Learning Model Predictive Control for iterative tasks. A Data-Driven Control Framework (1609.01387v7)

Abstract: A Learning Model Predictive Controller (LMPC) for iterative tasks is presented. The controller is reference-free and is able to improve its performance by learning from previous iterations. A safe set and a terminal cost function are used in order to guarantee recursive feasibility and non-increasing performance at each iteration. The paper presents the control design approach, and shows how to recursively construct terminal set and terminal cost from state and input trajectories of previous iterations. Simulation results show the effectiveness of the proposed control logic.

• The paper proposes a Learning Model Predictive Control (LMPC) framework that enables systems to learn and improve performance iteratively without needing a fixed reference trajectory, unlike traditional methods.
• The LMPC framework guarantees recursive feasibility and closed-loop stability by using a sampled safe set derived from successful state trajectories of prior iterations.
• Numerical simulations demonstrate that the LMPC iteratively reduces cost and converges towards optimal trajectories, enabling practical applications in adaptive control systems.

Learning Model Predictive Control for Iterative Tasks: A Data-Driven Control Framework

The research paper presents a novel control strategy known as Learning Model Predictive Control (LMPC) tailored for iterative tasks. This framework is built on the premise that repetitive tasks allow control systems to optimize by learning from their prior experiences, which is a deviation from traditional approaches like Iterative Learning Control (ILC) and Batch Model Predictive Control (BMPC). Unlike standard ILC, which relies on predefined reference trajectories, LMPC operates without any such reference, enhancing its applicability to complex and dynamic systems with uncertain parameters.

Core Contributions

1. Reference-Free Control Design: The LMPC framework is designed to improve performance iteratively by adapting based on previous trials. It formulates the control problem as an infinite horizon optimization without relying on fixed reference trajectories. This is especially beneficial for systems with complex nonlinear dynamics or where environmental factors change between iterations, such as autonomous vehicles navigating unpredictably varied terrains.
2. Recursive Feasibility and Stability: One significant contribution of the LMPC is its guarantee of recursive feasibility and closed-loop stability. The implementation involves a safe set and a terminal cost function derived from prior iterations, ensuring that the system adheres to state and input constraints consistently, thereby enhancing robustness against infeasibility at each step.
3. Sampled Safe Set Construction: A crucial aspect of the proposed method is the sampled safe set, which accumulates successful state trajectories over iterations. This set is used in defining terminal constraints and costs, aiding the controller in maintaining feasibility and stability as it iteratively improves the performance.
4. Convergence and Optimality: The paper theoretically demonstrates that, as the number of iterations approaches infinity, the LMPC's solution converges to a locally optimal trajectory for the defined problem. This convergence is rooted in the assumption of problem convexity, though the paper acknowledges potential limitations and extensions in non-convex scenarios.

Numerical Results and Implications

Simulations demonstrate the efficacy of the LMPC framework through two examples: a Constrained Linear Quadratic Regulator (CLQR) and a Dubins car problem. In both cases, the iterative control logic illustrates measurable performance improvements over iterations, reducing cost functions significantly from initial feasible trajectories to steady-state trajectories, the latter approximating optimal solutions to the respective control problems.

The implications of this research are profound for the field of automated control systems performing iterative tasks. Practically, the LMPC offers a pathway to deploy systems in environments where adaptability and learning from historical data can lead to substantial performance gains. For instance, this could be instrumental in autonomous driving, adaptive cruise control, and even dynamic resource allocation in smart grids.

Future Prospects

While the paper establishes a robust theoretical and practical groundwork for LMPC, further explorations into the domain of non-convex problems and robust optimization in the presence of real-world uncertainties present viable avenues for future research. Extending LMPC to more generalized stochastic settings or combining it with deep reinforcement learning techniques are promising areas that could enhance its capability to learn and adapt in more dynamic environments.

Moreover, reducing the computational burden of the LMPC and accelerating its real-time applicability through advanced optimization techniques or hardware acceleration is critical. This development is especially relevant for industries where real-time control and performance optimization are paramount, such as in robotics and industrial automation.

In sum, the proposed LMPC framework not only advances the state of iterative learning in control systems but also opens up numerous practical applications across several dynamic and complex control scenarios, laying a foundation for further innovations in the field of model predictive control.