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Deep learning has enjoyed much recent success, and applying state-of-the-art model learning methods to controls is an exciting prospect. However, there is a strong reluctance to use these methods on safety-critical systems, which have constraints on safety, stability, and real-time performance. We propose a framework which satisfies these constraints while allowing the use of deep neural networks for learning model uncertainties. Central to our method is the use of Bayesian model learning, which provides an avenue for maintaining appropriate degrees of caution in the face of the unknown. In the proposed approach, we develop an adaptive control framework leveraging the theory of stochastic CLFs (Control Lyapunov Functions) and stochastic CBFs (Control Barrier Functions) along with tractable Bayesian model learning via Gaussian Processes or Bayesian neural networks. Under reasonable assumptions, we guarantee stability and safety while adapting to unknown dynamics with probability 1. We demonstrate this architecture for high-speed terrestrial mobility targeting potential applications in safety-critical high-speed Mars rover missions.
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Safety and tracking stability are crucial for safety-critical systems such as self-driving cars, autonomous mobile robots, industrial manipulators. To efficiently control safety-critical systems to ensure their safety and achieve tracking stability, accurate system dynamic models are usually required. However, accurate system models are not always available in practice. In this paper, a learning-based safety-stability-driven control (LBSC) algorithm is presented to guarantee the safety and tracking stability for nonlinear safety-critical systems subject to control input constraints under model uncertainties. Gaussian Processes (GPs) are employed to learn the model error between the nominal model and the actual system dynamics, and the estimated mean and variance of the model error are used to quantify a high-confidence uncertainty bound. Using this estimated uncertainty bound, a safety barrier constraint is devised to ensure safety, and a stability constraint is developed to achieve rapid and accurate tracking. Then the proposed LBSC method is formulated as a quadratic program incorporating the safety barrier, the stability constraint, and the control constraints. The effectiveness of the LBSC method is illustrated on the safety-critical connected cruise control (CCC) system simulator under model uncertainties.
Control barrier functions have shown great success in addressing control problems with safety guarantees. These methods usually find the next safe control input by solving an online quadratic programming problem. However, model uncertainty is a big challenge in synthesizing controllers. This may lead to the generation of unsafe control actions, resulting in severe consequences. In this paper, we develop a learning framework to deal with system uncertainty. Our method mainly focuses on learning the dynamics of the control barrier function, especially for high relative degree with respect to a system. We show that for each order, the time derivative of the control barrier function can be separated into the time derivative of the nominal control barrier function and a remainder. This implies that we can use a neural network to learn the remainder so that we can approximate the dynamics of the real control barrier function. We show by simulation that our method can generate safe trajectories under parametric uncertainty using a differential drive robot model.
The repetitive tracking task for time-varying systems (TVSs) with non-repetitive time-varying parameters, which is also called non-repetitive TVSs, is realized in this paper using iterative learning control (ILC). A machine learning (ML) based nominal model update mechanism, which utilizes the linear regression technique to update the nominal model at each ILC trial only using the current trial information, is proposed for non-repetitive TVSs in order to enhance the ILC performance. Given that the ML mechanism forces the model uncertainties to remain within the ILC robust tolerance, an ILC update law is proposed to deal with non-repetitive TVSs. How to tune parameters inside ML and ILC algorithms to achieve the desired aggregate performance is also provided. The robustness and reliability of the proposed method are verified by simulations. Comparison with current state-of-the-art demonstrates its superior control performance in terms of controlling precision. This paper broadens ILC applications from time-invariant systems to non-repetitive TVSs, adopts ML regression technique to estimate non-repetitive time-varying parameters between two ILC trials and proposes a detailed parameter tuning mechanism to achieve desired performance, which are the main contributions.
Reinforcement learning (RL) is promising for complicated stochastic nonlinear control problems. Without using a mathematical model, an optimal controller can be learned from data evaluated by certain performance criteria through trial-and-error. However, the data-based learning approach is notorious for not guaranteeing stability, which is the most fundamental property for any control system. In this paper, the classic Lyapunovs method is explored to analyze the uniformly ultimate boundedness stability (UUB) solely based on data without using a mathematical model. It is further shown how RL with UUB guarantee can be applied to control dynamic systems with safety constraints. Based on the theoretical results, both off-policy and on-policy learning algorithms are proposed respectively. As a result, optimal controllers can be learned to guarantee UUB of the closed-loop system both at convergence and during learning. The proposed algorithms are evaluated on a series of robotic continuous control tasks with safety constraints. In comparison with the existing RL algorithms, the proposed method can achieve superior performance in terms of maintaining safety. As a qualitative evaluation of stability, our method shows impressive resilience even in the presence of external disturbances.
Neural networks have been increasingly applied for control in learning-enabled cyber-physical systems (LE-CPSs) and demonstrated great promises in improving system performance and efficiency, as well as reducing the need for complex physical models. However, the lack of safety guarantees for such neural network based controllers has significantly impeded their adoption in safety-critical CPSs. In this work, we propose a controller adaptation approach that automatically switches among multiple controllers, including neural network controllers, to guarantee system safety and improve energy efficiency. Our approach includes two key components based on formal methods and machine learning. First, we approximate each controller with a Bernstein-polynomial based hybrid system model under bounded disturbance, and compute a safe invariant set for each controller based on its corresponding hybrid system. Intuitively, the invariant set of a controller defines the state space where the system can always remain safe under its control. The union of the controllers invariants sets then define a safe adaptation space that is larger than (or equal to) that of each controller. Second, we develop a deep reinforcement learning method to learn a controller switching strategy for reducing the control/actuation energy cost, while with the help of a safety guard rule, ensuring that the system stays within the safe space. Experiments on a linear adaptive cruise control system and a non-linear Van der Pols oscillator demonstrate the effectiveness of our approach on energy saving and safety enhancement.
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