Nonlinear model predictive control (MPC) and reinforcement learning (RL) are two powerful control strategies with complementary advantages. This work shows how actor-critic RL techniques can be leveraged to improve the performance of MPC. The RL critic is used as an approximation of the optimal value function, and an actor rollout provides an initial guess for the primal variables of the MPC. A parallel control architecture is proposed where each MPC instance is solved twice for different initial guesses. Besides the actor rollout initialization, a shifted initialization from the previous solution is used. The control actions from the lowest-cost trajectory are applied to the system at each time step. We provide some theoretical justification of the proposed algorithm by establishing that the discounted closed-loop cost is upper-bounded by the discounted closed-loop cost of the original RL actor plus an error term that depends on the (sub)optimality of the RL actor and the accuracy of the critic. These results do not require globally optimal solutions and indicate that larger horizons mitigate the effect of errors in the critic approximation. The proposed algorithm is intended for applications where standard methods to construct terminal costs or constraints for MPC are impractical. The approach is demonstrated in an illustrative toy example and an autonomous driving overtaking scenario.

We investigate the suboptimality resulting from the application of nominal model predictive control (MPC) to a nonlinear discrete time stochastic system. The suboptimality is defined with respect to the corresponding stochastic optimal control problem (OCP) that minimizes the expected cost of the closed loop system. In this context, nominal MPC corresponds to a form of certainty-equivalent control (CEC). We prove that, in a smooth and unconstrained setting, the suboptimality growth is of fourth order with respect to the level of uncertainty, a parameter which we can think of as a standard deviation. This implies that the suboptimality does not grow very quickly as the level of uncertainty is increased, providing further insight into the practical success of nominal MPC. Similarly, the difference between the optimal and suboptimal control inputs is of second order. We illustrate the result on a simple numerical example, which we also use to show how the proven relationship may cease to hold in the presence of state constraints.

We consider a stage-varying nonlinear model predictive control (NMPC) formulation and provide a stability result for the corresponding closed-loop system under the assumption that cost and constraints are progressively tightening. We illustrate the generality of the stage-varying formulation pointing out various approaches proposed in the literature that can be cast as stage-varying and progressively tightening optimal control problems.

This study presents a novel state estimation approach integrating Deep Neural Networks (DNNs) into Moving Horizon Estimation (MHE). This is a shift from using traditional physics-based models within MHE towards data-driven techniques. Specifically, a Long Short-Term Memory (LSTM)-based DNN is trained using synthetic data derived from a high-fidelity thermal model of a Permanent Magnet Synchronous Machine (PMSM), applied within a thermal derating torque control strategy for battery electric vehicles. The trained DNN is directly embedded within an MHE formulation, forming a discrete-time nonlinear optimal control problem (OCP) solved via the acados optimization framework. Model-in-the-Loop simulations demonstrate accurate temperature estimation even under noisy sensor conditions and simulated sensor failures. Real-time implementation on embedded hardware confirms practical feasibility, achieving computational performance exceeding real-time requirements threefold. By integrating the learned LSTM-based dynamics directly into MHE, this work achieves state estimation accuracy, robustness, and adaptability while reducing modeling efforts and complexity. Overall, the results highlight the effectiveness of combining model-based and data-driven methods in safety-critical automotive control systems.