Sequential convexification method for model predictive control of nonlinear systems with continuous and discrete elements of operations

A predictive feedback controller for controlling a hybrid dynamical system with nonlinear dynamics and continuous and discrete elements of operation, the predictive feedback controller comprising:

• at least one processor;
• and a memory having instructions stored thereon that, when executed by the at least one processor, cause the predictive feedback controller to:
• accept feedback signal including measurements indicative of a current state of the hybrid dynamical system including one or a combination of a current state of the predictive controller, a current state of one or multiple actuators of the hybrid dynamical system, and a current state of outputs of the hybrid dynamical system;
• formulate a mixed-integer nonlinear programming (MINLP) problem optimizing an objective function subject to one or multiple constraints with a solution indicative of a control command for changing the current state of the hybrid dynamical system according to a control objective, wherein the constraints include equality constraints, inequality constraints, or both, and wherein the constraints and the control objective of the MINLP problem include one or multiple nonlinear functions of continuous optimization variables representing the continuous elements of the operation of the hybrid dynamical system and one or multiple linear functions of integer optimization variables representing the discrete elements of the operation of the hybrid dynamical system, such that the MINLP problem is formulated into a separable format ensuring that the discrete elements of the operation are present only in the linear functions of the MINLP problem;
• solve the MINLP problem over multiple iterations of a sequential convexification-based optimization procedure until a termination condition is met, wherein, to perform an iteration, the predictive feedback controller is configured to perform a partial convexification of a portion of a space of the solution including a current solution guess, wherein the partial convexification produces a convex approximation of the nonlinear functions of the MINLP without approximating the linear functions of the MINLP to produce a partially convexified MINLP;
• and
• update the current solution guess by solving a mixed-integer convex programming (MICP) formulation of the partially convexified MINLP problem;
• and
• submit the control command generated according to the solution of the MINLP problem to the hybrid dynamical system thereby causing a change of the current state of the hybrid dynamical system.