A Methodology for Designing a Nonlinear Feedback Controller via Parametric Optimization: State-Parameterized Nonlinear Programming Control

Abstract

Abstract This paper introduces a new technique for designing nonlinear feedback controllers that can effectively and efficiently control nonlinear and unstable dynamical systems. The technique, called State-Parameterized Nonlinear Programming Control (sp-NLPC), constructs an optimal control strategy that is a function of dynamical system states. This is achieved through an offline parametric optimization process using the predictive parameterized Pareto genetic algorithm (P3GA) and representing the optimized state-varying policy using radial basis function (RBF) metamodeling. The sp-NLPC technique avoids many limitations of alternative methods, such as the need to make strong assumptions about model form (e.g., linearity) and the demands of online optimization processes. The proposed method is benchmarked on the problems of controlling the highly nonlinear and inherently unstable systems: single and double inverted pendulums on a cart. Performance and computational efficiency are compared to several competing control design techniques. Results show that sp-NLPC outperforms and is more efficient than competing methods. The parametric solution strategy for sp-NLPC lends itself to use in Control Co-Design (CCD). Such extensions are discussed as part of future work.