Interior point methods for optimal control of discrete time systems
Journal of Optimization Theory and Applications
A numerically robust state-space approach to stable-predictive control strategies
Automatica (Journal of IFAC)
Application of interior-point methods to model predictive control
Journal of Optimization Theory and Applications
Feedback Systems: An Introduction for Scientists and Engineers
Feedback Systems: An Introduction for Scientists and Engineers
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The computational burden that model predictive control (MPC) imposes depends to a large extent on the way the optimal control problem is formulated as an optimization problem. We present a formulation where the input is expressed as an affine function of the state such that the closed-loop dynamics matrix becomes nilpotent. Using this approach and removing the equality constraints leads to a compact and sparse optimization problem to be solved at each sampling instant. The problem can be solved with a cost per interior-point iteration that is linear with respect to the horizon length, when this is bigger than the controllability index of the plant. The computational complexity of existing condensed approaches grow cubically with the horizon length, whereas existing non-condensed and sparse approaches also grow linearly, but with a greater proportionality constant than with the method presented here.