quadrature Based Element Methods: Theory and Applications is a comprehensive guide to these methods and their various applications in recent years. Due to the attractive features of rapid convergence, high accuracy, and computational efficiency, the differential quadrature method and its based element methods are increasingly being used to study problems in the area of structural mechanics, such as static, buckling and vibration problems of composite structures and functional material structures. This book covers new developments and their applications in detail, with accompanying FORTRAN and MATLAB programs to help you overcome difficult programming challenges. It summarises the variety of different quadrature formulations that can be found by varying the degree of polynomials, the treatment of boundary conditions and employing regular or irregular grid points, to help you choose the correct method for solving practical problems.

Primary liver cancer is the third most deadly and fifth most common cancer worldwide (~500,000 deaths annually), with a sharp increase of incidence in the United States in recent years. Hepatocellular carcinoma (HCC) and cholangiocarcinoma (CC) are the major types of primary liver cancer. Risk factors include gender, hepatitis B virus (HBV), hepatitis C virus (HCV), cirrhosis, metabolism diseases, diabetes, obesity, toxins, excess alcohol consumption and smoking. Liver cancer arises most frequently in inflammatory livers with extensive oxidative stress due to viral hepatitis which causes over 80% of HCC cases worldwide. Currently, survival remains dismal for most HCC and CC patients, largely due to the tumor's aggressiveness at the time of diagnosis and the lack of effective therapy.

The book focuses on symplectic pseudospectral methods for nonlinear optimal control problems and their applications. Both the fundamental principles and engineering practice are addressed. Symplectic pseudospectral methods for nonlinear optimal control problems with complicated factors (i.e., inequality constraints, state-delay, unspecific terminal time, etc.) are solved under the framework of indirect methods. The methods developed here offer a high degree of computational efficiency and accuracy when compared with popular direct pseudospectral methods. The methods are applied to solve optimal control problems arising in various engineering fields, particularly in path planning problems for autonomous vehicles. Given its scope, the book will benefit researchers, engineers and graduate students in the fields of automatic control, path planning, ordinary differential equations, etc.