Requirements and hard computational bounds for real-time optimization in safety-critical control systems

Real-time optimization in control is quickly becoming a reality. However, the practical implementation of control architectures based on real-time optimization faces significant certification problems, such as guarantees of convergence and time to converge. This paper derives computable upper bounds on the number of iterations and arithmetic operations required to solve a semidefinite program, whose constraints do not change but whose objective may be arbitrary. The relevance of this problem to current safety-critical control problems is illustrated by the application of the proposed ideas to a receding horizon control problem and a fighter aircraft control surface allocation problem.