Towards a Nonlinear Model Predictive Control using the Extended Modal Series Method

This paper addresses the Nonlinear Model Predictive Control of input-affine systems. Based on the Extended Modal Series Method, an explicit suboptimal control law is deduced that solves the two point boundary problem given by Pontryagin’s Maximum Principle in the related Nonlinear Optimal Control Problem. The deduction of the control law is presented and proven. Then the proposed controller is tested in simulation in the attitude control of a quadrotor, a highly nonlinear and unstable system. The simulation results indicate good performance and near optimal behavior. This work is a background for future development of control techniques for input-affine systems.

[1]  Naser Pariz,et al.  Solving infinite horizon nonlinear optimal control problems using an extended modal series method , 2011, Journal of Zhejiang University SCIENCE C.

[2]  Yue Sun,et al.  Modeling, identification and control of a quad-rotor drone using low-resolution sensing , 2012 .

[3]  Bart De Schutter,et al.  Model predictive control for continuous piecewise affine systems using optimistic optimization , 2016, 2016 American Control Conference (ACC).

[4]  Naser Pariz,et al.  A NOVEL MODAL SERIES REPRESENTATION APPROACH TO SOLVE A CLASS OF NONLINEAR OPTIMAL CONTROL PROBLEMS , 2011 .

[5]  Xun Gong,et al.  Fast Nonlinear Model Predictive Control on FPGA Using Particle Swarm Optimization , 2016, IEEE Transactions on Industrial Electronics.

[6]  Naser Pariz,et al.  Explaining and validating stressed power systems behavior using modal series , 2003 .

[7]  Ali Karimpour,et al.  An off-line NMPC strategy for continuous-time nonlinear systems using an extended modal series method , 2014 .

[8]  Ali Akbar Safavi,et al.  Fast nonlinear model predictive control for teleoperation systems using computationally efficient optimization techniques , 2014, 2014 22nd Iranian Conference on Electrical Engineering (ICEE).

[9]  S. Effati,et al.  Infinite horizon optimal control for nonlinear interconnected large‐scale dynamical systems with an application to optimal attitude control , 2012 .

[10]  D. Gan,et al.  Validation of power system non-linear modal analysis methods , 2007 .

[11]  Nasser L. Azad,et al.  A Nonlinear Model Predictive Controller With Multiagent Online Optimizer for Automotive Cold-Start Hydrocarbon Emission Reduction , 2016, IEEE Transactions on Vehicular Technology.

[12]  Gabriel H. Negri,et al.  Differential evolution optimization applied in multivariate nonlinear model-based predictive control , 2015, 2015 Latin America Congress on Computational Intelligence (LA-CCI).

[13]  Johannes J. Duistermaat,et al.  Multidimensional real analysis , 2004 .

[14]  Jun Wang,et al.  Model Predictive Control of Nonlinear Systems With Unmodeled Dynamics Based on Feedforward and Recurrent Neural Networks , 2012, IEEE Transactions on Industrial Informatics.