To bring complex systems into real world environments in a safe manner, they will have to be robust to uncertainties - both in the environment and the system. This paper investigates the safety of control systems under input disturbances, wherein the disturbances can capture uncertainties in the system. Safety, framed as forward invariance of sets in the state space, is ensured with the framework of control barrier functions (CBFs). Concretely, the definition of input to state safety (ISSf) is generalized to allow the synthesis of non-conservative, tunable controllers that are provably safe under varying disturbances. This is achieved by formulating the concept of tunable input to state safe control barrier functions (TISSf-CBFs) which guarantee safety for disturbances that vary with state and, therefore, provide less conservative means of accommodating uncertainty. The theoretical results are demonstrated with a simple control system with input disturbance and also applied to design a safe connected cruise controller for a heavy duty truck.
Safety and performance are often two competing objectives in sequential decision-making problems. Existing performant controllers, such as controllers derived from reinforcement learning algorithms, often fall short of safety guarantees. On the contrary, controllers that guarantee safety, such as those derived from classical control theory, require restrictive assumptions and are often conservative in performance. Our goal is to blend a performant and a safe controller to generate a single controller that is safer than the performant and accumulates higher rewards than the safe controller. To …
In this work, we present a compositional safety controller synthesis approach for the class of discrete-time linear control systems. Here, we leverage a state-of-the-art result on the computation of robust controlled invariant sets. To tackle the complexity of controller synthesis over complex interconnected systems, this paper introduces a decentralized controller synthesis scheme. Rather than treating the interconnected system as a whole, we first design local safety controllers for each subsystem separately to enforce local safety properties, with polytopic state and input constraints as we…
In this paper, we propose a construction scheme for a Safe-visor architecture for sandboxing unverified controllers, e.g., artificial intelligence-based (a.k.a. AI-based) controllers, in two-players non-cooperative stochastic games. Concretely, we leverage abstraction-based approaches to construct a supervisor that checks and decides whether or not to accept the inputs provided by the unverified controller, and a safety advisor that provides fallback control inputs to ensure safety whenever the unverified controller is rejected. Moreover, by leveraging an ($ε,δ$)-approximate probabilistic rela…
High performance but unverified controllers, e.g., artificial intelligence-based (a.k.a. AI-based) controllers, are widely employed in cyber-physical systems (CPSs) to accomplish complex control missions. However, guaranteeing the safety and reliability of CPSs with this kind of controllers is currently very challenging, which is of vital importance in many real-life safety-critical applications. To cope with this difficulty, we propose in this work a Safe-visor architecture for sandboxing unverified controllers in CPSs operating in noisy environments (a.k.a. stochastic CPSs). The proposed arc…
We introduce a novel learning-based approach to synthesize safe and robust controllers for autonomous Cyber-Physical Systems and, at the same time, to generate challenging tests. This procedure combines formal methods for model verification with Generative Adversarial Networks. The method learns two Neural Networks: the first one aims at generating troubling scenarios for the controller, while the second one aims at enforcing the safety constraints. We test the proposed method on a variety of case studies.
