Automated valet parking requires reliable long-range slot searching and precise low-speed docking in confined structured lots. This paper proposes a hierarchical cruise-to-park framework that combines nonlinear model predictive control (NMPC) for predefined-route cruising with a Twin Delayed Deep Deterministic Policy Gradient (TD3) agent for terminal parking. The system is implemented in a structured Simulink environment with Unreal Engine-based geometry-aware sensing modules. During cruising, a camera-based module detects available slots and triggers the transition to parking. The NMPC uses a custom cost function to improve tracking on curved approaches, while the TD3 policy uses LiDAR feedback and reward shaping with an explicit time penalty to encourage efficient, stable docking. Simulation results demonstrate smooth phase transition, accurate cruising, and effective terminal parking in the training slot. Validation on six previously unseen target slots within the same parking-lot environment shows encouraging intra-lot target-slot transferability without retraining. Additional PPO and SAC comparisons and a time-penalty ablation further evaluate the relative learning performance and the effect of reward design, supporting the proposed architecture as a practical baseline for integrated cruise-to-park automated valet parking studies.

ABSTRACT Based on the progress in intelligent ship technology, this paper investigates the path-following safety challenge for an underactuated airboat operating with unmeasured velocities and under uncertain disturbances. A comprehensive control scheme is developed to enable simultaneous path following and collision avoidance against both static and moving obstacles. The proposed methodology employs a neural network-based observer to estimate the unavailable velocity states and unknown external disturbances. A nonlinear model predictive control (NMPC) framework is subsequently constructed, integrating path-following with obstacle avoidance capabilities. This controller ensures the airboat follows a desired path at specified speed while performing safe evasion maneuvers in compliance with international collision rules (COLREGs). The airboat's nonlinear dynamic model is used to predict system behavior over a finite time horizon. For validation, simulation experiments are conducted in MATLAB and Gazebo, respectively. Experimental results confirm the algorithm's effectiveness in enabling safe navigation through static and moving obstacles during path-following operations.

To enhance the aerodynamic efficiency of micro aerial vehicles (MAVs) with rotary wings, a bio-inspired hybrid flapping-wing rotor (HFWR) configuration can be designed that achieves a power efficiency more than twice that of conventional rotors. Nevertheless, up to the present, the controllable flight of HFWR has so far eluded realization due to severe flapping-induced structural vibrations and nonlinear coupling between aerodynamic and elastic dynamics. This paper provides a practical step toward stable, controllable HFWR flight through two key innovations: a thrust-vectoring gimbal architecture that delivers continuous control moments under strong oscillations, and an enhanced nonlinear model predictive control (E-MPC) framework implemented as a distributed two-layer architecture. In this architecture, the outer layer consists of a lower-rate offboard MPC that generates constraint-aware attitude trim and bias commands, while the inner layer is a high-rate onboard proportional angular-rate loop that provides rapid damping of high-frequency perturbations caused by flapping-induced vibrations and communication or optimization latency. Hover and yaw flight tests demonstrate that the integrated architecture improves attitude stability compared with cascade PID and a baseline offboard MPC without the onboard rate loop, reducing peak deviation, overshoot, and steady-state error by up to 83%, 92%, and 80%, respectively, while substantially lowering control energy. These results demonstrate a practical pathway toward stable control of flapping-rotor MAVs for the first time, bridging the gap between bio-inspired aerodynamic efficiency and flight controllability.

Energy-intensive refrigeration systems require predictive models that remain informative under counterfactual control trajectories, not only on archived operation. This paper develops a control-oriented multi-step state model and a nonlinear model predictive control framework for an indoor ice-rink refrigeration system. Historical state, control, and exogenous variables are encoded jointly with an admissible future control trajectory, and a normalized thermal-balance residual is added to the training objective. A lightweight conditioned transformer predicts ice temperature, return-glycol temperature, supply-glycol temperature, and compressor power over a 30 min horizon. The selected weakly regularized model with regularization coefficient λphys = 0.001 decreases the normalized thermal-balance root-mean-square error on the horizon tail by 30.29% relative to the base model while increasing the average ice-temperature root-mean-square error by only 1.90%. In a surrogate-based counterfactual four-day evaluation, the resulting nonlinear model predictive controller reduces predicted daily energy by 4.84%, terminal violation share by 17.32%, mean absolute terminal ice-temperature deviation by 18.74%, and the mean objective value by 30.82% relative to historical admissible setpoint tracking. The mean full control cycle time is 0.0311 s, confirming real-time feasibility for a 5 min supervisory update interval. All controller results are surrogate-based rather than field-deployed and therefore represent receding-horizon benchmark results under learned-model evaluation, not realized field savings.

