Infinite Horizon Optimal Control : Deterministic and Stochastic Systems

Online-Ressource (XVI, 332 Seiten)

The first edition was published in 1987 as Volume 290 of the series "Lecture Notes in Economics and Mathematical Systems".

1 Dynamical Systems with Unbounded Time Interval in Engineering, Ecology and Economics1.1 Introduction -- 1.2 The regulator problem -- 1.3 The pest control problem and other problems of optimal control of interacting species -- 1.4 The optimal economic growth problem -- 1.5 Definition of optimality on an unbounded time interval -- 1.6 Uniformly optimal solutions are agreeable -- 2 Necessary Conditions and Sufficient Conditions for Optimality -- 2.1 Introduction -- 2.2 The maximum principle with a finite horizon -- 2.3 The optimality principle -- 2.4 A maximum principle for an infinite horizon control problem -- 2.5 Sufficient conditions for overtaking optimality -- 3 Asymptotic Stability and the Turnpike Property in Some Simple Control Problems -- 3.1 Introduction -- 3.2 Saddle point property of the Hamiltonian in a convex problem of Lagrange. Implications on local asymptotic stability of optimally controlled systems -- 3.3 An exact turnpike property: Optimal fish harvest -- 3.4 Use of a phase diagram for a one-state-variable control problem: The simple optimal economic growth model -- 4 Global Asymptotic Stability and Existence of Optimal Trajectories for Infinite Horizon Autonomous Convex Systems -- 4.1 Introduction -- 4.2 The class of systems considered -- 4.3 Convergence toward the Von Neumann Set for weakly overtaking trajectories -- 4.4 The turnpike property -- 4.5 Global asymptotic stability for extremal trajectories -- 4.6 A Lyapunov function approach for GAS of optimal trajectories -- 4.7 Sufficient conditions for overtaking optimality -- 4.8 Existence of optimal trajectories -- 4.9 Overtaking optimality under relaxed assumptions -- 5 The Reduction to Finite Rewards -- 5.1 Introduction -- 5.2 The Property R -- 5.3 The connection between continuous and discrete time control systems -- 5.4 Existence of a reduction to finite rewards -- 5.5 A representation formula and turnpike properties of optimal controls -- 5.6 Systems with unbounded rewards and with discounting factors -- 5.7 Infinite horizon tracking of periodic signals -- 5.8 Optimal trajectories and turnpike properties of infinite horizon autonomous nonconvex systems -- 5.9 Two special cases: Scalar systems, and integrands in a separated form -- 6 Asymptotic Stability with a Discounted Criterion; Global and Local Analysis -- 6.1 Introduction -- 6.2 Modified Hamiltonian systems -- 6.3 Cass-Shell conditions for GAS of modified Hamiltonian systems -- 6.4 Brock-Sheinkman conditions for GAS of modified Hamiltonian systems -- 6.5 Another useful condition for GAS -- 6.6 Neighboring extremals, the second variation and analysis of local asymptotic stability of a stationary point, using the optimal linear quadratic regulator problem -- 6.7 The turnpike property for finite horizon optimal control problems with discounting -- 7 Turnpike Properties and Existence of Overtaking Optimal Solutions for Classes of Nonautonomous Nonconvex Control Problems -- 7.1 Introduction -- 7.2 G-supported trajectories -- 7.3 Carathéodory’s method for finite horizon optimal control problems -- 7.4 Carathéodory’s method for infinite horizon optimal control problems -- 7.5 The growth condition (?) and the compactness of the set of admissible trajectories -- 7.6 Upper closure and the existence of strongly optimal solutions -- 7.7 The existence of overtaking optimal solutions -- 8 Control of Systems with Integrodifferential Equations -- 8.1 Introduction -- 8.2 The basic model -- 8.3 Linear hereditary operators and an upper closure theorem -- 8.4 Existence of overtaking optimal solutions -- 8.5 Examples -- 9 Extensions to Distributed Parameter Systems -- 9.1 Introduction -- 9.2 Examples -- 9.3 Semigroups of operators and linear control systems -- 9.4 The optimal control problem -- 9.5 The turnpike properties -- 9.6 Existence of overtaking optimal solutions -- 9.7 More on the examples -- 9.8 The extension to systems with distributed parameters and boundary controls -- 10 Stochastic Control with the Overtaking Criterion -- 10.1 Introduction -- 10.2 The reduction to finite costs and the infinite-horizon Bellman equation -- 10.3 Infinite-horizon stochastic tracking -- 10.4 Optimal control of nonlinear diffusions in ?n -- 10.5 On almost-sure overtaking optimality -- 11 Maximum Principle and Turnpike Properties for Systems with Random Modal Jumps -- 11.1 Introduction -- 11.2 Optimal control under random stopping time -- 11.3 Turnpike properties -- 11.4 Piecewise Deterministic Control Systems -- 11.5 Global turnpike property for constant jump rates 3.

10.1007/978-3-642-76755-5 [DOI]

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