Infinite horizon optimal control. Theory and applications
The main problem of the research in the monograph is a qualitative analysis of the behavior of optimal trajectories, in the first place a convergence to the point of phase space which is a solution of a static optimization problem. The statements on this convergence are usually called turnpike theorems. Chapter 1 gives examples of optimal control problems on unbounded time intervals in the field of economics, ecology and technology. The definitions of optimal control are introduced with a meaning for divergence of integrals in the optimality functional. Chapter 2 presents necessary and sufficient conditions for optimality in the form of a maximum principle for trajectories with infinite horizon duration. Chapter 3 presents some problems where turnpike behavior of optimal trajectories can be fixed with the help of simple devices. Chapter 4 considers convex autonomous problems with the help of large variations of trajectories. Autonomous systems with a nonautonomous functional of optimality, where the nonautonomous component is a decreasing exponent, are considered in chapter 5. Chapter 6 gives statements on the convergence of optimal trajectories for nonautonomous and nonconvex problems. Chapter 7 is devoted to the existence of solutions on infinite time intervals for nonautonomous control systems. Chapter 8 analyses optimal processes with infinite time for linear equations with distributed parameters interpreted as usual differential equations in Hilbert space. The book will promote the development of a new trend in optimal control connected with qualitative research of optimal processes of large and infinite duration [see also, the reviewer, Avtom. Telemekh. 1983, No.9, 58-66 (1983; Zbl 0562.93055); ibid. 1981, No.8, 119-130 (1981; Zbl 0489.93036); and the reviewer together with \textit{A. I. Panasyuk}, Prikl. Mat. Mekh. 49, 524-535 (1985; Zbl 0614.49015)].
linear equations with distributed parameters
scientific article; zbMATH DE number 4060189