The Value Iteration Network (VIN) is an end-to-end differentiable neural network architecture for planning. It exhibits strong generalization to unseen domains by incorporating a differentiable planning module that operates on a latent Markov Decision Process (MDP). However, VINs struggle to scale to long-term and large-scale planning tasks, such as navigating a $100\times 100$ maze---a task that typically requires thousands of planning steps to solve. We observe that this deficiency is due to two issues: the representation capacity of the latent MDP and the planning module's depth. We address these by augmenting the latent MDP with a dynamic transition kernel, dramatically improving its representational capacity, and, to mitigate the vanishing gradient problem, introduce an "adaptive highway loss" that constructs skip connections to improve gradient flow. We evaluate our method on 2D/3D maze navigation environments, continuous control, and the real-world Lunar rover navigation task. We find that our new method, named Dynamic Transition VIN (DT-VIN), scales to 5000 layers and solves challenging versions of the above tasks. Altogether, we believe that DT-VIN represents a concrete step forward in performing long-term large-scale planning in complex environments.

Reinforcement learning (RL) with delays is challenging as sensory perceptions lag behind the actual events: the RL agent needs to estimate the real state of its environment based on past observations. State-of-the-art (SOTA) methods typically employ recursive, step-by-step forecasting of states. This can cause the accumulation of compounding errors. To tackle this problem, our novel belief estimation method, named Directly Forecasting Belief Transformer (DFBT), directly forecasts states from observations without incrementally estimating intermediate states step-by-step. We theoretically demonstrate that DFBT greatly reduces compounding errors of existing recursively forecasting methods, yielding stronger performance guarantees. In experiments with D4RL offline datasets, DFBT reduces compounding errors with remarkable prediction accuracy. DFBT’s capability to forecast state sequences also facilitates multi-step bootstrapping, thus greatly improving learning efficiency. On the MuJoCo benchmark, our DFBT-based method substantially outperforms SOTA baselines. Code is available at https://github.com/QingyuanWuNothing/DFBT.

We present REGLO, a novel methodology for repairing pretrained neural networks to satisfy global robustness and individual fairness properties. A neural network is said to be globally robust with respect to a given input region if and only if all the input points in the region are locally robust. This notion of global robustness also captures the notion of individual fairness as a special case. We prove that any counterexample to a global robustness property must exhibit a corresponding large gradient. For ReLU networks, this result allows us to efficiently identify the linear regions that violate a given global robustness property. By formulating and solving a suitable robust convex optimization problem, REGLO then computes a minimal weight change that will provably repair these violating linear regions.

Abstract Autonomous systems are increasingly implemented using end-to-end learning-based controllers. Such controllers make decisions that are executed on the real system, with images as one of the primary sensing modalities. Deep neural networks form a fundamental building block of such controllers. Unfortunately, the existing neural-network verification tools do not scale to inputs with thousands of dimensions—especially when the individual inputs (such as pixels) are devoid of clear physical meaning. This paper takes a step towards connecting exhaustive closed-loop verification with high-dimensional controllers. Our key insight is that the behavior of a high-dimensional vision-based controller can be approximated with several low-dimensional controllers. To balance the approximation accuracy and verifiability of our low-dimensional controllers, we leverage the latest verification-aware knowledge distillation. Then, we inflate low-dimensional reachability results with statistical approximation errors, yielding a high-confidence reachability guarantee for the high-dimensional controller. We investigate two inflation techniques—based on trajectories and control actions—both of which show convincing performance in three OpenAI gym benchmarks.

Reinforcement learning (RL) is challenging in the common case of delays between events and their sensory perceptions. State-of-the-art (SOTA) state augmentation techniques either suffer from state space explosion or performance degeneration in stochastic environments. To address these challenges, we present a novel *Auxiliary-Delayed Reinforcement Learning (AD-RL)* method that leverages auxiliary tasks involving short delays to accelerate RL with long delays, without compromising performance in stochastic environments. Specifically, AD-RL learns a value function for short delays and uses bootstrapping and policy improvement techniques to adjust it for long delays. We theoretically show that this can greatly reduce the sample complexity. On deterministic and stochastic benchmarks, our method significantly outperforms the SOTAs in both sample efficiency and policy performance. Code is available at https://github.com/QingyuanWuNothing/AD-RL.

