A volterra series interpretation of some higher order conditions in optimal control

The present paper studies the Mayer problem with higher order evolution differential inclusions and functional constraints of optimal control theory (PFC); to this end first we use an interesting auxiliary problem with second order discrete-time and discrete approximate inclusions (PFD). Are proved necessary and sufficient conditions incorporating the Euler–Lagrange inclusion, the Hamiltonian inclusion, the transversality and complementary slackness conditions. The basic concept of obtaining optimal conditions is locally adjoint mappings and equivalence results. Then combining these results and passing to the limit in the discrete approximations we establish new sufficient optimality conditions for second order continuous-time evolution inclusions. This approach and results make a bridge between optimal control problem with higher order differential inclusion (PFC) and constrained mathematical programming problems in finite-dimensional spaces. Formulation of the transversality and complementary slackness conditions for second order differential inclusions play a substantial role in the next investigations without which it is hardly ever possible to get any optimality conditions; consequently, these results are generalized to the problem with an arbitrary higher order differential inclusion. Furthermore, application of these results is demonstrated by solving some semilinear problem with second and third order differential inclusions.

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Distributed optimal control law design for a class of higher order linear multi-agent systems and its application to Euler-Lagrangian systems

2020 39th Chinese Control Conference (CCC) ◽

10.23919/ccc50068.2020.9188585 ◽

2020 ◽

Author(s):

Ranran Li

Keyword(s):

Optimal Control ◽

Higher Order ◽

Control Law ◽

Lagrangian Systems ◽

Multi Agent Systems ◽

Distributed Optimal Control ◽

Order Linear ◽

Agent Systems ◽

Multi Agent

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Higher order variational integrators in optimal control theory

PAMM ◽

10.1002/pamm.201610399 ◽

2016 ◽

Vol 16 (1) ◽

pp. 821-822

Author(s):

Sina Ober-Blöbaum

Keyword(s):

Optimal Control ◽

Control Theory ◽

Optimal Control Theory ◽

Higher Order ◽

Variational Integrators

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Stratifications of equivariant varieties

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700023315 ◽

1977 ◽

Vol 16 (2) ◽

pp. 279-295 ◽

Cited By ~ 13

Author(s):

M.J. Field

Keyword(s):

Lie Group ◽

General Position ◽

Higher Order ◽

Order Conditions ◽

Compact Lie Group ◽

Algebraic Varieties ◽

Equivariant Maps

Let G be a compact Lie group and V and W be linear G spaces. A study is made of the canonical stratification of some algebraic varieties that arise naturally in the theory of C∞ equivariant maps from V to W. The main corollary of our results is the equivalence of Bierstone's concept of “equivariant general position” with our own of “G transversal”. The paper concludes with a description of Bierstone's higher order conditions for equivariant maps in the framework of equisingularity sequences.

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