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Safety is one of the fundamental challenges in control theory. Recently,multi-step optimal control problems for discrete-time dynamical systems wereformulated to enforce stability, while subject to input constraints as well assafety-critical requirements using discrete-time control barrier functionswithin a model predictive control (MPC) framework. Existing work usually focuson the feasibility or the safety for the optimization problem, and the majorityof the existing work restrict the discussions to relative-degree one controlbarrier functions. Additionally, the real-time computation is challenging whena large horizon is considered in the MPC problem for relative-degree one orhigh-order control barrier functions. In this paper, we propose a frameworkthat solves the safety-critical MPC problem in an iterative optimization, whichis applicable for any relative-degree control barrier functions. In theproposed formulation, the nonlinear system dynamics as well as the safetyconstraints modeled as discrete-time high-order control barrier functions(DHOCBF) are linearized at each time step. Our formulation is generally validfor any control barrier function with an arbitrary relative-degree. Theadvantages of fast computational performance with safety guarantee are analyzedand validated with numerical results.

Iterative Convex Optimization for Model Predictive Control with Discrete-Time High-Order Control Barrier Functions