Time-distributed optimization for real-time model predictive control: Stability, robustness, and constraint satisfaction

Abstract

Time-distributed optimization is an implementation strategy that can significantly reduce the computational burden of model predictive control. When using this strategy, optimization iterations are distributed over time by maintaining a running solution estimate for the optimal control problem and updating it at each sampling instant. The resulting controller can be viewed as a dynamic compensator which is placed in closed-loop with the plant. This paper presents a general systems theoretic analysis framework for time-distributed optimization. The coupled plant-optimizer system is analyzed using input-to-state stability concepts and sufficient conditions for stability and constraint satisfaction are derived. In particular, we demonstrate that it is possible to recover the qualitative stability, robustness, and constraint satisfaction properties of the optimal model predictive control feedback law using a finite number of optimization algorithm iterations per sampling instant. When applied to time-distributed sequential quadratic programming, the framework significantly extends the existing theoretical analysis for the real-time iteration scheme. Numerical simulations are presented that demonstrate the effectiveness of the scheme.