Trajectory generation and trajectory prediction are two critical tasks in autonomous driving, which generate various trajectories for testing during development and predict the trajectories of surrounding vehicles during operation, respectively. In recent years, emerging data-driven deep learning-based methods have shown great promise for these two tasks in learning various traffic scenarios and improving average performance without assuming physical models. However, it remains a challenging problem for these methods to ensure that the generated/predicted trajectories are physically realistic. This challenge arises because learning-based approaches often function as opaque black boxes and do not adhere to physical laws. Conversely, existing model-based methods provide physically feasible results but are constrained by predefined model structures, limiting their capabilities to address complex scenarios. To address the limitations of these two types of approaches, we propose a new method that integrates kinematic knowledge into neural stochastic differential equations (SDE) and designs a variational autoencoder based on this latent kinematics-aware SDE (LK-SDE) to generate vehicle motions. Experimental results demonstrate that our method significantly outperforms both model-based and learning-based baselines in producing physically realistic and precisely controllable vehicle trajectories. Additionally, it performs well in predicting unobservable physical variables in the latent space.

In environments with delayed observation, state augmentation by including actions within the delay window is adopted to retrieve Markovian property to enable reinforcement learning (RL). Whereas, state-of-the-art (SOTA) RL techniques with Temporal-Difference (TD) learning frameworks commonly suffer from learning inefficiency, due to the significant expansion of the augmented state space with the delay. To improve the learning efficiency without sacrificing performance, this work novelly introduces Variational Delayed Policy Optimization (VDPO), reforming delayed RL as a variational inference problem. This problem is further modelled as a two-step iterative optimization problem, where the first step is TD learning in the delay-free environment with a small state space, and the second step is behaviour cloning which can be addressed much more efficiently than TD learning. We not only provide a theoretical analysis of VDPO in terms of sample complexity and performance, but also empirically demonstrate that VDPO can achieve consistent performance with SOTA methods, with a significant enhancement of sample efficiency (approximately 50\% less amount of samples) in the MuJoCo benchmark.

Neural networks (NNs) playing the role of controllers have demonstrated impressive empirical performance on challenging control problems. However, the potential adoption of NN controllers in real-life applications has been significantly impeded by the growing concerns over the safety of these NN-controlled systems (NNCSs). In this work, we present POLAR-Express, an efficient and precise formal reachability analysis tool for verifying the safety of NNCSs. POLAR-Express uses Taylor model (TM) arithmetic to propagate TMs layer-by-layer across an NN to compute an overapproximation of the NN. It can be applied to analyze any feedforward NNs with continuous activation functions, such as ReLU, Sigmoid, and Tanh activation functions that cover the common benchmarks for NNCS reachability analysis. Compared with its earlier prototype POLAR, we develop a novel approach in POLAR-Express to propagate TMs more efficiently and precisely across ReLU activation functions, and provide parallel computation support for TM propagation, thus significantly improving the efficiency and scalability. Across the comparison with six other state-of-the-art tools on a diverse set of common benchmarks, POLAR-Express achieves the best verification efficiency and tightness in the reachable set analysis. POLAR-Express is publicly available athttps://github.com/ChaoHuang2018/POLAR_Tool.

Connected and autonomous vehicles (CAVs) can realize many revolutionary applications, but it is expected to have mixed-traffic including CAVs and human-driving vehicles (HVs) together for decades. In this paper, we target the problem of mixed-traffic intersection management and schedule CAVs to control the subsequent HVs. We develop a dynamic programming approach and a mixed integer linear programming (MILP) formulation to optimally solve the problems with the corresponding intersection models. We then propose an MILP-based approach which is more efficient and real-time-applicable than solving the optimal MILP formulation, while keeping good solution quality as well as outperforming the first-come-first-served (FCFS) approach. Experimental results and SUMO simulation indicate that controlling CAVs by our approaches is effective to regulate mixed-traffic even if the CAV penetration rate is low, which brings incentive to early adoption of CAVs.

Neural-network-based (NN-based) planners have been increasingly used to enhance the performance of planning for autonomous vehicles. However, it is often difficult for NN-based planners to balance efficiency and safety in complicated scenarios, especially under real-world communication disturbance. To tackle this challenge, we present a safety-guaranteed framework for NN-based planners in connected vehicle environments with communication disturbance. Given any NN-based planner with no safety-guarantee, the framework generates a robust compound planner embedding the NN-based planner to ensure overall system safety. Moreover, with the aid of an information filter for imperfect communication and an aggressive approach for the estimation of the unsafe set, the compound planner could achieve similar or better efficiency than the given NN-based planner. A comprehensive case study of unprotected left turn and extensive simulations demonstrate the effectiveness of our framework.

