Titlebook: Control Theory from the Geometric Viewpoint; Andrei A. Agrachev,Yuri L. Sachkov Book 2004 Springer-Verlag Berlin Heidelberg 2004 Lie brack

過去分詞

Attainable Sets,In this chapter we study general properties of attainable sets. We consider families of vector fields . on a smooth manifold . that satisfy the property.In this case the system . is called ., or .. By the analytic version of the Orbit Theorem (Corollary 5.17), orbits of a bracket-generating system are open subsets of the state space ..

Paradox

Examples of Optimal Control Problems,In this chapter we apply Pontryagin Maximum Principle to solve concrete optimal control problems.

Pastry

踉蹌

Linear Time-Optimal Problem,In this chapter we study the following optimal control problem:.where . is a compact convex polytope in ?., and A and . are constant matrices of order . × . and . × . respectively. Such problem is called ..

戰(zhàn)役

Linear-Quadratic Problem,In this chapter we study a class of optimal control problems very popular in applications, .. That is, we consider linear systems with quadratic cost functional:..

PET-scan

Sufficient Optimality Conditions, Hamilton-Jacobi Equation, and Dynamic Programming,Pontryagin Maximum Principle is a universal and powerful necessary optimality condition, but the theory of sufficient optimality conditions is not so complete. In this section we consider an approach to sufficient optimality conditions that generalizes fields of extremals of the Classical Calculus of Variations.

Decimate

Allergic

Urologist

狂亂

Elements of Chronological Calculus,dea is to replace a nonlinear object, a smooth manifold .,by a linear, although infinite-dimensional one: the commutative algebra of smooth functions on . (for details, see [19], [22]). For basic definitions and facts of functional analysis used in this chapter, one can consult e.g. [144].