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 effic…
This paper investigates the car-following problem and proposes a nonlinear controller that considers driving comfort, safety concerns, steady-state response and transient response. This controller is designed based on the demands of lower cost, faster response, increased comfort, enhanced safety and elevated extendability from the automotive industry. Design insights and intuitions are provided in detail. Also, theoretical analysis are performed on plant stability, string stability and tracking performance of the closed-loop system. Conditions and guidelines are provided on the selection of co…
Switching control strategies that unite a potentially high-performance but uncertified controller and a stabilizing albeit conservative controller are shown to be able to balance safety with efficiency, but have been less studied under partial observation of state. To address this gap, we propose a switching control strategy for partially observed linear-Gaussian systems with provable performance guarantees. We show that the proposed switching strategy is both safe and efficient, in the sense that: (1) the linear-quadratic cost of the system is always bounded even if the original uncertified c…
This paper proposes an on-policy reinforcement learning (RL) control algorithm that solves the optimal regulation problem for a class of uncertain continuous-time nonlinear systems under user-defined state constraints. We formulate the safe RL problem as the minimization of the Hamiltonian subject to a constraint on the time-derivative of a barrier Lyapunov function (BLF). We subsequently use the analytical solution of the optimization problem to modify the Actor-Critic-Identifier architecture to learn the optimal control policy safely. The proposed method does not require the presence of exte…
Research Institute of Trustworthy Autonomous Systems, SUSTech（南方科技大学可信自主系统研究院）；School of Automation, Hangzhou Dianzi University（杭州电子科技大学自动化学院）；Verimag, Université Grenoble Alpes（格勒诺布尔阿尔卑斯大学Verimag实验室）
We design and experimentally evaluate a hybrid safe-by-construction collision avoidance controller for autonomous vehicles. The controller combines into a single architecture the respective advantages of an adaptive controller and a discrete safe controller. The adaptive controller relies on model predictive control to achieve optimal efficiency in nominal conditions. The safe controller avoids collision by applying two different policies, for nominal and out-of-nominal conditions, respectively. We present design principles for both the adaptive and the safe controller and show how each one ca…
We present a novel class of nonlinear controllers that interpolates among differently behaving linear controllers as a case study for recently proposed Linear and Nonlinear System Level Synthesis framework. The structure of the nonlinear controller allows for simultaneously satisfying performance and safety objectives defined for small- and large-disturbance regimes. The proposed controller is distributed, handles delays, sparse actuation, and localizes disturbances. We show our nonlinear controller always outperforms its linear counterpart for constrained LQR problems. We further demonstrate …
Learning-based controllers, such as neural network (NN) controllers, can show high empirical performance but lack formal safety guarantees. To address this issue, control barrier functions (CBFs) have been applied as a safety filter to monitor and modify the outputs of learning-based controllers in order to guarantee the safety of the closed-loop system. However, such modification can be myopic with unpredictable long-term effects. In this work, we propose a safe-by-construction NN controller which employs differentiable CBF-based safety layers, and investigate the performance of safe-by-const…
In this paper we propose sufficient conditions to synthesizing reach-avoid controllers for deterministic systems modelled by ordinary differential equations and stochastic systems modeled by stochastic differential equations based on the notion of control guidance-barrier functions. We begin with considering deterministic systems. Given an open safe set, a target set and a nominal controller, we attempt to synthesize a reach-avoid controller, which modifies the nominal controller in a minimal way enforcing the reach-avoid objective, i.e., the system will enter the target set eventually while s…
University of Michigan（密歇根大学）；Plus.ai Inc.（智加科技公司）；California Institute of Technology（加州理工学院）；Visteon Corporation（伟世通公司）
Accomplishing safe and efficient driving is one of the predominant challenges in the controller design of connected automated vehicles (CAVs). It is often more convenient to address these goals separately and integrate the resulting controllers. In this study, we propose a controller integration scheme to fuse performance-based controllers and safety-oriented controllers safely for the longitudinal motion of a CAV. The resulting structure is compatible with a large class of controllers, and offers flexibility to design each controller individually without affecting the performance of the other…
In this paper, we provide a direct data-driven approach to synthesize safety controllers for unknown linear systems affected by unknown-but-bounded disturbances, in which identifying the unknown model is not required. First, we propose a notion of $γ$-robust safety invariant ($γ$-RSI) sets and their associated state-feedback controllers, which can be applied to enforce invariance properties. Then, we formulate a data-driven computation of these sets in terms of convex optimization problems with linear matrix inequalities (LMI) as constraints, which can be solved based on a finite number of dat…
Researchers have developed various cascaded controllers and non-cascaded controllers for the navigation and control of quadrotors in recent years. It is vital to ensure the safety of a quadrotor both in normal state and in abnormal state if a controller tends to make the quadrotor unsafe. To this end, this paper proposes a non-cascaded Control Barrier Function (CBF) for a quadrotor controlled by either cascaded controllers or a non-cascaded controller. Incorporated with a Quadratic Programming (QP), the non-cascaded CBF can simultaneously regulate the magnitude of the total thrust and the torq…