It is quite challenging to ensure the safety of reinforcement learning (RL) agents in an unknown and stochastic environment under hard constraints that require the system state not to reach certain specified unsafe regions. Many popular safe RL methods such as those based on the Constrained Markov Decision Process (CMDP) paradigm formulate safety violations in a cost function and try to constrain the expectation of cumulative cost under a threshold. However, it is often difficult to effectively capture and enforce hard reachability-based safety constraints indirectly with such constraints on safety violation cost. In this work, we leverage the notion of barrier function to explicitly encode the hard safety chance constraints, and given that the environment is unknown, relax them to our design of *generative-model-based soft barrier functions*. Based on such soft barriers, we propose a novel safe RL approach with bi-level optimization that can jointly learn the unknown environment and optimize the control policy, while effectively avoiding the unsafe region with safety probability optimization. Experiments on a set of examples demonstrate that our approach can effectively enforce hard safety chance constraints and significantly outperform CMDP-based baseline methods in system safe rates measured via simulations.

The robustness of deep neural networks in safety-critical systems has received significant interest recently, which measures how sensitive the model output is under input perturbations. While most previous works focused on the local robustness property, the studies of the global robustness property, i.e., the robustness in the entire input space, are still lacking. In this work, we formulate the global robustness certification problem for ReLU neural networks and present an efficient approach to address it. Our approach includes a novel interleaving twin-network encoding scheme and an over-approximation algorithm leveraging relaxation and refinement techniques. Its timing efficiency and effectiveness are evaluated and compared with other state-of-the-art global robustness certification methods, and demonstrated via case studies on practical applications.

A weakly-hard fault model can be captured by an (m,k) constraint, where 0≤ m ≤ k , meaning that there are at most m bad events (faults) among any k consecutive events. In this article, we use a weakly-hard fault model to constrain the occurrences of faults in system inputs. We develop approaches to verify properties for all possible values of (m,k) , where k is smaller than or equal to a given K , in an exact and efficient manner. By verifying all possible values of (m,k) , we define weakly-hard requirements for the system environment and design a runtime monitor based on counting the number of faults in system inputs. If the system environment satisfies the weakly-hard requirements, then the satisfaction of desired properties is guaranteed; otherwise, the runtime monitor can notify the system to switch to a safe mode. This is especially essential for cyber-physical systems that need to provide guarantees with limited resources and the existence of faults. Experimental results with discrete second-order control, network routing, vehicle following, and lane changing demonstrate the generality and the efficiency of the proposed approaches.

In the current control design of safety-critical cyber-physical systems, formal verification techniques are typically applied after the controller is designed to evaluate whether the required properties (e.g., safety) are satisfied. However, due to the increasing system complexity and the fundamental hardness of designing a controller with formal guarantees, such an open-loop process of design-then-verify often results in many iterations and fails to provide the necessary guarantees. In this paper, we propose a correct-by-construction control learning framework that integrates the verification into the control design process in a closed-loop manner, i.e., design-while-verify. Specifically, we leverage the verification results (computed reachable set of the system state) to construct feedback metrics for control learning, which measure how likely the current design of control parameters can meet the required reach-avoid property for safety and goal-reaching. We formulate an optimization problem based on such metrics for tuning the controller parameters, and develop an approximated gradient descent algorithm with a difference method to solve the optimization problem and learn the controller. The learned controller is formally guaranteed to meet the required reach-avoid property. By treating verifiability as a first-class objective and effectively leveraging the verification results during the control learning process, our approach can significantly improve the chance of finding a control design with formal property guarantees, demonstrated in a set of experiments that use model-based or neural network based controllers.

