Thesis Seminar: Robust Model Predictive Control with a Reactive Safety Mode

John M. Carson III
Department of Mechanical Engineering, Caltech

Control policies designed for practical engineering applications, such as aerospace and mechanical vehicles, must provide adherence to physical state and control constraints and be robust to uncertainty affecting the system dynamics and constraints.When the algorithms that produce these policies are pushed online (e.g., policies generated by using onboard computers), the algorithms must be computationally efficient and reliable.The contributions in this thesis build upon the framework of MPC (Model Predictive Control) to create a computationally-efficient, robust MPC algorithm with guaranteed re-solvability and a reactive safety mode, available at any time, to ensure system safety from changes in state constraints (e.g., other vehicles crossing/stopping in the feasible path, or unexpected ground proximity in spacecraft landing scenarios).

The framework of MPC, also known as receding horizon control, makes use of a nominal dynamics model to predict and optimize system response to a feedforwardcontrol policy that is computed online by recursively re-solving a finite-horizon optimization problem.Uncertainty between the nominal model and the actual system dynamics, along with constraint uncertainty can cause feasibility, and hence, robustness issues with the traditional MPC algorithm.A robust MPC algorithm with guaranteed re-solvability is developed by adding a separate feedback policy to generate aninvariant tube to ensure actual system trajectories remain in the proximity of the feedforwardnominal trajectory at all times without violating state or control constraints.The tube is constructed through a characterization of the uncertainty between the nominal model and the actual system dynamics.To address uncertainty in state constraints, a reactive safety mode is blended into the control algorithm.The safety mode, if activated, guarantees containment within an invariant set about a safety reference for all time and guarantees satisfaction of control and safety state constraints.

Explicit design methods are provided for implementation of the algorithm to a class of systems with uncertain nonlinear terms that have norm-bounded derivatives.The algorithm is demonstrated in simulation of a spacecraft descending toward the surface of an asteroid with an uncertain gravity model, as well as uncertainty in the expected surface altitude.Additional realistic effects such as control-input uncertainty, sensor noise, and unknown disturbances are included to further test the algorithm in a realistic engineering implementation.


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