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Fault-Tolerant MPC Control for Trajectory Tracking

David Laranjinho, Daniel Silvestre

Abstract

An MPC controller uses a model of the dynamical system to plan an optimal control strategy for a finite horizon, which makes its performance intrinsically tied to the quality of the model. When faults occur, the compromised model will degrade the performance of the MPC with this impact being dependent on the designed cost function. In this paper, we aim to devise a strategy that combines active fault identification while driving the system towards the desired trajectory. The explored approaches make use of an exact formulation of the problem in terms of set-based propagation resorting to Constrained Convex Generators (CCGs) and a suboptimal version that resorts to the SVD decomposition to achieve the active fault isolation in order to adapt the model in runtime.

Fault-Tolerant MPC Control for Trajectory Tracking

Abstract

An MPC controller uses a model of the dynamical system to plan an optimal control strategy for a finite horizon, which makes its performance intrinsically tied to the quality of the model. When faults occur, the compromised model will degrade the performance of the MPC with this impact being dependent on the designed cost function. In this paper, we aim to devise a strategy that combines active fault identification while driving the system towards the desired trajectory. The explored approaches make use of an exact formulation of the problem in terms of set-based propagation resorting to Constrained Convex Generators (CCGs) and a suboptimal version that resorts to the SVD decomposition to achieve the active fault isolation in order to adapt the model in runtime.

Paper Structure

This paper contains 8 sections, 1 theorem, 30 equations, 4 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Optimal Set Separation with CCG
  4. Multiplication of Sets
  5. Reachable Set in State-Control Space
  6. Set Separation based on Singular Value Decomposition
  7. Simulations
  8. Conclusion

Key Result

Proposition 1

Consider three Constrained Convex Generators (CCGs) as in Definition def:CCG: and a matrix $R \in \mathbb{R}^{m \times n}$ and a vector $t \in \mathbb{R}^{m}$. The three set operations are defined as:

Figures (4)

  • Figure 1: Reachable sets using the CCG propagation for a horizon of $N=4$ projected on the position coordinates.
  • Figure 2: Reachable sets using the SVD method for a horizon of $N=4$ projected on the position coordinates.
  • Figure 3: Reachable set propagation using the method in Set-Based-afd that uses $H$-rep polytopes for a horizon of $N=3$.
  • Figure 4: Reachable set propagation using the proposed CCG method for a horizon of $N=3$.

Theorems & Definitions (2)

  • Definition 1: Constrained Convex Generators
  • Proposition 1