Assessment and Future Directions of Nonlinear Model Predictive ...

A Computationally Efficient Scheduled Model Predictive Control Algorithm 59150h (cm)1005000 100 200 300 400 500 600 700 800 900 100030h (cm)201000 10 20 30 40 50 60 70 80 90 1003u (kg/s)2100 100 200 300 400 500 600 700 800 900 1000Time (sec)(Fig. 2. Time responses of the regulations from x(0) = (7.5, 15) T to the equilibrium(19.753, 100) T , 1.7710 ) . First formulation: solid line - state and input; dotted line -estimated state. Second formulation: dashed line - state and input; dashed dotted line- estimated state.uncertainty Ω with four vertices {J(h eq1 +δh 1,h eq2 +δh 2), J(h eq1 +δh 1,h eq2 −δh 2),J(h eq1 − δh 1,h eq2 + δh 2), J(h eq1 − δh 1,h eq2 − δh 2)}, where J(h 1 ,h 2 ) is the Jacobianmatrix at (h eq1 ,heq 2 )T . The second formulation is to use the nonlinear modelwithin a neighborhood (Π h ,Π u ) and only enforce the constraint over a finitecontrol horizon of N = 3 with a terminal constraint and a terminal cost asspecified in Remark 1. Figure 1 shows the transitions by using the two controllerformulations. Figure 2 shows the time responses. Close-up views of the responsesof the state and the estimated state are provided to show convergence of theobservers.The first formulation performs better than the second one, becausecontrol switches of the second formulation happen close to the intermediateequilibrium points. (For performance improvement see Remark 3 ). On a GatewayPC with Pentium III processor (1000MHz, Cache RAM 256KB and totalmemory 256MB) and using Matlab LMI toolbox for the first formulationand optimization toolbox for the second approach, the numerical complexityof the two controller formulations are 0.5 second and 0.15 second per step,respectively.5 ConclusionsIn this paper, we have proposed a stabilizing scheduled output feedback MPCformulation for constrained nonlinear systems with large operating regions. Since