The integration of renewable energy sources in microgrids (MGs) enhances system efficiency but increases vulnerability to cyberattacks such as false data injection (FDI) attacks. This paper presents a robust data-driven nonlinear model predictive control (NLMPC) framework with the integration with Bayesian Neural Networks (BNNs). The BNN offers probabilistic state estimation, allowing uncertainty-aware prediction and early anomaly detection. By integration BNN within the NLMPC, the framework obtains combined detection, mitigation, and control of cyberattacks. Simulation results show that the proposed framework detects FDI attacks within 0.1s, and stability is restored within 0.4s. Frequency deviation is reduced by 99.7%, while active and reactive power fluctuation decreases by 85% and 87%, respectively. Moreover, battery storage operation remains within a safe limit. These results validate the effectiveness of the proposed framework for real-time cyber-resilient microgrids control under uncertainty and attack scenarios.

Biological systems regulate motion and suppress unwanted vibrations through learning, adaptation, and predictive control under uncertainty. Inspired by these principles, Bayesian system identification has emerged as a powerful framework for modeling and estimation, particularly in the presence of uncertainty in structural systems. Flexible structures in aerospace and robotics require advanced control to mitigate vibrations under model uncertainty. This paper proposes a data-driven strategy leveraging a Gaussian Process (GP) integrated within a Nonlinear Model Predictive Control (NMPC) framework. The core innovation lies in using a Gaussian Process Nonlinear AutoRegressive model with eXogenous input (GP-NARX) as a probabilistic predictor to capture structural dynamics while quantifying uncertainty. The operational mechanism involves a tight coupling where the GP provides multi-step-ahead forecasts that the NMPC optimizer uses to minimize a cost function subject to constraints. Validated through simulations on Duffing oscillators, linear oscillators, and cantilever beams, the GP-NMPC achieved an 88.2% reduction in displacement amplitude compared to uncontrolled systems. Quantitative analysis shows high predictive accuracy, with a Root Mean Square Error (RMSE) of 0.0031 and a Standardized Mean-Squared Error (SMSE) below 0.05. Furthermore, Mean Standardized Log Loss (MSLL) evaluations confirm the reliability of the predictive uncertainty within the control loop. These results demonstrate strong performance in both regulation and tracking tasks, justifying this Bayesian-predictive coupling as a powerful approach for high-performance structural vibration control and a potential foundation for bio-inspired mechanical design.

Enhanced imitation learning of robust nonlinear model predictive control via temporal convolutional neural network for DC shipboard microgrid.

Data-driven nonlinear model predictive control for AUV trajectory tracking under oceanic disturbances.

In signalized urban traffic, the need for energy-efficient trajectory optimization is increasingly pressing. Conventional approaches treat signal phases as discrete passing windows; in multi-intersection corridors this hampers global optimality, yields discontinuous speed plans, and fragments control decisions. Prior work has used time windows to guide speed, but has not systematically modeled the linkage between the speed feasibility domain and vehicle-level control feasibility. We propose a signal-coupled velocity field control method that maps discrete signal phase and timing data into a continuously varying speed–position feasibility domain along the path, providing a real-time, signal-aware admissible speed range. By integrating traffic-signal constraints with vehicle dynamics and other physical limits, a composite speed upper bound is formed and used to generate reference trajectories within a nonlinear model predictive control (NMPC) framework. In a path–time formulation, longitudinal dynamic reachability is further coupled to produce a dynamic upper bound, which is embedded as a key constraint in NMPC. This tightly links signal information and vehicle dynamics in a single optimization layer. Simulation studies across multiple intersections show smoother speed profiles, markedly fewer full stops, and reductions of approximately 15%–18% in energy consumption per 100 km, together with lower safety exposure. The results demonstrate coordinated improvements in efficiency, energy use, and safety.

Reversible solid oxide fuel cells (rSOCs) offer the flexibilityto operate in tandem with the electric grid by switching between fuelcell and electrolysis modes based on real-time electricity prices.However, their complex, tightly coupled dynamic behavior poses significantchallenges in determining optimal operating strategies. In this work,we present an economic nonlinear model predictive control (E-NMPC)framework to optimize the operation of rSOCs. The proposed E-NMPCis applied to a detailed rSOC flowsheet model that includes a utilityscale rSOC module as well as balance-of-plant equipment necessaryfor thermal management. Our results demonstrate that in fuel cellmode, the E-NMPC strategy reduces hydrogen consumption compared toconventional set-point tracking NMPC, while maintaining the same levelof electricity output. Also, in electrolysis mode, the E-NMPC yieldsa marginal improvement in hydrogen production. In addition, we explorethe integration of a battery with the rSOC system to enhance flexibilityin meeting electricity production and consumption targets.

