Nonlinear Model Predictive Control:Challenges and Opportunities

Linear Model Predictive Control has achieved a state of considerable maturity. With over two thousand applications, linear model predictive control is the preferred method of control in several application areas; a major motivation for its use is the presence of hard constraints on controls and states that are difficult to handle by other methods. Theoretical understanding has progressed and, while there remain open problems, notably in estimation, adaptation and robustness, success in implementation and maturity in underlying theory ensure the continuing development and application of linear model predictive control. Research on Nonlinear Model Predictive Control is at an interesting point. While applications are few, they appear to be rapidly increasing. There is a noticeable convergence in the methodologies proposed in the literature. Open problems include, as in linear model predictive control, estimation, adaptation and robustness but, in addition, there is a daunting challenge: the solution, online, of non-convex optimal control problems. This paper reviews the convergence of methodologies for Nonlinear Model Predictive Control, assesses the challenges arising from uncertainty and from non-convexity of the optimal control problem, and attempts to define fruitful avenues for future research.