The book presents, in a systematic manner, the optimal controls under different mathematical models in fermentation processes. Variant mathematical models – i.e., those for multistage systems; switched autonomous systems; time-dependent and state-dependent switched systems; multistage time-delay systems and switched time-delay systems – for fed-batch fermentation processes are proposed and the theories and algorithms of their optimal control problems are studied and discussed. By putting forward novel methods and innovative tools, the book provides a state-of-the-art and comprehensive systematic treatment of optimal control problems arising in fermentation processes. It not only develops nonlinear dynamical system, optimal control theory and optimization algorithms, but can also help to increase productivity and provide valuable reference material on commercial fermentation processes.

The book presents, in a systematic manner, the optimal controls under different mathematical models in fermentation processes. Variant mathematical models – i.e., those for multistage systems; switched autonomous systems; time-dependent and state-dependent switched systems; multistage time-delay systems and switched time-delay systems – for fed-batch fermentation processes are proposed and the theories and algorithms of their optimal control problems are studied and discussed. By putting forward novel methods and innovative tools, the book provides a state-of-the-art and comprehensive systematic treatment of optimal control problems arising in fermentation processes. It not only develops nonlinear dynamical system, optimal control theory and optimization algorithms, but can also help to increase productivity and provide valuable reference material on commercial fermentation processes.

Fractional optimal control problems (FOCPs) are a generalization of the conventional optimal control problems of integer order in the sense that the dynamics are governed by fractional systems.  FOCPs arise in many fields such as mathematics, engineering, biology, economics, finance and management. It is often impossible to obtain analytical solutions of nonlinear FOCPs in general. Thus, establishing optimization theory and finding effective numerical methods for nonlinear FOCPs have become an active research topic. In this book, we will investigate the optimality theories and numerical solution methods of a variety of nonlinear FOCPs including delay nonlinear FOCP, free final time nonlinear FOCP, robust nonlinear FOCP, nonlinear FOCPs with Atangan-Baleanu derivatives and nonlinear FOCPs with conformable derivatives.Numerical solution of fractional optimal control has been an emerging research topic which has attracted much attention in the past few years from both researchers and practitioners, as advances in this area will be very useful for solving real-world optimal control problems which cannot be solved using conventional methods. The objective of this book is to present systematically various fractional optimal control problems of practical importance. By bringing forward fresh novel methods and innovative tools, we are to provide a state-of-the-art and comprehensive systematic treatment of nonlinear fractional optimal control problems, mostly from our previous research results. This can not only develop fractional systems, optimal control theory, and optimization algorithms but also serve as a reference for applied and computational of optimal control problems.The book will be attractive to researchers in various fields of mathematics, control theory and engineering and practitioners who wants to solve their real-life fractional optimal control problems. Graduate students in related fields will also find this book useful for their training and research.

The book presents, in a systematic manner, the optimal controls under different mathematical models in fermentation processes. Variant mathematical models – i.e., those for multistage systems; switched autonomous systems; time-dependent and state-dependent switched systems; multistage time-delay systems and switched time-delay systems – for fed-batch fermentation processes are proposed and the theories and algorithms of their optimal control problems are studied and discussed. By putting forward novel methods and innovative tools, the book provides a state-of-the-art and comprehensive systematic treatment of optimal control problems arising in fermentation processes. It not only develops nonlinear dynamical system, optimal control theory and optimization algorithms, but can also help to increase productivity and provide valuable reference material on commercial fermentation processes.

The book presents, in a systematic manner, the optimal controls under different mathematical models in fermentation processes. Variant mathematical models – i.e., those for multistage systems; switched autonomous systems; time-dependent and state-dependent switched systems; multistage time-delay systems and switched time-delay systems – for fed-batch fermentation processes are proposed and the theories and algorithms of their optimal control problems are studied and discussed. By putting forward novel methods and innovative tools, the book provides a state-of-the-art and comprehensive systematic treatment of optimal control problems arising in fermentation processes. It not only develops nonlinear dynamical system, optimal control theory and optimization algorithms, but can also help to increase productivity and provide valuable reference material on commercial fermentation processes.

Fractional optimal control problems (FOCPs) are a generalization of the conventional optimal control problems of integer order in the sense that the dynamics are governed by fractional systems.  FOCPs arise in many fields such as mathematics, engineering, biology, economics, finance and management. It is often impossible to obtain analytical solutions of nonlinear FOCPs in general. Thus, establishing optimization theory and finding effective numerical methods for nonlinear FOCPs have become an active research topic. In this book, we will investigate the optimality theories and numerical solution methods of a variety of nonlinear FOCPs including delay nonlinear FOCP, free final time nonlinear FOCP, robust nonlinear FOCP, nonlinear FOCPs with Atangan-Baleanu derivatives and nonlinear FOCPs with conformable derivatives.Numerical solution of fractional optimal control has been an emerging research topic which has attracted much attention in the past few years from both researchers and practitioners, as advances in this area will be very useful for solving real-world optimal control problems which cannot be solved using conventional methods. The objective of this book is to present systematically various fractional optimal control problems of practical importance. By bringing forward fresh novel methods and innovative tools, we are to provide a state-of-the-art and comprehensive systematic treatment of nonlinear fractional optimal control problems, mostly from our previous research results. This can not only develop fractional systems, optimal control theory, and optimization algorithms but also serve as a reference for applied and computational of optimal control problems.The book will be attractive to researchers in various fields of mathematics, control theory and engineering and practitioners who wants to solve their real-life fractional optimal control problems. Graduate students in related fields will also find this book useful for their training and research.