Tham khảo tài liệu 'model predictive control part 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Robust Adaptive Model Predictive Control of Nonlinear Systems 33 The issue of robustness to measurement error is addressed in Tuna et al. 2005 . On one hand nominal robustness to measurement noise of an MPC feedback was already established in Grimm et al. 2003 for discrete-time systems and in Findeisen et al. 2003 for sampled-data implementations. However Tuna et al. 2005 demonstrates that as the sampling frequency becomes arbitrarily fast the margin of this robustness may approach zero. This stems from the fact that the feedback Kmpc x of 11 is inherently discontinuous in x if the indicated minimization is performed globally on a nonconvex surface which by Coron Rosier 1994 Hermes 1967 enables a fast measurement dither to generate flow in any direction contained in the convex hull of the discontinuous closed-loop vectorfield. In other words additional attractors or unstable infeasible modes can be introduced into the closed-loop behaviour by arbitrarily small measurement noise. Although Tuna et al. 2005 deals specifically with situations of obstacle avoidance or stabilization to a target set containing disconnected points other examples of problematic nonconvexities are depicted in Figure 1. In each of the scenarios depicted in Figure 1 measurement dithering could conceivably induce flow along the dashed trajectories thereby resulting in either constraint violation or convergence to an undesired equilibrium. Two different techniques were suggested in Tuna et al. 2005 for restoring robustness to the measurement error both of which involve adding a hysteresis-type behaviour in the optimization to prevent arbitrary switching of the solution between separate minimizers . making the optimization behaviour more decisive . Fig. 1. Examples of nonconvexities susceptible to measurement error 10. Robust MPC Review of Nonlinear MPC for Uncertain Systems While a vast majority of the robust-MPC literature has been developed within the framework of discrete-time .
