Feedback control design and model reduction for strongly nonlinear systems

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In an attempt to bridge the gap between nonlinear control theory and practice, in the next five years, the proposed research program will seek to address the problem of reduction of nonlinear system complexity for the purpose of control design implementation. Since multi-body dynamical systems pose many challenging nonlinear control problems, the reference systems under study is the class of controlled Hamiltonian or Lagrangian mechanical systems with constraints. Examples include stabilizing control of vertical structures such as standing or walking humans. With this goal in mind the research program is summarized as follows: (A) Development of a systematic framework for control-oriented modeling, nonlinear control problem simplification and reduction for strongly nonlinear systems, with reference to the class of system considered. Strongly nonlinear systems are these which do not lend themselves to control design and analysis via linearization approaches. The principal objectives in control problem simplifcation are to facilitate: (i) assessment of stabilizability and reachability regions for a given class of admissible control inputs, (ii) construction of semi-global stablilizing feedback laws with the emphasis on real-time application regimes. (B) Development of computationally tractable, semi-global nonlinear control design approaches that can be applied to stabilization of vertical structures in potential felds and locomotion control of multi-body systems under actuation and mobility constraints. The envisaged design approaches will employ the concepts of invariance under transformations and energy conversion and balancing rather than energy shaping. The proposed methods for combined modeling and control will employ the spatial operator algebra as a modern and powerful tool for computational complexity reduction in mechanical system design, control, and analysis. Applications include advanced robotic control design, spatial models for postural balance aiming at quantitative prediction of loss of balance in humans, and other problems in biomechanics.