Model predictive control (MPC) with reduced-order template models has proven effective for dynamic legged locomotion, but loco-manipulation introduces additional complexity requiring efficient algorithms for high-degree-of-freedom (DoF) systems. This letter presents a computationally efficient nonlinear MPC (NMPC) framework tailored for loco-manipulation tasks of quadrupedal robots equipped with robotic manipulators whose dynamics are non-negligible relative to those of the quadruped. The proposed framework adopts a decomposition strategy that couples locomotion template models—such as the single rigid body model—with a full-order dynamic model of the robotic manipulator for torque-level control. This decomposition enables efficient real-time solution of the NMPC problem in a receding horizon fashion. The optimal state and input trajectories generated by the NMPC for locomotion are tracked by a low-level nonlinear whole-body controller, while the optimal torque commands for the manipulator are directly applied. The layered control architecture is validated through extensive numerical simulations and hardware experiments on a 15-kg Go2 quadrupedal robot augmented with a 4.4-kg 4-DoF Kinova arm. Given that the Kinova arm dynamics are non-negligible relative to the Go2 base, the proposed NMPC framework demonstrates robust stability in performing diverse loco-manipulation tasks, effectively handling external disturbances, payload variations, and uneven terrain.

Autonomous aerial systems are increasingly essential for transportation and delivery tasks in complex environments where ground access is limited or unsafe for direct placement. In airdrop missions, these platforms face the dual challenges of abrupt control mode switching and inherent system delays along with control errors. To address these issues, this paper presents an autonomous airdrop system based on an aerial manipulator (AM). The introduction of additional actuated degrees of freedom (DoF) enables active compensation for UAV tracking errors. By imposing smooth and continuous constraints on the parabolic landing point, the proposed approach generates aerial throwing trajectories that are less sensitive to the timing of payload release. A hierarchical disturbance compensation strategy is incorporated into the Nonlinear Model Predictive Control (NMPC) framework to mitigate the effects of sudden changes in system parameters, while the predictive capabilities of NMPC are further exploited to improve the precision of aerial throwing. Both simulation and real-world experimental results demonstrate that the proposed system achieves greater agility and precision in airdrop missions.

Multistage economic MPC for systems with a cyclic steady state: A gas network case study

Safety-critical motion optimization for quadruped robots on offshore platforms: A hierarchical nonlinear model predictive control framework based on foothold optimization and control barrier function

Ensuring frequency stability in multi-area power systems under diverse disturbances remains a major challenge. This paper proposes an AI-enhanced self-tuning nonlinear-proportional-integrator-derivative denoising filter (NL-PIDF) controller designed within an artificial neural network (ANN)-based nonlinear model predictive control (NMPC) framework and optimized using a novel Hybrid Cat-Pikas Optimization (HCPO) algorithm. The ANN predictor identifies the nonlinear system dynamics, while an error compensator mitigates steady-state offsets caused by prediction errors. To further enhance dynamic stability, a superconducting magnetic energy storage (SMES) unit is integrated in Area 1, and high-voltage direct current (HVDC) tie-lines are employed between selected areas. The approach is evaluated on a nonlinear three-area power system including steam, gas, and combined-cycle turbines, considering key nonlinearities such as the reheater, generation rate constraint (GRC), governor deadband (GDB), and boiler dynamics (BD). Simulation results, supported by time-domain and eigenvalue analyses, demonstrate significant improvements in damping frequency oscillations and inter-area power exchanges compared with conventional controllers. The proposed strategy achieves faster settling, reduced overshoot/undershoot, and enhanced robustness under random step, sinusoidal load disturbances, and wide parameter variations. In such a way that the proposed strategy reduces frequency overshoot by ≈45%, improves settling time by ≈38%, and lowers ITSE by ≈52% compared with conventional tuned PID and recent metaheuristic-based controllers, confirming its robustness against load disturbances and system nonlinearities.

Autonomous Unmanned Aerial Vehicles (UAVs) landings on moving aerial platforms present substantial challenges, including real-time feasible path planning and the design of robust control schemes to mitigate disturbances. This paper presents a novel docking strategy for UAVs that integrates dynamic path optimization with a Nonlinear Model Predictive Control (NMPC) framework. The proposed approach initiates with a global planner to generate collision-free, kinodynamically feasible paths, which are subsequently refined using a local planner that employs B-spline formulation alongside gradient-based optimization methods. To enhance control stability, particularly during the landing phase, the NMPC controller is augmented with a dynamic downwash model that compensates for aerodynamic disturbances. Extensive validation in both simulation and real-world experiments demonstrates that the proposed method achieves robust trajectory tracking, reduced landing errors, and improved platform stability. Simulation results show the proposed planner reaches a maximum velocity of 3.49 m/s and an average velocity of 2.07 m/s with a 100% landing success rate. Real-world experiments indicate that with the downwash model, vertical oscillations during landing are reduced by nearly 79% while the overall vertical landing error drops by over 60%.

