Controllers for dynamical systems that operate in safety-critical settings must account for stochastic disturbances. Such disturbances are often modeled as process noise in a dynamical system, and common assumptions are that the underlying distributions are known and/or Gaussian. In practice, however, these assumptions may be unrealistic and can lead to poor approximations of the true noise distribution. We present a novel controller synthesis method that does not rely on any explicit representation of the noise distributions. In particular, we address the problem of computing a controller that provides probabilistic guarantees on safely reaching a target, while also avoiding unsafe regions of the state space. First, we abstract the continuous control system into a finite-state model that captures noise by probabilistic transitions between discrete states. As a key contribution, we adapt tools from the scenario approach to compute probably approximately correct (PAC) bounds on these transition probabilities, based on a finite number of samples of the noise. We capture these bounds in the transition probability intervals of a so-called interval Markov decision process (iMDP). This iMDP is, with a user-specified confidence probability, robust against uncertainty in the transition probabilities, and the tightness of the probability intervals can be controlled through the number of samples. We use state-of-the-art verification techniques to provide guarantees on the iMDP and compute a controller for which these guarantees carry over to the original control system. In addition, we develop a tailored computational scheme that reduces the complexity of the synthesis of these guarantees on the iMDP. Benchmarks on realistic control systems show the practical applicability of our method, even when the iMDP has hundreds of millions of transitions.

This paper presents algorithms to solve analysis and controller synthesis problems for dynamical systems modeled as a recurrent single-hidden-layer rectified linear unit neural network (ReLU NN), or equivalently, a piecewise affine dynamical system. Such models are interesting since they may arise through the use of modern machine learning methods for system identification, or as closed-loop solutions in certain classes of model predictive control (MPC) problems. A key idea in the proposed approach is to use piecewise affine Lyapunov functions parametrized as ReLU neural networks, and similarly parametrized controllers. This compatible representation between the Lyapunov function and the dynamics simplifies the automation of analysis of and controller synthesis for learned models. Our method of verifying a candidate Lyapunov function is faster than methods based on mixed integer programming. We ‘learn’ controllers and Lyapunov functions using both weight updates and network architecture search, without gradients. We demonstrate the proposed algorithm on examples involving learned models, explicit MPC controllers, and constrained controller synthesis.

Advances in machine learning technologies in recent years have facilitated developments in autonomous robotic systems. Designing these autonomous systems typically requires manually specified models of the robotic system and world when using classical control-based strategies, or time consuming and computationally expensive data-driven training when using learning-based strategies. Combination of classical control and learning-based strategies may mitigate both requirements. However, the performance of the combined control system is not obvious given that there are two separate controllers. This paper focuses on one such combination, which uses gravity-compensation together with reinforcement learning (RL). We present a study of the effects of gravity compensation on the performance of two reinforcement learning algorithms when solving reaching tasks using a simulated seven-degree-of-freedom robotic arm. The results of our study demonstrate that gravity compensation coupled with RL can reduce the training required in reaching tasks involving elevated target locations, but not all target locations.