Sensitivity-based Methods For The Efficient Solution Of Constrained Optimal Control And Nonlinear Model Predictive Control Problems

With the rapid development of computer software and hardware,there is a clear tendency to extend the applications of model predictive control(MPC)to systems with fast dynamics,such as automobile,aircraft,etc.For this extension,efficient algorithms for the solution of optimal control problems(OCPs)and techniques to reduce the computational cost in the procedure of receding-horizon optimizations are indispensable.This thesis tries to solve several technical problems involved in the design of efficient algorithms for nonlinear MPC.It is well known that adjoint methods,applied to solve OCPs,have a restriction that the number of constraints shall be less than that of optimization variables.Otherwise,they are less efficient than the forward methods.In the first part of this thesis,an efficient adjoint method is proposed to solve OCPs for index-1differential algebraic systems with continuous-time inequality constraints.Instead of being discretized on time grid,these continuous-time inequality constraints are transformed into integrals and penalized in the cost through an exact penalty function.Thus,all the constraints except for box constraints on optimization variables can be removed.As a result,the efficiency of adjoint methods can be ensured.Furthermore,a lifted implicit Runge-Kutta integrator with adjoint sensitivity propagation is employed to accelerate the function and gradient evaluation procedure.Besides this,Lagrange interpolation is enrolled to approximate the integrals such that dense grid is not necessary.Numerical simulations on the point-to-point optimal maneuvering of a Delta robot demonstrate that the computational speed of the proposed adjoint algorithm is comparable to the forward one.In the presence of large computational cost,the delay between the measurement and feedback in MPC is not negligible.In the worst case,feedback delay can destabilize the closed-loop system.In the second part of this thesis,an efficient nonlinear MPC algorithm is designed,which divides the original problem into on-line and background parts,and reduces the feedback delay based on nonlinear programming(NLP)sensitivity.Before the measurement is available,an optimal control is solved based on prediction of this measurement.Once the measurement is obtained,NLP sensitivity is analyzed to update the control.The NLP solver Ipopt is integrated with sIPOPT to realize this efficient sensitivity-update strategy.Furthermore,warm-start of receding-horizon optimizations is realized in Ipopt.The designed MPC algorithm is verified by numerical simulations of regulating the set-point of a Delta robot in the presence of modeling uncertainty.Simulation results demonstrate that the proposed algorithm can reduce the feedback delay significantly.