Systems and methods for automatically ensuring the stability and controllability of a nonlinear control system

A non-transitory computer-readable medium for automatically ensuring stability and controllability of a nonlinear control system and storing instructions that, when executed by a processor, cause the processor to:

• receive, at a nonlinear model predictive controller, optimal control problem code representing an optimal control problem that includes a cost function, one or more constraints, and a continuous time model representing a nonlinear dynamical system;
• discretize automatically the continuous time model to produce a discrete time model of the nonlinear dynamical system, wherein the discrete time model includes one or more parameters;
• check automatically, during an offline phase, the one or more parameters by sweeping at least one of the one or more parameters through a predetermined operational range to identify one or more regions in a parameter space in which the discrete time model is both stable and controllable when used by the nonlinear model predictive controller, wherein stability is determined based on eigenvalues of the discrete time model and controllability is determined based on a Controllability Gramian of the discrete time model;
• and
• control, at least in part, operation of the nonlinear dynamical system in an online phase using the nonlinear model predictive controller, wherein the nonlinear model predictive controller is configured with values of the one or more parameters that lie within the one or more regions of the parameter space.

A method, comprising:

• receiving, at a nonlinear model predictive controller, optimal control problem code representing an optimal control problem that includes a cost function, one or more constraints, and a continuous time model representing a nonlinear dynamical system;
• discretizing automatically the continuous time model to produce a discrete time model of the nonlinear dynamical system, wherein the discrete time model includes one or more parameters;
• checking automatically, during an offline phase, the one or more parameters by sweeping at least one of the one or more parameters through a predetermined operational range to identify one or more regions in a parameter space in which the discrete time model is both stable and controllable when used by the nonlinear model predictive controller, wherein stability is determined based on eigenvalues of the discrete time model and controllability is determined based on a Controllability Gramian of the discrete time model;
• and
• controlling, at least in part, operation of the nonlinear dynamical system in an online phase using the nonlinear model predictive controller, wherein the nonlinear model predictive controller is configured with values of the one or more parameters that lie within the one or more regions of the parameter space.