Revisiting Certainty Equivalence: The Structural Coupling Between Estimation and Control in Underactuated Nonlinear Systems

Koopman-based model predictive control for nonlinear systems with bounded model uncertainty

Asynchronous Model Predictive Control Under Model Mismatch: Stability and Performance Guarantees

Certainty-equivalence model predictive control (CE-MPC) is widely used for its simplicity and efficiency, but theoretical guarantees under asynchronous feedback remain limited. This paper establishes stability and performance guarantees for asynchronous CE-MPC of input-constrained nonlinear systems. We first derive a nominal stability condition and competitive-ratio bound that explicitly account for inter-execution intervals without prescribing a feedback mechanism. A value-function perturbation analysis for quadratic stage costs then accommodates additive, potentially non-smooth model mismatch without constraint qualification conditions. Combining these results yields stability criteria and competitive-ratio bounds for CE-MPC under general asynchronous feedback, including event/self-triggered and multi-step MPC. The guarantees explicitly relate prediction horizon, inter-execution time, and uncertainty magnitude, quantifying performance degradation relative to an ideal infinite-horizon controller. These results clarify tradeoffs between feedback frequency, model accuracy, and horizon length, guiding asynchronous MPC design using approximate or learned models.

Fixed-Time Stable Fault-Tolerant Control of Underactuated Hovercraft via Physics-Informed Neural Adaptation

This study addresses the trajectory tracking control problem for an underactuated hovercraft subject to additive bias and multiplicative loss-of-effectiveness thruster faults under environmental disturbances. In these systems, actuator degradation structurally breaks the differential flatness mapping, driving nominal controllers to generate control actions that induce severe actuator saturation and cause instability. To resolve this challenge, a hierarchical physics-informed neural adaptive control (PINAC) framework is proposed. First, a gated-recurrent-unit physics-informed neural observer (PINO) is designed to isolate thruster faults from exogenous hydrodynamic disturbances. Second, a constrained Safe-TD3 reinforcement learning agent functions as a supervisor, computing an online dilation factor to slow down the mission timeline, thereby reconfiguring the reference trajectory to accommodate degraded actuator boundaries. Third, a low-level non-singular terminal sliding mode (NTSM) controller is implemented as a tracking-guarantee layer. Unlike classical asymptotic schemes where convergence is only achieved as time approaches infinity, or finite-time controllers where the settling time depends on the initial state, the proposed PINAC framework guarantees practical fixed-time stability, ensuring that the settling-time bound is independent of initial conditions. Simulation results demonstrate that the designed controller prevents actuator saturation, provides smooth trajectory adjustment, and reduces tracking errors under severe composite faults.

Fault- and saturation-aware quadrotor tracking via MRAC with an RL-inspired adaptive reference governor

This paper presents a hybrid, constraint-aware tracking architecture for quadrotor UAVs that explicitly targets the failure mode arising from the combination of actuator saturation and loss-of-effectiveness (LOE) faults. While model-based controllers augmented with adaptive terms can compensate for matched uncertainties locally, their performance can still collapse when the commanded trajectory becomes infeasible under post-fault authority reduction, leading to prolonged saturation and rapidly growing tracking errors. To address this issue, an policy-based adaptive reference governor with optional offline parameter tuning is introduced that shapes the commanded reference in real time, without modifying the stabilizing control law. The governor is implemented as a bounded, rate-limited first-order reference filter whose channel-wise time constants and rate limits are generated by a compact parametric policy driven by interpretable features: output-error norm, output-rate proxy, saturation ratio, and a fault indicator. The policy parameters may optionally be refined offline via a toolbox-free CEM-like random search, yielding a lightweight and reproducible parameter-tuning procedure that is reproducible and safety-oriented by construction. Nonlinear simulations under two regimes–(A) nominal operation without saturation/faults and (B) simultaneous rotor-speed saturation with an LOE fault–demonstrate the effectiveness of policy-based adaptive reference shaping in improving practical feasibility under constrained operation. In nominal conditions, the proposed governor improves practical performance by substantially reducing peak control magnitude, control energy, and control-rate activity while maintaining bounded tracking. In the stress regime, baseline configurations exhibit sustained saturation and divergence, whereas the RL-inspired governor maintains bounded tracking, eliminates time spent at saturation, and reduces error and effort metrics by orders of magnitude. These results indicate that embedding a low-dimensional parametric policy at the reference level provides an effective and safety-compatible mechanism for fault- and constraint-aware quadrotor tracking.

Robust Safety Filtering for Input-Constrained Underactuated Linear Systems

We present a robust safety-filtering framework for input-constrained underactuated linear systems subject to unknown disturbances. A baseline H-$\infty$ input is derived from a zero-sum differential game, while a disturbance observer supplies an estimate and a transient error bound. The baseline input is adjusted using the disturbance estimate, while the estimate and its error bound are used to define robust high-order control barrier function constraints; forward invariance holds as long as the admissible-input set remains nonempty. For scalar-input systems, pointwise feasibility is determined from an exact input interval, and the interval width defines the feasibility margin. A finite-horizon H-$\infty$ performance balance accounts for the accumulated deviation of the applied input from the baseline H-$\infty$ policy. Simulations on a linearized two-wheeled balancing robot show how position and body-pitch constraints compete for the same bounded wheel-torque input.

Global Fixed‐Time Exact Tracking for Uncertain High‐Order Nonlinear Systems With Quantized Input

This article investigates the problem of global fixed‐time (FT) exact tracking control for high‐order nonlinear systems (HONSs) characterized by input quantization and external disturbances. Most existing approaches for handling unknown nonlinearities rely on radial basis function neural networks (RBFNNs) or fuzzy logic systems (FLS), which typically ensure only ultimately semi‐globally bounded stability. To address this limitation, an FT output tracking control strategy with prescribed performance is developed by integrating the barrier Lyapunov function (BLF) technique with an auxiliary power integrator and a bounded estimation method. The proposed scheme guarantees that the tracking error converges to zero within an FT, while ensuring the global boundedness of all closed‐loop signals and the strict satisfaction of state constraints. Moreover, the control design does not require function approximation, parameter identification, or command filtering, and effectively avoids the singularity problem. The effectiveness of the proposed method is validated through two numerical examples.