A simple proof of the discrete time geometric Pontryagin maximum principle

  title={A simple proof of the discrete time geometric Pontryagin maximum principle},
  author={K. MishalAssifP. and Debasish Chatterjee and Ravi N. Banavar},

Robust Discrete-Time Pontryagin Maximum Principle on Matrix Lie Groups

A version of the Pontryagin maximum principle (PMP) is presented that encapsulates first-order necessary conditions that the optimal control and disturbance trajectories must satisfy in a discrete-time robust optimal control problem on matrix Lie groups.

Optimal Multiplexing of Discrete-Time Constrained Control Systems on Matrix Lie Groups

This article provides first-order necessary conditions for optimality in the form of a Pontryagin maximum principle for optimal control problems for an ensemble of control systems in a centralized setting.

A geometric approach for the optimal control of difference inclusions

A framework suitable for the study of difference inclusions for which the state evolves on a manifold is introduced and necessary conditions for optimality are developed for a broad class of discrete-time problems of dynamic optimization.

On optimal multiplexing of an ensemble of discrete-time constrained control systems on matrix Lie groups

This work provides first-order necessary conditions for optimality in the form of suitable Pontryagin maximum principle in this problem of constrained optimal control for an ensemble of control systems.

A geometric approach for the optimal control of difference inclusions

Difference inclusions provide a discrete-time analogue of differential inclusions, which in turn play an important role in the theories of optimal control, implicit differential equations, and



The Discrete-Time Geometric Maximum Principle

A new theorem can be used to derive Lie group variational integrators in Hamiltonian form; to establish a maximum principle for control problems in the absence of state constraints; and to provide sufficient conditions for exact penalization techniques in the presence of state or mixed constraints.

Control Theory from the Geometric Viewpoint

Geometrical methods have had a profound impact in the development of modern nonlinear control theory. Fundamental results such as the orbit theorem, feedback linearization, disturbance decoupling or

Functional Analysis, Calculus of Variations and Optimal Control

Normed Spaces.- Convex sets and functions.- Weak topologies.- Convex analysis.- Banach spaces.- Lebesgue spaces.- Hilbert spaces.- Additional exercises for Part I.- Optimization and multipliers.-

the Method of Tents in the Theory of Extremal Problems

The method of tents is a unified method of solving various kinds of extremal problems. It is a development of the method of Milyutin and Dubovitskii, but it removes their restrictive assumption that

Foundations of optimal control theory

Abstract : This complete and authoritative presentation of the current status of control theory offers a useful foundation for both study and research. With emphasis on general nonlinear differential

Optimal Control and Applications to Aerospace: Some Results and Challenges

This article surveys the usual techniques of nonlinear optimal control such as the Pontryagin Maximum Principle and the conjugate point theory, and how they can be implemented numerically, with a

Convex Optimization Theory

An insightful, concise, and rigorous treatment of the basic theory of convex sets and functions in finite dimensions, and the Dual problem the feasible if it is they, and how to relax the hessian matrix in terms of linear programming.

Introduction to Smooth Manifolds

Preface.- 1 Smooth Manifolds.- 2 Smooth Maps.- 3 Tangent Vectors.- 4 Submersions, Immersions, and Embeddings.- 5 Submanifolds.- 6 Sard's Theorem.- 7 Lie Groups.- 8 Vector Fields.- 9 Integral Curves