A Lifted Implicit Integrator Based Algorithm For Efficient Solution Of Optimal Control Problems Involving Differential-algebraic Equations

With the rapid development of modern manufacturing,science and technology,the scale of the system object is increasing gradually and the structure is becoming more complex.The state trajectories of many dynamic systems are constrained,and it is not the most convenient way to model these systems by ordinary-differential equations.In this thesis,constrained dynamic systems are modeled as differential-algebraic equations instead of ordinary-differential equations.On this basis,we discuss the fast solution of the initial value problem for index-1 differential-algebraic equations,and the efficient sequential solution algorithms for their corresponding optimal control problems.Firstly,on the basis of time-scaling transformation,the control is parameterized as a piecewise constant function with variable magnitudes and switching time instants.Compared to control parameterization with equidistant time grids,the degree of freedom to change switching time instants increases the chance of finding the optimal solution.Secondly,for the derived approximate nonlinear programming problem,a function evaluation algorithm based on an implicit Runge-Kutta integrator is proposed with efficient sensitivity computation employing the implicit function theorem and algorithmic differentiation.Then,by utilizing a predictor-corrector strategy,an improved function evaluation algorithm is proposed with reduced Newton iterations.Finally,this algorithm is integrated with a nonlinear programming solver Ipopt to design the optimal control solver,which is verified by numerical experiments for the solution of the point-to-point optimal control for a Delta robot.Numerical experiments and theoretical analysis demonstrate that this optimal control solver possesses much improved computational efficiency.