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Safe control designs for robotic systems remain challenging because of the difficulties of explicitly solving optimal control with nonlinear dynamics perturbed by stochastic noise. However, recent technological advances in computing devices enable online optimization or sampling-based methods to solve control problems. For example, Control Barrier Functions (CBFs) have been proposed to numerically solve convex optimization problems that ensure the control input to stay in the safe set. Model Predictive Path Integral (MPPI) control uses forward sampling of stochastic differential equations to solve optimal control problems online. Both control algorithms are widely used for nonlinear systems because they avoid calculating the derivatives of the nonlinear dynamic functions. In this paper, we use Stochastic Control Barrier Functions (SCBFs) constraints to limit sample regions in the samplingbased algorithm, ensuring safety in a probabilistic sense and improving sample efficiency with a stochastic differential equation. We also show that our algorithm needs fewer samples than the original MPPI algorithm does by providing a sampling complexity analysis. 

Road condition is an important environmental factor for autonomous vehicle control. A dramatic change in the road condition from the nominal status is a source of uncertainty that can lead to a system failure. Once the vehicle encounters an uncertain environment, such as hitting an ice patch, it is too late to reduce the speed, and the vehicle can lose control. To cope with unforeseen uncertainties in advance, we study a proactive robust adaptive control architecture for autonomous vehicles' lane-keeping control problems. The data center generates a prior environmental uncertainty estimate by combining weather forecasts and measurements from anonymous vehicles through a spatio-temporal filter. The prior estimate contributes to designing a robust heading controller and nominal longitudinal velocity for proactive adaptation to each new condition. The control parameters are updated based on posterior information fusion with on-board measurements. 

Unmanned aerial vehicles (UAVs) suffer from sensor drifts in GPS denied environments, which can lead to potentially dangerous situations. To avoid intolerable sensor drifts in the presence of GPS spoofing attacks, we propose a safety constrained control framework that adapts the UAV at a path re-planning level to support resilient state estimation against GPS spoofing attacks. The attack detector is used to detect GPS spoofing attacks and provides a switching criterion between the robust control mode and emergency control mode. An attacker location tracker (ALT) is developed to track the attacker's location and estimate the spoofing device's output power by the unscented Kalman filter (UKF) with sliding window outputs. Using the estimates from ALT, we design an escape controller (ESC) based on the model predictive controller (MPC) such that the UAV escapes from the effective range of the spoofing device within the escape time. 

In this paper, an attack-resilient estimation algorithm is developed for linear discrete-time stochastic systems with inequality constraints on the actuator attacks and states. The proposed algorithm consists of the optimal estimation and information aggregation. The optimal estimation provides minimum-variance unbiased (MVU) estimates, and then they are projected onto the constrained space in the information aggregation step. It is shown that the estimation errors and their covariances from the proposed algorithm are less than those from the unconstrained algorithm. Moreover, we proved that the state estimation errors of the proposed estimation algorithm are practically exponentially stable. A simulation on mobile robots demonstrates the effectiveness of the proposed algorithm compared to an existing algorithm.