Hard constraints explicit model predictive control of an inverted pendulum

In this paper, explicit model predictive controller is applied to an inverted pendulum apparatus. Explicit solutions to constrained linear model predictive controller can be computed by solving multi-parametric quadratic programs. The solution is a piecewise affine function, which can be evaluated at each sample to obtain the optimal control law. The on-line computation effort is restricted to a table-lookup. This admits implementation on low cost hardware at high sampling frequencies in real-time systems with high reliability and low software complexity. This is useful for systems with limited power and CPU resources.