Research On NMPC Based On Reduced Precision Solution

Nonlinear model predictive control (NMPC) with high real-time requirements requires repeatedly solving the optimal control problems (OCPs) in one sampling interval, so that the input can be injected into the controlled system. It is difficult to solve the nonlinear OCPs with differential equations as its constraints timely. Computational delay arising in the solution procedure may destroy the controller performance even the stability of the closed loop. To shorten the computation time and reduce the computation delay, the paper studies NMPC algorithm from the perspective of optimization algorithm. The main research work are the following:1) A kind of termination criteria named Reduced Precision Solution (RPS) Criteria is proposed to reduce the computation time for solving the nonlinear OCPs. Solving the dynamic optimization problem is one of the bottleneck problem for development of NMPC algorithm based on nonlinear first-principle model equations. Most of existing optimization algorithms are based on the traditional convergence criteria, that is, Himmelblau rules. This is a kind of rigid criteria, which can only give "convergence" and "not convergence" as conclusions and can not effectively reflect the extent of convergence and margin of improvement. By defining a series of indices to measure the degree of convergence and the margin of improvement, RPS criteria can decide whether to iterate deeply. The numerical experiments illustrate that the SQP algorithm with RPS criteria can quickly solve the OCPs with good approximate solution.2) The NMPC framework based on feasibility-perturbed sequential quadratic programming (FP-SQP) algorithm with RPS criteria is proposed. When the optimization procedure of OCPs is required to stop prematurely, the obtained iterate should be feasible so that can be used as input acting on system. The FP-SQP with RPS criteria is suitable to deal with this problem. Simulation results show that this method can save computation time, reduce the computational delay, and improve the control performance eventually;3) Based on input-to-state stability (ISS) theory, the stability of NMPC with RPS criteria (rps-NMPC) is proved theoretically. Moreover, the effect of the reduced precision suboptimal solution on the stability is also analyzed. The simulations illustrate that the rps-NMPC owns robustness and stability when model mismatch and external disturbances exist.4) Moving horizon estimation (MHE) algorithm based on wavelet denoising is proposed. Taking the fact that there are external disturbances, model mismatch and the impact of noise in the measurement process into account, MHE is an effective method for state estimation. However, the estimation results are affected by the quality of the measurement data. In this paper, measurement data de-noising based on wavelet analysis is proposed to eliminate the noise and get more accurate output infomation, then the de-noised data is passed to the MHE estimator to get the state estimation. Experiments show that this method can effectively reduce the adverse effect caused by noise on the measured signals.5) MHE algorithm based on RPS criteria is proposed to get good estimation by reducing computational delay. MHE problem needs to be solved in one sampling interval, long computation time makes the state estimation can not be passed to the controller timely, thereby degrading the controller performance. Therefore, the RPS criteria are used to solve the nonlinear MHE problem, the experiments show that this method can reduce the solution time, and the state estimation doesn't get worse. Finally, simulation results illustrate that the computation time is reduced and proper state estimation is obtained simultaneously.