No Arabic abstract
The human insulin-glucose metabolism is a time-varying process, which is partly caused by the changing insulin sensitivity of the body. This insulin sensitivity follows a circadian rhythm and its effects should be anticipated by any automated insulin delivery system. This paper presents an extension of our previous work on automated insulin delivery by developing a controller suitable for humans with Type 1 Diabetes Mellitus. Furthermore, we enhance the controller with a new kernel function for the Gaussian Process and deal with noisy measurements, as well as, the noisy training data for the Gaussian Process, arising therefrom. This enables us to move the proposed control algorithm, a combination of Model Predictive Controller and a Gaussian Process, closer towards clinical application. Simulation results on the University of Virginia/Padova FDA-accepted metabolic simulator are presented for a meal schedule with random carbohydrate sizes and random times of carbohydrate uptake to show the performance of the proposed control scheme.
This paper proposes a novel framework for addressing the challenge of autonomous overtaking and obstacle avoidance, which incorporates the overtaking path planning into Gaussian Process-based model predictive control (GPMPC). Compared with the conventional control strategies, this approach has two main advantages. Firstly, combining Gaussian Process (GP) regression with a nominal model allows for learning from model mismatch and unmodeled dynamics, which enhances a simple model and delivers significantly better results. Due to the approximation for propagating uncertainties, we can furthermore satisfy the constraints and thereby safety of the vehicle is ensured. Secondly, we convert the geometric relationship between the ego vehicle and other obstacle vehicles into the constraints. Without relying on a higherlevel path planner, this approach substantially reduces the computational burden. In addition, we transform the state constraints under the model predictive control (MPC) framework into a soft constraint and incorporate it as relaxed barrier function into the cost function, which makes the optimizer more efficient. Simulation results reveal the usefulness of the proposed approach.
This paper proposes an off-line algorithm, called Recurrent Model Predictive Control (RMPC), to solve general nonlinear finite-horizon optimal control problems. Unlike traditional Model Predictive Control (MPC) algorithms, it can make full use of the current computing resources and adaptively select the longest model prediction horizon. Our algorithm employs a recurrent function to approximate the optimal policy, which maps the system states and reference values directly to the control inputs. The number of prediction steps is equal to the number of recurrent cycles of the learned policy function. With an arbitrary initial policy function, the proposed RMPC algorithm can converge to the optimal policy by directly minimizing the designed loss function. We further prove the convergence and optimality of the RMPC algorithm thorough Bellman optimality principle, and demonstrate its generality and efficiency using two numerical examples.
We propose Kernel Predictive Control (KPC), a learning-based predictive control strategy that enjoys deterministic guarantees of safety. Noise-corrupted samples of the unknown system dynamics are used to learn several models through the formalism of non-parametric kernel regression. By treating each prediction step individually, we dispense with the need of propagating sets through highly non-linear maps, a procedure that often involves multiple conservative approximation steps. Finite-sample error bounds are then used to enforce state-feasibility by employing an efficient robust formulation. We then present a relaxation strategy that exploits on-line data to weaken the optimization problem constraints while preserving safety. Two numerical examples are provided to illustrate the applicability of the proposed control method.
In this paper, we present an iterative Model Predictive Control (MPC) design for piecewise nonlinear systems. We consider finite time control tasks where the goal of the controller is to steer the system from a starting configuration to a goal state while minimizing a cost function. First, we present an algorithm that leverages a feasible trajectory that completes the task to construct a control policy which guarantees that state and input constraints are recursively satisfied and that the closed-loop system reaches the goal state in finite time. Utilizing this construction, we present a policy iteration scheme that iteratively generates safe trajectories which have non-decreasing performance. Finally, we test the proposed strategy on a discretized Spring Loaded Inverted Pendulum (SLIP) model with massless legs. We show that our methodology is robust to changes in initial conditions and disturbances acting on the system. Furthermore, we demonstrate the effectiveness of our policy iteration algorithm in a minimum time control task.
We propose a learning-based, distributionally robust model predictive control approach towards the design of adaptive cruise control (ACC) systems. We model the preceding vehicle as an autonomous stochastic system, using a hybrid model with continuous dynamics and discrete, Markovian inputs. We estimate the (unknown) transition probabilities of this model empirically using observed mode transitions and simultaneously determine sets of probability vectors (ambiguity sets) around these estimates, that contain the true transition probabilities with high confidence. We then solve a risk-averse optimal control problem that assumes the worst-case distributions in these sets. We furthermore derive a robust terminal constraint set and use it to establish recursive feasibility of the resulting MPC scheme. We validate the theoretical results and demonstrate desirable properties of the scheme through closed-loop simulations.