The robustness of deep neural networks has received significant interest recently, especially when being deployed in safety-critical systems, as it is important to analyze how sensitive the model output is under input perturbations. While most previous works focused on the local robustness property around an input sample, the studies of the global robustness property, which bounds the maximum output change under perturbations over the entire input space, are still lacking. In this work, we formulate the global robustness certification for neural networks with ReLU activation functions as a mixed-integer linear programming (MILP) problem, and present an efficient approach to address it. Our approach includes a novel interleaving twin-network encoding scheme, where two copies of the neural network are encoded side-by-side with extra interleaving dependencies added between them, and an over-approximation algorithm leveraging relaxation and refinement techniques to reduce complexity. Experiments demonstrate the timing efficiency of our work when compared with previous global robustness certification methods and the tightness of our over-approximation. A case study of closed-loop control safety verification is conducted, and demonstrates the importance and practicality of our approach for certifying the global robustness of neural networks in safety-critical systems.

Future autonomous systems will employ sophisticated machine learning techniques for the sensing and perception of the surroundings and the making corresponding decisions for planning, control, and other actions. They often operate in highly dynamic, uncertain and challenging environment, and need to meet stringent timing, resource, and mission requirements. In particular, it is critical and yet very challenging to ensure the safety of these autonomous systems, given the uncertainties of the system inputs, the constant disturbances on the system operations, and the lack of analyzability for many machine learning methods (particularly those based on neural networks). In this paper, we will discuss some of these challenges, and present our work in developing automated, quantitative, and formalized methods and tools for ensuring the safety of autonomous systems in their design and during their runtime adaptation. We argue that it is essential to take a holistic approach in addressing system safety and other safety-related properties, vertically across the functional, software, and hardware layers, and horizontally across the autonomy pipeline of sensing, perception, planning, and control modules. This approach could be further extended from a single autonomous system to a multi-agent system where multiple autonomous agents perform tasks in a collaborative manner. We will use connected and autonomous vehicles (CAVs) as the main application domain to illustrate the importance of such holistic approach and show our initial efforts in this direction.

Neural networks are being increasingly applied to control and decision making for learning-enabled cyber-physical systems (LE-CPSs). They have shown promising performance without requiring the development of complex physical models; however, their adoption is significantly hindered by the concerns on their safety, robustness, and efficiency. In this work, we propose COCKTAIL, a novel design framework that automatically learns a neural network based controller from multiple existing control methods (experts) that could be either model-based or neural network based. In particular, COCKTAIL first performs reinforcement learning to learn an optimal system-level adaptive mixing strategy that incorporates the underlying experts with dynamically-assigned weights, and then conducts a teacher-student distillation with probabilistic adversarial training and regularization to synthesize a student neural network controller with improved control robustness (measured by a safe control rate metric with respect to adversarial attacks or measurement noises), control energy efficiency, and verifiability (measured by the computation time for verification). Experiments on three non-linear systems demonstrate significant advantages of our approach on these properties over various baseline methods.

Future autonomous systems will rely on advanced sensors and deep neural networks for perceiving the environment, and then utilize the perceived information for system planning, control, adaptation, and general decision making. However, due to the inherent uncertainties from the dynamic environment and the lack of methodologies for predicting neural network behavior, the perception modules in autonomous systems often could not provide deterministic guarantees and may sometimes lead the system into unsafe states (e.g., as evident by a number of high-profile accidents with experimental autonomous vehicles). This has significantly impeded the broader application of machine learning techniques, particularly those based on deep neural networks, in safety-critical systems. In this paper, we will discuss these challenges, define open research problems, and introduce our recent work in developing formal methods for quantitatively bounding the output uncertainty of perception neural networks with respect to input perturbations, and leveraging such bounds to formally ensure the safety of system control. Unlike most existing works that only focus on either the perception module or the control module, our approach provides a holistic end-to-end framework that bounds the perception uncertainty and addresses its impact on control.

During the operation of many real-time safety-critical systems, there are often strong needs for adapting to a dynamic environment or evolving mission objectives, e.g., increasing sampling and control frequencies of some functions to improve their performance under certain situations. However, a system's ability to adapt is often limited by tight resource constraints and rigid periodic execution requirements. In this work, we present a cross-layer approach to improve system adaptability by allowing proactive skipping of task executions, so that the resources can be either saved directly or re-allocated to other tasks for their performance improvement. Our approach includes three novel elements: (1) formal methods for deriving the feasible skipping choices of control tasks with safety guarantees at the functional layer, (2) a schedulability analysis method for assessing system feasibility at the architectural layer under allowed task job skippings, and (3) a runtime adaptation algorithm that efficiently explores job skipping choices and task priorities for meeting system adaptation requirements while ensuring system safety and timing correctness. Experiments demonstrate the effectiveness of our approach in meeting system adaptation needs.

