Approximate explicit model predictive control using high-level canonical piecewise-affine functions

摘要

Explicit model predictive control (eMPC) enables conventional MPC to be used to fast sampling systems and implemented by low-cost embedded devices. The primary limitation of eMPC is that the complexities of eMPC solutions are often exponential functions of problem sizes. In this paper, high-level canonical piecewise-affine (HL-CPWA) functions are introduced to approximate eMPC solutions. A HL-CPWA function uses a global and compact functional form to approximate any continuous eMPC controller to arbitrary precision. This guarantees minimal memory storage requirement and fast online computational time to represent and calculate suboptimal eMPC solutions. The HL-CPWA eMPC feedback laws have explicit analytical expressions, which can be easily implemented by elementary 'circuit blocks'. This facilitates the use of constrained MPC in small-scale industrial and consumer electronics applications.