In this thesis human jumping and pedaling are analyzed using optimal control theory. The human body is mechanically modeled as 3 rigid links with 8 group muscles for each leg and 1 rigid link for the upper body. The jumps which maximize the vertical height reached by the subject's center of mass while jumping from an initial squat posture or an erect posture are studied. The pedaling process is a bicycle-rider system. The rider's hips are fixed on the saddle, the feet are rigidly attached to the pedals and the upper body is stationary. So, the process is modeled as 2-five bar linkages moving in the plane, fixed at the hip joint and at a crank axis. The performance criterion is minimization of the time required for one cycle of the crank.

The systems are described mathematically by nonlinear differential equations which are linear in the controls. The system equations consist of limb mechanics, muscle dynamics and muscle activation dynamics. The optimal control is assumed to be of bang-bang type with a finite number of switchings. A new computational algorithm for bang-bang control of these highly nonlinear and large scale dynamic systems is developed. The controls are determined by using the projection of the gradient of the cost function with respect to the control input switching times on the control Hamiltonian function of the system. The controls maximize this Hamiltonian function, holding the state and costate trajectories fixed. An optimization algorithm to get the best values for unknown initial state variables on a constraint set defined by linear equalities and inequalities is developed.

The necessary conditions for optimal control of a redundant dynamic system and a reduced dynamic system to represent the pedaling process are developed. This along with the algorithm for bang-bang control is used to obtain the optimal control inputs of the pedaling process.

The computational results for human jumping are compared with experimental results.