We introduce SAW, a tool for safety analysis of weakly-hard systems, in which traditional hard timing constraints are relaxed to allow bounded deadline misses for improving design flexibility and runtime resiliency. Safety verification is a key issue for weakly-hard systems, as it ensures system safety under allowed deadline misses. Previous works are either for linear systems only, or limited to a certain type of nonlinear systems (e.g., systems that satisfy exponential stability and Lipschitz continuity of the system dynamics). In this work, we propose a new technique for infinite-time safety verification of general nonlinear weakly-hard systems. Our approach first discretizes the safe state set into grids and constructs a directed graph, where nodes represent the grids and edges represent the reachability relation. Based on graph theory and dynamic programming, our approach can effectively find the safe initial set (consisting of a set of grids), from which the system can be proven safe under given weakly-hard constraints. Experimental results demonstrate the effectiveness of our approach, when compared with the state-of-the-art. An open source implementation of our tool is available at https://github.com/551100kk/SAW . The virtual machine where the tool is ready to run can be found at https://www.csie.ntu.edu.tw/~r08922054/SAW.ova .

Control schemes for autonomous systems are often designed in a way that anticipates the worst case in any situation. At runtime, however, there could exist opportunities to leverage the characteristics of specific environment and operation context for more efficient control. In this work, we develop an online intermittent-control framework that combines formal verification with model-based optimization and deep reinforcement learning to opportunistically skip certain control computation and actuation to save actuation energy and computational resources without compromising system safety. Experiments on an adaptive cruise control system demonstrate that our approach can achieve significant energy and computation savings.

Future autonomous systems will employ complex sensing, computation, and communication components for their perception, planning, control, and coordination, and could operate in highly dynamic and uncertain environment with safety and security assurance. To realize this vision, we have to better understand and address the challenges from the "unknowns" - the unexpected disturbances from component faults, environmental interference, and malicious attacks, as well as the inherent uncertainties in system inputs, model inaccuracies, and machine learning techniques (particularly those based on neural networks). In this work, we will discuss these challenges, propose our approaches in addressing them, and present some of the initial results. In particular, we will introduce a cross-layer framework for modeling and mitigating execution uncertainties (e.g., timing violations, soft errors) with weakly-hard paradigm, quantitative and formal methods for ensuring safe and time-predictable application of neural networks in both perception and decision making, and safety-assured adaptation strategies in dynamic environment.

Neural networks have been increasingly applied to 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 Pol's oscillator demonstrate the effectiveness of our approach on energy saving and safety enhancement.

In this paper, we revisit model predictive control (MPC) for the classical wheeled mobile robot (WMR) navigation problem. We prove that the reachable set based hierarchical MPC (HMPC), a state-of-the-art MPC, cannot handle WMR navigation in theory due to the non-existence of non-trivial linear system with an under-approximate reachable set of WMR. Nevertheless, we propose a virtual linear leader guided MPC (VLL-MPC) to enable HMPC structure. Different from current HMPCs, we use a virtual linear system with an under-approximate path set rather than the traditional trace set to guide the WMR. We provide a valid construction of the virtual linear leader. We prove the stability of VLL-MPC, and discuss its complexity. In the experiment, we demonstrate the advantage of VLL-MPC empirically by comparing it with NMPC, LMPC and anytime RRT* in several scenarios.

In this article, we present a layer-wise refinement method for neural network output range analysis. While approaches such as nonlinear programming (NLP) can directly model the high nonlinearity brought by neural networks in output range analysis, they are known to be difficult to solve in general. We propose to use a convex polygonal relaxation (overapproximation) of the activation functions to cope with the nonlinearity. This allows us to encode the relaxed problem into a mixedinteger linear program (MILP), and control the tightness of the relaxation by adjusting the number of segments in the polygon. Starting with a segment number of 1 for each neuron, which coincides with a linear programming (LP) relaxation, our approach selects neurons layer by layer to iteratively refine this relaxation. To tackle the increase of the number of integer variables with tighter refinement, we bridge the propagation-based method and the programming-based method by dividing and sliding the layerwise constraints. Specifically, given a sliding number s, for the neurons in layer l, we only encode the constraints of the layers between l - s and l. We show that our overall framework is sound and provides a valid overapproximation. Experiments on deep neural networks demonstrate significant improvement on output range analysis precision using our approach compared to the state-of-the-art.