Fast and safe voltage regulation algorithms can serve as fundamental schemes for achieving a high level of renewable penetration in the modern distribution power grids. Faced with uncertain or even unknown distribution grid models and fast-changing power injections, model-free deep reinforcement learning (DRL) algorithms have been proposed to find the reactive power injections for inverters while optimizing the voltage profiles. However, such data-driven controllers can not guarantee satisfaction of the hard operational constraints, such as maintaining voltage profiles within a certain range o…
The well-known quote from George Box states that: "All models are wrong, but some are useful." To develop more useful models, we quantify the inaccuracy with which a given model represents a system of interest, so that we may leverage this quantity to facilitate controller synthesis and verification. Specifically, we develop a procedure that identifies a sim2real gap that holds with a minimum probability. Augmenting the nominal model with our identified sim2real gap produces an uncertain model which we prove is an accurate representor of system behavior. We leverage this uncertain model to syn…
Inverter-based distributed energy resources provide the possibility for fast time-scale voltage control by quickly adjusting their reactive power. The power-electronic interfaces allow these resources to realize almost arbitrary control law, but designing these decentralized controllers is nontrivial. Reinforcement learning (RL) approaches are becoming increasingly popular to search for policy parameterized by neural networks. It is difficult, however, to enforce that the learned controllers are safe, in the sense that they may introduce instabilities into the system. This paper proposes a saf…
This paper addresses the synthesis of safety-critical controllers using estimate feedback. We propose an observer-controller interconnection to ensure that the nonlinear system remains safe despite bounded disturbances on the system dynamics and measurements that correspond to partial state information. The co-design of observers and controllers is critical, since even in undisturbed cases, observers and controllers designed independently may not render the system safe. We propose two approaches to synthesize observer-controller interconnections. The first approach utilizes Input-to-State Stab…
Current cyber-physical systems (CPS) are expected to accomplish complex tasks. To achieve this goal, high performance, but unverified controllers (e.g. deep neural network, black-box controllers from third parties) are applied, which makes it very challenging to keep the overall CPS safe. By sandboxing these controllers, we are not only able to use them but also to enforce safety properties over the controlled physical systems at the same time. However, current available solutions for sandboxing controllers are just applicable to deterministic (a.k.a. non-stochastic) systems, possibly affected…
This paper proposes a Robust Safe Control Architecture (RSCA) for safe-decision making. The system to be controlled is a vehicle in the presence of bounded disturbances. The RSCA consists of two parts: a Supervisor MPC and a Controller MPC. Both the Supervisor and the Controller are tube MPCs (TMPCs). The Supervisor MPC provides a safety certificate for an operating controller and a backup control input in every step. After an unsafe action by the operating controller is predicted, the Controller MPC takes over the system. In this paper, a method for the computation of a terminal set is propos…
As we transition towards the deployment of data-driven controllers for black-box cyberphysical systems, complying with hard safety constraints becomes a primary concern. Two key aspects should be addressed when input-output data are corrupted by noise: how much uncertainty can one tolerate without compromising safety, and to what extent is the control performance affected? By focusing on finite-horizon constrained linear-quadratic problems, we provide an answer to these questions in terms of the model mismatch incurred during a preliminary identification phase. We propose a control design proc…
Data-based safe gain-scheduling controllers are presented for discrete-time linear parameter-varying systems (LPV) with polytopic models. First, $λ$-contractivity conditions are provided under which safety and stability of the LPV systems are unified through Minkowski functions of the safe sets. Then, to bypass the requirement to identify the system dynamics, a data-based representation of the closed-loop LPV system is provided to directly exploit collected data and construct a safe controller. It is shown that weaker data richness requirements are needed to directly learn a closed-loop safe c…
This paper presents an automated, model-free, data-driven method for the safe tuning of PID cascade controller gains based on Bayesian optimization. The optimization objective is composed of data-driven performance metrics and modeled using Gaussian processes. We further introduce a data-driven constraint that captures the stability requirements from system data. Numerical evaluation shows that the proposed approach outperforms relay feedback autotuning and quickly converges to the global optimum, thanks to a tailored stopping criterion. We demonstrate the performance of the method in simulati…
The objective of this research is to enable safety-critical systems to simultaneously learn and execute optimal control policies in a safe manner to achieve complex autonomy. Learning optimal policies via trial and error, i.e., traditional reinforcement learning, is difficult to implement in safety-critical systems, particularly when task restarts are unavailable. Safe model-based reinforcement learning techniques based on a barrier transformation have recently been developed to address this problem. However, these methods rely on full state feedback, limiting their usability in a real-world e…