To enhance the safety and efficiency of the power grid system, a finite-horizon chance constrained optimisation problem is formulated to suppress the load frequency deviation resulting from stochastic uncertainties (e.g. wind energies and load disturbances) and to reduce the mechanical power cost, meanwhile maintaining quality specifications. Especially, using a scenario-based approach, Gaussian process models are built to quantify stochastic uncertainties and to evaluate the model cost and constraint functions over the prediction horizon, which yields a tractable stochastic nonlinear model predictive control (SNMPC) framework for handling chance constrained load frequency control problems with Gaussian parametric uncertainties. Comparative study between the GP-SNMPC framework and scenario generation SMPC framework is carried out, which demonstrates that the GP-SNMPC framework is more computationally efficient and delivers a better performance in keeping load frequency balance while maintaining the system constraints.

In complex and variable terrains, affine formation control, with its flexible formation adjustment ability, can achieve various formation shapes to adapt well to the environment. Notably, the existing affine formation research based on stress matrices require the variation parameters for translation, rotation, scaling, and shearing of formations to be predesigned offline. To address this, we propose a novel method for online affine parameter adjustment that enables self-reconfiguration of formations in multiobstacle environments. By adopting artificial potential field environment excitation, the proposed motion planning algorithm can dynamically adjust the affine transformation parameters online, and realize the self-reconfiguration of formation shape to avoid collision. Then, a distributed model predictive controller is proposed for multiagent systems, which actively utilizes historical control input information to flexibly adjust controller performance while avoiding algebraic loops between neighboring agent controllers. The algorithm separates stability and performance optimization within the nonlinear model predictive control framework, ensuring both the feasibility and stability of the underlying optimization. Finally, the simulation results confirm the effectiveness of the proposed controller.

As renewable energy sources become more widespread and energy consumption continues to grow, there is an urgent requirement for smarter, more flexible control methods to manage microgrids (MGs) effectively. This study proposes a data-driven nonlinear model predictive control (NLMPC) framework for optimized MG operation, emphasizing energy storage system (ESS) integration. Effective MG management is crucial given increasing renewable penetration and energy demands. This framework coordinates distributed generation (DG) units, including rotating and non-rotating resources, with a battery ESS in a dynamic MG environment. Leveraging Gaussian Process Regression (GPR), the framework accurately models the complex dynamics of both DG units and the ESS. Unlike traditional model-based approaches, GPR learns system behavior from operational data, enabling precise performance prediction under varying conditions. This accuracy is crucial for optimized resource dispatch and efficient MG operation. GPR models capture ESS charging/discharging characteristics, efficiency, and state-of-charge (SOC) dynamics for informed ESS utilization. To address renewable energy uncertainties, Monte Carlo simulations are incorporated. This allows robust evaluation of the control strategy under various scenarios, ensuring MG stability and reliability despite fluctuating renewable generation. By considering these uncertainties, the NLMPC controller proactively manages DG and ESS dispatch, mitigating forecast errors and maximizing renewable energy use. The framework aims to achieve optimal power flow, balancing supply and demand while respecting operational constraints. This includes constraints on DG units, the ESS (SOC limits, charge/discharge rates), and overall MG operation (voltage and frequency stability). The NLMPC controller dynamically adjusts DG and ESS setpoints to minimize costs, maximize renewable energy use, and ensure MG stability and reliability. Simulation results demonstrate the framework’s effectiveness. Significant cost savings (approximately 39.2% compared to Conventional MPC and 41.5% compared to Adaptive MPC) and voltage stability improvements (28.57% and 52.38% respectively) are achieved. These improvements stem from accurate system dynamics modeling, robust uncertainty handling, and coordinated DG and ESS control.

ABSTRACT This paper introduces a novel nonlinear model predictive control (NMPC) framework that incorporates a lifting technique to enhance control performance for nonlinear systems. While the lifting technique has been widely used in linear systems to capture intersample behavior, their application to nonlinear systems remains unexplored. We address this gap by formulating an NMPC scheme that combines fast‐sample/fast‐hold approximations and numerical methods to approximate system dynamics and cost functions. The proposed approach is validated through two case studies: the Van der Pol oscillator and the inverted pendulum on a cart. The Simulation results demonstrate that the lifted NMPC outperforms conventional NMPC in terms of reduced settling time and improved control accuracy. These findings underscore the potential of the lifting‐based NMPC for efficient control of nonlinear systems, offering a practical solution for real‐time applications.