Design of Approximate Explicit Model Predictive Controller Using Parametric Optimization

Abstract

This paper introduces a new technique, called stateparameterized nonlinear programming control (spNLPC), for designing a feedback controller that can stabilize intrinsically unstable nonlinear dynamical systems using parametric optimization. Stabilitypreserving constraints are included in the optimization problem solved offline by the predictive parameterized Pareto genetic algorithm (P3GA), a constrained nonlinear parametric optimization algorithm. The optimal control policy is approximated from P3GA output using radial basis function (RBF) metamodeling. The spNLPC technique requires fewer assumptions and is more dataefficient than alternative methods. Two nonlinear systems (single and double inverted pendulums on a cart) are used as benchmarking problems. Performance and computational efficiency are compared to several competing control design techniques. Results show that spNLPC outperforms and is more efficient than competing methods. A qualitative investigation on phase plane analysis for the controlled systems is presented to ensure stability. The approximating statedependent solution for the control input lends itself to applications of control design for control codesign (CCD). Such extensions are discussed as part of future work.