mpt3

Multi-Parametric Toolbox 3 - GitHub

Synthesis of MPC controllers in MPT3 is based on two principles: Constraints and penalties are specified directly in the prediction model. Every MPC controller in MPT3 starts as an on-line MPC regulator. Explicit controllers are only synthesized on demand. Regulation problem. Tracking problem.

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MPT3 allows to create models of linear time-invariant (LTI) models of the form {$ \begin{align} x(t+\Delta t) = A x(t) + B u(t) \\ y(t) = Cx(t) + Du(t) \end{align}$} where {$ x(t) $} is the state vector at time {$t$}, {$u(t)$} is the vector of control inputs, {$y(t)$} are the system's outputs, and {$\Delta t$} represents the sampling time.

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MPT3 is a Matlab-based toolbox for parametric optimization, computational geometry and model predictive control. It offers features such as demos, YALMIP, closed-loop simulations, code generation, invariant sets, Lyapunov functions and more.