Related papers: Infinite-Horizon Value Function Approximation for …
Model Predictive Control (MPC) is a classic tool for optimal control of complex, real-world systems. Although it has been successfully applied to a wide range of challenging tasks in robotics, it is fundamentally limited by the prediction…
These notes present preliminary results regarding two different approximations of linear infinite-horizon optimal control problems arising in model predictive control. Input and state trajectories are parametrized with basis functions and a…
We propose a Model Predictive Control (MPC) with a single-step prediction horizon to approximate the solution of infinite horizon optimal control problems with the expected sum of convex stage costs for constrained linear uncertain systems.…
Predictive control is frequently used for control problems involving constraints. Being an optimization based technique utilizing a user specified so-called stage cost, performance properties, i.e., bounds on the infinite horizon…
Path Integral Control methods were developed for stochastic optimal control covering a wide class of finite horizon formulations with control affine nonlinear dynamics. Characteristic for this class is that the HJB equation is linear and…
Stability under model predictive control (MPC) schemes is frequently ensured by terminal ingredients. Employing a (control) Lyapunov function as the terminal cost constitutes a common choice. Learning-based methods may be used to construct…
In this paper, we consider the infinite horizon optimal control problem for nonlinear systems. Under the conditions of controllability of the linearized system around the origin, and nonlinear controllability of the system to a terminal set…
Online approximation of an infinite horizon optimal path-following strategy for a kinematic unicycle is considered. The solution to the optimal control problem is approximated using an approximate dynamic programming technique that uses…
The expansion in automation of increasingly fast applications and low-power edge devices poses a particular challenge for optimization based control algorithms, like model predictive control. Our proposed machine-learning supported approach…
This paper develops algorithms for high-dimensional stochastic control problems based on deep learning and dynamic programming. Unlike classical approximate dynamic programming approaches, we first approximate the optimal policy by means of…
We propose a machine learning algorithm for solving finite-horizon stochastic control problems based on a deep neural network representation of the optimal policy functions. The algorithm has three features: (1) It can solve…
The minimization of energy-like cost functionals is addressed in the context of optimal control problems. For a general class of dynamical systems, with possibly unstable and nonlinear free dynamics, it is shown that a sequence of solutions…
Horizon length and model accuracy are defining factors when designing a Model Predictive Controller. While long horizons and detailed models have a positive effect on control performance, computational complexity increases. As predictions…
We study risk-sensitive control of continuous time Markov chains taking values in discrete state space. We study both finite and infinite horizon problems. In the finite horizon problem we characterise the value function via HJB equation…
We investigate conditions of optimality for an infinite horizon control problem and consider their correspondence with the value function. Assuming Lipschitz continuity of the value function, we prove that sensitivity relations plus the…
This paper proposes a differentiable linear quadratic Model Predictive Control (MPC) framework for safe imitation learning. The infinite-horizon cost is enforced using a terminal cost function obtained from the discrete-time algebraic…
In the last decades, control problems with infinite horizons and discount factors have become increasingly central not only for economics but also for applications in artificial intelligence and machine learning. The strong links between…
A self-learning approach for optimal feedback gains for finite-horizon nonlinear continuous time control systems is proposed and analysed. It relies on parameter dependent approximations to the optimal value function obtained from a family…
We deal with the convergence of the value function of an approximate control problem with uncertain dynamics to the value function of a nonlinear optimal control problem. The assumptions on the dynamics and the costs are rather general and…
A self-learning optimal control algorithm for episodic fixed-horizon manufacturing processes with time-discrete control actions is proposed and evaluated on a simulated deep drawing process. The control model is built during consecutive…