Weakly-hard systems are real-time systems that can tolerate occasional deadline misses in a bounded manner. Compared with traditional systems with hard deadline constraints, they provide more scheduling flexibility, and thus expand the design space for system configuration and reconfiguration. A key question for such a system is precisely to what degree it can tolerate deadline misses while still meeting its functional requirements. In this paper, we provide a formal treatment to the verification problem of a general class of weakly-hard systems. We discuss relaxation and over-approximation techniques for managing the complexity of reachability analysis, and develop algorithms based upon these for verifying the safety of weakly-hard systems. Experiments demonstrate the effectiveness of our approach in understanding the impact of and guiding the selection among different weakly-hard constraints.

Neural networks are widely used in many applications ranging from classification to control. While these networks are composed of simple arithmetic operations, they are challenging to formally verify for properties such as reachability due to the presence of nonlinear activation functions. In this paper, we make the observation that Lipschitz continuity of a neural network not only can play a major role in the construction of reachable sets for neural-network controlled systems but also can be systematically controlled during training of the neural network. We build on this observation to develop a novel verification-aware knowledge distillation framework that transfers the knowledge of a trained network to a new and easier-to-verify network. Experimental results show that our method can substantially improve reachability analysis of neural-network controlled systems for several state-of-the-art tools.

Applying neural networks as controllers in dynamical systems has shown great promises. However, it is critical yet challenging to verify the safety of such control systems with neural-network controllers in the loop. Previous methods for verifying neural network controlled systems are limited to a few specific activation functions. In this work, we propose a new reachability analysis approach based on Bernstein polynomials that can verify neural-network controlled systems with a more general form of activation functions, i.e., as long as they ensure that the neural networks are Lipschitz continuous. Specifically, we consider abstracting feedforward neural networks with Bernstein polynomials for a small subset of inputs. To quantify the error introduced by abstraction, we provide both theoretical error bound estimation based on the theory of Bernstein polynomials and more practical sampling based error bound estimation, following a tight Lipschitz constant estimation approach based on forward reachability analysis. Compared with previous methods, our approach addresses a much broader set of neural networks, including heterogeneous neural networks that contain multiple types of activation functions. Experiment results on a variety of benchmarks show the effectiveness of our approach.

With rapid advancement of advanced driver assistance systems (ADAS) and autonomous driving functions, modern vehicles have become ever more intelligent than before. Sophisticated machine learning techniques have being developed for vehicle perception, planning and control. However, this also brings significant challenges to the design, implementation and validation of automotive systems, stemming from the fast-growing functional complexity, the adoption of advanced architectural components such as multicore CPUs and GPUs, the dynamic and uncertain physical environment, and the stringent requirements on various system metrics such as safety, security, reliability, performance, fault tolerance, extensibility, and cost. To address these challenges, new design methodologies, algorithms and tools are greatly needed. This paper will discuss the challenges in designing next-generation connected and autonomous vehicles, and the need of design automation techniques to tackle them.

Multi-robot navigation control in the absence of reference trajectory is rather challenging as it is expected to ensure stability and feasibility while still offer fast computation on control decisions. The intrinsic high complexity of switched linear dynamical robots makes the problem even more challenging. In this paper, we propose a novel HMPC based method to address the navigation problem of multiple robots with switched linear dynamics. We develop a new technique to compute the reachable sets of switched linear systems and use them to enable the parallel computation of control parameters. We present theoretical results on stability, feasibility and complexity of the proposed approach, and demonstrate its empirical advance in performance against other approaches.

The problem of probabilistic safety verification of stochastic hybrid systems is to check whether the probability that a given system will reach an unsafe region from certain initial states can be bounded by some given probability threshold. The paper considers stochastic hybrid systems where the behavior is governed by polynomial equalities and inequalities, as for usual hybrid systems, but the initial states follow some stochastic distributions. It proposes a new barrier certificate based method for probabilistic safety verification which guarantees the absolute safety in a infinite time horizon that is beyond the reach of existing techniques using either statistical model checking or probabilistic reachable set computation. It also gives a novel computational approach, by building and solving a constrained optimization problem coming from verification conditions of barrier certificates, to compute the lower bound on safety probabilities which can be compared with the given threshold. Experimental evidence is provided demonstrating the applicability of our approach on several benchmarks.