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Sensors are the means by which cyber-physical systems perceive their own state as well as the state of their environment. Any attack on sensor measurements, or their transmission, has the potential to lead to catastrophic consequences since control actions would be based on an incorrect state estimate. In this chapter, we introduce the secure state estimation problem, discuss under which conditions it can be solved, and review existing algorithms.

In this paper, we consider the problem of automatically designing a Rectified Linear Unit (ReLU) Neural Network (NN) architecture (number of layers and number of neurons per layer) with the guarantee that it is sufficiently parametrized to control a nonlinear system. Whereas current state-of-the-art techniques are based on hand-picked architectures or heuristic-based search to find such NN architectures, our approach exploits a given model of the system to design an architecture; as a result, we provide a guarantee that the resulting NN architecture is sufficient to implement a controller that satisfies an achievable specification. Our approach exploits two basic ideas. First, we assume that the system can be controlled by a Lipschitz-continuous state-feedback controller that is unknown but whose Lipschitz constant is upper-bounded by a known constant; then using this assumption, we bound the number of affine functions needed to construct a Continuous Piecewise Affine (CPWA) function that can approximate the unknown Lipschitz-continuous controller. Second, we utilize the authors’ recent results on the Two-Level Lattice (TLL) NN architecture, a novel NN architecture that was shown to be parameterized directly by the number of affine functions that comprise the CPWA function it realizes. We also evaluate our method by designing a NN architecture to control an inverted pendulum.

We propose an efficient multi-robot motion planning algorithm for missions captured by linear temporal logic (LTL) specifications, in the presence of bounded disturbances and denial-of-service (DoS) attacks against the communication between robots and base stations. Given an LTL formula Ψ, our goal is to construct robot trajectories, and associated control strategies, to satisfy Ψ and continuously establish communication paths between robots and base stations despite the DoS attacks and the disturbances on the robot states. Our approach combines and extends results from robust control and efficient motion planning via satisfiability modulo convex programming (SMC). We first compute a feedback controller that rejects the disturbance together with a perturbation of the DoS-free workspace that accounts for the worst-case disturbance scenario. On the perturbed workspace, we formulate the planning problem as a feasibility problem over Boolean and convex constraints, respectively capturing the DoS-resilient mission constraints and the constraints on the nominal, disturbance-free, robot dynamics. Numerical results show the effectiveness of our algorithm in providing DoS-resilient plans that are robust to disturbances and support the execution of complex missions.

This paper discusses the problem of reconstructing the state of a linear time invariant system when some of its actuators and sensors are compromised by an adversarial agent. In the model considered in this paper, the adversarial agent attacks an input (output) by manipulating its value arbitrarily, i.e., we impose no constraints (statistical or otherwise) on how control commands (sensor measurements) are changed by the adversary other than a bound on the number of attacked actuators and sensors In the first part of this paper, we introduce the notion of sparse strong observability and we show that is a necessary and sufficient condition for correctly reconstructing the state despite the considered attacks. In the second half of this work, we propose an observer to harness the complexity of this intrinsically combinatorial problem, by leveraging satisfiability modulo theory solving. Numerical simulations illustrate the effectiveness and scalability of our observer.

In this paper, we consider the problem of automatically designing a Rectified Linear Unit (ReLU) Neural Network (NN) architecture that is sufficient to implement the optimal Model Predictive Control (MPC) strategy for an LTI system with quadratic cost. Specifically, we propose AReN, an algorithm to generate Assured ReLU Architectures. AReN takes as input an LTI system with quadratic cost specification, and outputs a ReLU NN architecture with the assurance that there exist network weights that exactly implement the associated MPC controller. AReN thus offers new insight into the design of ReLU NN architectures for the control of LTI systems: instead of training a heuristically chosen NN architecture on data -- or iterating over many architectures until a suitable one is found -- AReN can suggest an adequate NN architecture before training begins. While several previous works were inspired by the fact that both ReLU NN controllers and optimal MPC controller are both Continuous, Piecewise-Linear (CPWL) functions, exploiting this similarity to design NN architectures with correctness guarantees has remained elusive. AReN achieves this using two novel features. First, we reinterpret a recent result about the implementation of CPWL functions via ReLU NNs to show that a CPWL function may be implemented by a ReLU architecture that is determined by the number of distinct affine regions in the function. Second, we show that we can efficiently over-approximate the number of affine regions in the optimal MPC controller without solving the MPC problem exactly. Together, these results connect the MPC problem to a ReLU NN implementation without explicitly solving the MPC and directly translates this feature to a ReLU NN architecture that comes with the assurance that it can implement the MPC controller. We show through numerical results the effectiveness of AReN in designing an NN architecture.

The recent trends in the automotive industry towards autonomous vehicles bring the problem of pedestrian avoidance to the forefront of a long list of safety concerns. In this paper we propose a closed-form solution to this problem by explicitly computing closed-form expressions for subsets of the state space where an autonomous vehicle is guaranteed to avoid collisions with a pedestrian. These sets, being controlled invariant, immediately lead to control laws for pedestrian avoidance.

This paper presents an online, dynamic, and distributed message scheduling of communication packets over the controller area network (CAN) bus. Using online, dynamic, and distributed scheduling of messages, one can obtain better temporal characteristics for networked embedded control systems. The scheduling algorithm is implemented as a hardware unit which is augmented to the communication controller on all of the communicating nodes in the system. This insures minimum change in the current platforms used in CAN-based control applications like those found heavily in automotive and aerospace applications. We provide a number of experiments held over a physical CAN bus for controlling an automotive active suspension system and showing the effect of the proposed scheduling implementation on the quality of the control loop.

Safety critical automotive systems require tight real-time constraints. This letter presents a case study for embedded implementation of a model predictive controller (MPC) used to control an automotive active suspension system. It proposes a special purpose coprocessor for solving the online mathematical optimization needed by the controller, while maintaining real-time constraints imposed by system dynamics. Mathematical formulation for the optimum usage of hardware resources is provided and verified for its applicability on a proposed platform.

We consider the problem of designing a Luenberger-like observer for linear systems whose sensor measurements are corrupted by a malicious attacker. The attacker capabilities are limited in the sense that only a subset of all the sensors can be attacked although this subset is unknown. This leads to the problem of reconstructing the system state when the measurements are corrupted by sparse noise and we propose an observer that recursively updates the state estimate as new measurements become available. We show that by utilizing event-triggered techniques, the proposed observer is computationally more efficient than previously reported solutions to the secure state reconstruction problem.

Robustness is the property that a system only exhibits small deviations from the nominal behavior upon the occurrence of small disturbances. While the importance of robustness in engineering design is well accepted, it is less clear how to verify and design discrete systems for robustness. We present a theory of input-output robustness for discrete systems inspired by existing notions of input-output stability (IO-stability) in continuous control theory. We show that IO-stability captures two intuitive goals of robustness: bounded disturbances lead to bounded deviations from nominal behavior, and the effect of a sporadic disturbance disappears in finitely many steps. We show that existing notions of robustness for discrete systems do not have these two properties. For systems modeled as finite-state transducers, we show that IO-stability can be verified and the synthesis problem can be solved in polynomial time. We illustrate our theory using a reference broadcast synchronization protocol for wireless networks.

This paper applies the generalized predictive control (GPC) to a class of active suspension automotive systems. It introduces both physical and digital necessary models for simulation and control law design. Experimental environment is designed in order to get real time identification and control verification results. Real time CAN-bus Networked Embedded Control System (NECS) represents the backbone of this environment. Real-Time experimental results show the efficiency of the proposed tuning of the GPC controller in order to get a ride-comfort with an acceptable level of exerted energy.