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On the Optimal Control of Impulsive Hybrid Systems on Riemannian Manifolds
- SIAM JOURNAL ON CONTROL AND OPTIMIZATION, HYBRID MINIMUM PRINCIPLE ON LIE GROUPS AND EXPONENTIAL GRADIENT HMP ALGORITHM 31 HTTP://ARXIV.ORG/ABS/1209.4609
, 2012
"... This paper provides a geometrical derivation of the Hybrid Minimum Principle (HMP) for autonomous impulsive hybrid systems on Riemannian manifolds, i.e. systems where the manifold valued component of the hybrid state trajectory may have a jump discontinuity when the discrete component changes value ..."
Abstract
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This paper provides a geometrical derivation of the Hybrid Minimum Principle (HMP) for autonomous impulsive hybrid systems on Riemannian manifolds, i.e. systems where the manifold valued component of the hybrid state trajectory may have a jump discontinuity when the discrete component changes value. The analysis is expressed in terms of extremal trajectories on the cotangent bundle of the manifold state space. In the case of autonomous hybrid systems, switching manifolds are defined as smooth embedded submanifolds of the state manifold and the jump function is defined as a smooth map on the switching manifold. The HMP results are obtained in the case of time invariant switching manifolds and state jumps on Riemannian manifolds.
On the LQ-Based Optimization Techniques for Impulsive Hybrid Control Systems
"... Abstract-This paper deals with a quadratic optimization problem for linear impulsive hybrid systems. We study a class of LQ-type impulsive hybrid optimal control problems (OCPs) and consider the application of the hybrid Maximum Principle (MP). Our aim is to investigate the natural relationship bet ..."
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Abstract-This paper deals with a quadratic optimization problem for linear impulsive hybrid systems. We study a class of LQ-type impulsive hybrid optimal control problems (OCPs) and consider the application of the hybrid Maximum Principle (MP). Our aim is to investigate the natural relationship between the Pontryagin-type MP and the Bellman Dynamic Programming (DP) approach. As next we develop the "hybrid" Riccati formalism and discuss some related computational aspects.
