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00051863 Carlson, Dean A. Haurie, Alain B. Leizarowitz, Arie Infinite horizon optimal control. Deterministic and stochastic systems. 2nd, rev. and enl. ed. Berlin etc.: Springer-Verlag. xvi, 332 p. (1991). 1991 Berlin etc.: Springer-Verlag EN qualitative analysis of optimal trajectories turnpike theorems unbounded time intervals optimal control maximum principle for trajectories global asymptotic stability infinite horizon finite horizon discount overtaking optimal solutions integro-differential equations distributed parameters differential equations in Hilbert space random modal jumps Zbl 0649.49001 [For a review of the first edition (1987) see Zbl 0649.49001.] The main topic of this monograph is a qualitative analysis of optimal trajectories behaviors. Statements about the convergence of trajectories 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. --- Chapter 2 presents a necessary and sufficient conditions of optimality in the form of a maximum principle for trajectories with infinite horizon. --- Chapter 3 represents some simple control problems where turnpike behavior of optimal trajectories can be fixed. --- Chapter 4 considers global asymptotic stability and existence of optimal trajectories for infinite horizon autonomous convex systems. --- The next chapter deals with an approach which is called the reduction to finite rewards. An important aspect of the method developed here is related to continuous and discrete-time control systems. --- Chapter 6 gives a global and local analysis of asymptotic stability with a discounted criterion. The turnpike properties for finite horizon optimal control problems with discount are given. --- Chapter 7 is devoted to the existence of turnpike properties and overtaking optimal solutions for classes of nonautonomous nonconvex control problems. --- Chapter 8 analyses optimal processes with infinite time for integro-differential equations (the basic model is described by an integro-differential equation). The optimal steady-state problems are formulated and then the existence of overtaking optimal solutions is studied. A turnpike theorem and examples are given. --- Chapter 9 analyses optimal processes with infinite time for linear equations which have distributed parameters. These equations are interpreted as differential equations in Hilbert space. --- Chapter 10 considers stochastic control with the overtaking criterion. --- The next chapter deals with random modal jumps. The turnpike properties of the jumps are obtained. The book promotes the development of a new trend in optimal control which is connected with the qualitative research of optimal processes of large and infinite duration. V.B.Kovalevsky