过去分词
发表于 2025-3-26 21:07:06
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
发表于 2025-3-27 04:18:48
Examples of Optimal Control Problems,In this chapter we apply Pontryagin Maximum Principle to solve concrete optimal control problems.
Pastry
发表于 2025-3-27 07:50:35
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踉跄
发表于 2025-3-27 10:26:12
Linear Time-Optimal Problem,In this chapter we study the following optimal control problem:.where . is a compact convex polytope in ℝ., and A and . are constant matrices of order . × . and . × . respectively. Such problem is called ..
战役
发表于 2025-3-27 17:34:03
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
发表于 2025-3-27 20:24:01
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
发表于 2025-3-28 01:32:31
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Allergic
发表于 2025-3-28 03:26:16
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Urologist
发表于 2025-3-28 08:14:13
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狂乱
发表于 2025-3-28 11:41:01
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 , ). For basic definitions and facts of functional analysis used in this chapter, one can consult e.g. .