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**1 - 5**of**5**### Multitime control strategies for skilled movements

, 2013

"... The paper presents a two-time motor control strategies for skilled movements. There are found movements which are optimum with various ”costs”, given by double integrals and different PDEs constraints (Newton Law as first order PDEs, multitime hyperbolic-parabolic Newton Law, multitime elliptic Ne ..."

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The paper presents a two-time motor control strategies for skilled movements. There are found movements which are optimum with various ”costs”, given by double integrals and different PDEs constraints (Newton Law as first order PDEs, multitime hyperbolic-parabolic Newton Law, multitime elliptic Newton Law). For simplicity, the movements, the constraints and the costs depend upon two independent variables. The model-based investigation of human and human-like motions is an important interdisciplinary research topic which involves aspects of biomechanics, physiology, orthopedics, psychology, neurosciences, robotics, sport, computer graphics and applied mathematics. In this context, the detailed study on a joint level of basic locomotion forms such as two-time walking and running is of particular interest due to the high demand on dynamic coordination, actuator efficiency and balance control. Two-time mathematical models can help to better understand the basic underlying mechanisms of these motions and to improve them. In this paper, we present the mathematical point of view of our research group on dynamic human motions which show how optimization can help to generate very natural two-time looking motions.

### Multitime optimal control for linear PDEs with curvilinear cost functional

, 2013

"... In this paper, the multitime optimal control problem consists in devising a control such as to transfer a completely integrable linear PDE system from some given initial state to a specified target (which may be fixed or moving) in an optimal multitime characterized by a minimum mechanical work. Fo ..."

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In this paper, the multitime optimal control problem consists in devising a control such as to transfer a completely integrable linear PDE system from some given initial state to a specified target (which may be fixed or moving) in an optimal multitime characterized by a minimum mechanical work. For that we use an appropriate curvilinear integral action. This kind of problems are based on Hamiltonian 1-forms depending linearly on the controls. They exhibits additional features which we now discuss. Firstly, we underline some historical data of interest for optimal problems with curvilinear integral cost. Secondly, our original results concentrate on: (1) the existence of multitime optimal controls for problems associated to a curvilinear integral action and a linear m-flow type PDE system, (2) some properties of the reachable set, (3) the maximum principle for linear multitime optimal control problems fixed by a curvilinear integral action and an m-flow type PDE system, (4) the bang-bang optimal solution, (5) two basic examples: control of a two-time rocket railroad car and of a two-time vibrating spring.