adaptive model predictive control

This work addresses the challenge of real-time robotic arm control in dynamically cluttered environments, where agents must balance rapid responsiveness with foresightful obstacle avoidance to prevent myopic constraint violations. The authors propose a task-space receding horizon controller that generates collision-free terminal pose references through short-horizon, contact-consistent forward simulations respecting non-penetration constraints, then computes only the first-step minimum-acceleration control input that smoothly transitions toward this reference. By integrating the strengths of receding horizon and reactive control, the method efficiently embeds information about contacts, moving obstacles, and self-collisions using inflated convex geometry and an iterative dynamics solver—without requiring full trajectory optimization. Simulations with 40 degrees of freedom demonstrate that a moderate horizon length effectively balances foresight, responsiveness, and computational cost, while hardware experiments on a 6-DOF manipulator confirm strong sim-to-real transfer, outperforming MPC and dynamic optimization fabric approaches in success rate under dynamic clutter while meeting real-time requirements.

Model Predictive Control (MPC) suffers from high computational complexity in long horizons and difficulty guaranteeing closed-loop stability in short horizons. To address this, we propose the “Observed Control” framework, which exploits the rigorous duality between state estimation and MPC. It employs the Kalman smoother as a unified optimization backbone to explicitly decouple the reactive and predictive components of the control law. The framework supports online control synthesis for arbitrary horizon lengths and incorporates an adaptive optimization termination criterion to enable early convergence. By integrating extended or unscented Kalman filtering for nonlinear systems, the method ensures closed-loop stability while reducing computational complexity to linear in horizon length. Numerical experiments on nonlinear systems demonstrate its efficiency, scalability, and robustness—achieving real-time performance without sacrificing stability or prediction fidelity.

Real-time autonomous navigation for embedded unmanned aerial vehicles (UAVs) faces a fundamental challenge: conventional nonlinear model predictive control (NMPC) cannot meet millisecond-level closed-loop timing requirements under severe computational constraints. Method: This paper proposes an embedded-friendly hierarchical NMPC architecture that decouples long-horizon safety-aware planning from short-horizon high-frequency tracking. The planning layer employs a large-horizon, low-frequency (~100 ms) NMPC to ensure global feasibility and obstacle avoidance; the tracking layer uses a small-horizon, high-frequency (~5 ms) lightweight MPC for responsive trajectory following. Contribution/Results: We establish theoretical guarantees on recursive feasibility and obstacle-avoidance safety. Engineering deployment is achieved via constraint simplification, hierarchical optimization, and real-time C++ implementation on ARM processors. Experimental validation on a quadrotor demonstrates a 5× increase in planning horizon, significantly improved navigation success rate and trajectory quality over monolithic NMPC baselines in complex static environments.

This paper investigates the suboptimality of nominal model-predictive linear-quadratic (LQ) control for unknown linear systems, characterizing a fundamental trade-off among model mismatch, terminal cost approximation error, and prediction horizon length. We develop a novel perturbation analysis framework for the Riccati difference equation, establishing—for the first time—a quantitative relationship between horizon length and the system’s controllability index. Theoretically, we prove that a finite horizon bounded by the controllability index suffices to approximate infinite-horizon optimal performance, and that horizons of length one or infinity are often optimal. Based on this insight, we derive the first adaptive horizon-selection criterion tailored for learning-based control, yielding a tight suboptimality upper bound, an $O(log T)$ regret guarantee, and optimal sample complexity.

This work addresses nonlinear systems subject to unknown dynamics and external disturbances. Methodologically, it proposes an integrated online system identification and model predictive control (MPC) framework that combines reproducing kernel Hilbert space (RKHS) modeling, random Fourier feature approximation, online least-squares parameter adaptation, and learning-based receding-horizon MPC—compatible with control-affine structures. The approach achieves sublinear dynamic regret against an adversarial clairvoyant controller for the first time, while ensuring finite-time near-optimality and asymptotic convergence to optimality. To jointly handle modeling errors and exogenous disturbances, it introduces self-supervised learning and state- and input-adaptive disturbance modeling. Extensive validation is conducted on an inverted pendulum, quadrotor simulation, and real-world quadrotor hardware under challenging conditions—including wind gusts, ground effect, and aerodynamic drag—demonstrating robustness and high-precision trajectory tracking performance.

