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Funnel Control Under Hard and Soft Output Constraints

Farhad Mehdifar, Charalampos P. Bechlioulis, Dimos V. Dimarogonas

TL;DR

This work tackles safe and performance-constrained control of uncertain Euler–Lagrangian systems by combining online Constraint Consistent Funnel (CCF) planning with a low-complexity, model-free Prescribed Performance Control (PPC) funnel controller. Hard safety constraints are always respected, while soft performance constraints are pursued when feasible, with the funnel boundaries adaptively adjusted via nonnegative modifiers to handle hard/soft incompatibilities. The main contributions are (i) an online funnel planning scheme that yields a continuous, feasible CCF even under time-varying constraint conflicts, and (ii) a robust PPC funnel controller that enforces the planned CCF for uncertain EL dynamics, with a stability proof establishing forward completeness and bounded closed-loop signals. The approach is validated on a mobile-robot tracking task within a box-shaped safe region, highlighting low computational demand and practical applicability to safety-critical motion tasks.

Abstract

This paper proposes a funnel control method under time-varying hard and soft output constraints. First, an online funnel planning scheme is designed that generates a constraint consistent funnel, which always respects hard (safety) constraints, and soft (performance) constraints are met only when they are not conflicting with the hard constraints. Next, the prescribed performance control method is employed for designing a robust low-complexity funnel-based controller for uncertain nonlinear Euler-Lagrangian systems such that the outputs always remain within the planned constraint consistent funnels. Finally, the results are verified with a simulation example of a mobile robot tracking a moving object while staying in a box-constrained safe space.

Funnel Control Under Hard and Soft Output Constraints

TL;DR

This work tackles safe and performance-constrained control of uncertain Euler–Lagrangian systems by combining online Constraint Consistent Funnel (CCF) planning with a low-complexity, model-free Prescribed Performance Control (PPC) funnel controller. Hard safety constraints are always respected, while soft performance constraints are pursued when feasible, with the funnel boundaries adaptively adjusted via nonnegative modifiers to handle hard/soft incompatibilities. The main contributions are (i) an online funnel planning scheme that yields a continuous, feasible CCF even under time-varying constraint conflicts, and (ii) a robust PPC funnel controller that enforces the planned CCF for uncertain EL dynamics, with a stability proof establishing forward completeness and bounded closed-loop signals. The approach is validated on a mobile-robot tracking task within a box-shaped safe region, highlighting low computational demand and practical applicability to safety-critical motion tasks.

Abstract

This paper proposes a funnel control method under time-varying hard and soft output constraints. First, an online funnel planning scheme is designed that generates a constraint consistent funnel, which always respects hard (safety) constraints, and soft (performance) constraints are met only when they are not conflicting with the hard constraints. Next, the prescribed performance control method is employed for designing a robust low-complexity funnel-based controller for uncertain nonlinear Euler-Lagrangian systems such that the outputs always remain within the planned constraint consistent funnels. Finally, the results are verified with a simulation example of a mobile robot tracking a moving object while staying in a box-constrained safe space.
Paper Structure (8 sections, 2 theorems, 23 equations, 7 figures)

This paper contains 8 sections, 2 theorems, 23 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Main Results
  4. Online Constraint Consistent Funnel Planning
  5. Funnel-Based Controller Design
  6. Stability Analysis
  7. Simulation Results
  8. Conclusions

Key Result

Lemma 1

Under Assumptions assum_soft_hard_bounds and assum: ini_compat, equations non_smooth_funn_modif and eq:modif_signals_dyn construct $\rho^L_i(t)$ and $\rho^U_i(t)$ such that: (i) $\dot{\rho}^L_i, \dot{\rho}^U_i, \rho^L_i, \rho^U_i \in \mathcal{L}_\infty$ (are bounded signals), and (ii) $\rho^U_i(t) -

Figures (7)

  • Figure 1: (a) compatible ($\forall t \geq 0$), and (b) incompatible hard and soft constraints.
  • Figure 2: Left: mobile robot. Right: mobile robot's trajectory (blue line) tracking a moving object (dashed line) under hard constraints (red line) with $k_c = 3$
  • Figure 3: $x_1(t)$ and $x_2(t)$ evolution within CCFs under hard and soft constraints with $k_c = 3$.
  • Figure 4: Evolution of the modification signals with $k_c = 3$.
  • Figure 5: Mobile robot's trajectory (blue line) tracking a moving object (dashed line) under hard constraints (red line) with $k_c = 0.3$.
  • ...and 2 more figures

Theorems & Definitions (7)

  • Remark 1
  • Lemma 1
  • proof
  • Remark 2: Smooth CCF
  • Remark 3
  • Theorem 1
  • proof