This study addresses the lack of a systematic synthesis in research on integrating reinforcement learning (RL) with model predictive control (MPC) for linear systems by proposing the first multidimensional taxonomy tailored to this domain. Drawing on a comprehensive literature review up to 2025, the work establishes a classification framework along five dimensions: RL role, algorithm type, MPC formulation, cost function structure, and application area, followed by an integrative cross-dimensional analysis. The study elucidates representative integration strategies, traces methodological evolution, and identifies key challenges—including computational burden, sample efficiency, robustness, and closed-loop guarantees—thereby offering a structured reference and practical guidance for both theoretical analysis and architectural design in RL–MPC systems.

This work addresses the challenge of achieving both high performance and provable safety for autonomous systems operating in real-world environments, where conventional model predictive control (MPC) often fails to guarantee safety beyond the finite prediction horizon. The authors propose a novel approach that constructs terminal constraints using a safety value function derived from reachability analysis, ensuring that the planned trajectory terminates within a controlled invariant safe set. This formulation guarantees recursive feasibility while enabling real-time, provably safe trajectory optimization with high task performance. In contrast to existing methods that rely on local linearization or overly conservative approximations, the proposed technique significantly reduces conservatism and enhances expressiveness of safety guarantees. Simulations and hardware experiments on a Flexiv Rizon 10s robotic arm demonstrate that the method substantially improves constraint satisfaction and robustness compared to standard MPC and reactive safety filters, without compromising task performance.

This work proposes Drifting MPC, a novel framework for offline reinforcement learning in settings where the system dynamics are unknown and trajectory simulation is infeasible. Drifting MPC uniquely integrates a drift generative model with model predictive control to learn a conditional trajectory distribution from offline data that balances data support and cost optimality. The method explicitly optimizes task-specific costs while maintaining fidelity to the empirical data distribution, and it is theoretically shown that the resulting distribution constitutes the unique solution that optimally trades off optimality against consistency with the data prior. Empirical results demonstrate that Drifting MPC efficiently generates near-optimal trajectories with low per-step computational overhead, significantly reducing trajectory generation time compared to diffusion-model baselines.

Existing motion planning methods for nonholonomic systems under nonconvex constraints lack theoretical guarantees of convergence. Method: This paper proposes an output-tracking model predictive control (MPC) framework, incorporating slack variables, designing a terminal set and terminal cost tailored to nonholonomic dynamics, and establishing rigorous closed-loop asymptotic convergence and goal reachability under verifiable, realistic assumptions. Contribution/Results: To the best of our knowledge, this is the first MPC-based planning approach that provides theoretical completeness for nonholonomic systems subject to nonconvex constraints. Comprehensive simulations and experiments on canonical nonconvex scenarios demonstrate the method’s feasibility, closed-loop stability, and computational efficiency—thereby bridging a critical gap between empirical practice and theoretical rigor in nonholonomic motion planning.

To address the computational intractability of real-time model predictive control (MPC) for systems exhibiting coexisting fast and slow dynamics—particularly under long prediction horizons and high-fidelity modeling—this paper proposes a multi-timescale MPC framework leveraging the exponential decay property of sensitivity indices. Within the prediction horizon, the method progressively simplifies the dynamic model while exponentially increasing the integration step size, thereby balancing short-term accuracy and long-term behavioral fidelity. Integrating model order reduction, multi-scale numerical integration, and standard MPC, the approach establishes a computationally efficient optimization paradigm with provable performance guarantees. Evaluated on three robotic control benchmarks, the proposed method achieves nearly tenfold speedup over conventional MPC while maintaining constraint satisfaction and enabling high-sampling-rate real-time control—significantly enhancing the online feasibility of MPC for complex, multi-timescale dynamical systems.