Recent technological advances in communications and computation have spurred a broad interest in control law architectures involving the monitoring, coordination, integration, and operation of sensing, computing, and communication components that tightly interact with the physical processes that they control. These systems are known as cyber-physical systems and due to their use of open computation and communication platform architectures, controlled cyber-physical systems are vulnerable to adversarial attacks. In this technical note, we propose a novel adaptive control architecture for addressing security and safety in cyber-physical systems. Specifically, we develop an adaptive controller that guarantees uniform ultimate boundedness of the closed-loop dynamical system in the face of adversarial sensor and actuator attacks that are time-varying and partial asymptotic stability when the sensor and actuator attacks are time-invariant. Finally, we provide a numerical example to illustrate the efficacy of the proposed adaptive control architecture.

The accuracy of sensor measurements is critical to the design of high-performance control systems since sensor uncertainties can significantly deteriorate achievable closed-loop dynamical system performance. Sensor uncertainty can arise due to low sensor quality, sensor failure or detrimental environmental conditions. For example, relatively cheap sensor suites are used for low-cost, small-scale unmanned vehicle applications that can result in inaccurate sensor measurements. Alternatively, sensor measurements can also be corrupted by malicious attacks if dynamical systems are controlled through large-scale, multilayered communication networks as is the case in cyber-physical systems. This paper presents several adaptive control architectures for stabilisation of linear dynamical systems in the presence of sensor uncertainty and sensor attacks. Specifically, we propose new and novel adaptive controllers for state-independent and state-dependent sensor uncertainties. In particular, we show that the proposed controllers guarantee asymptotic stability of the closed-loop dynamical system when the sensor uncertainties are time-invariant and uniform ultimate boundedness when the uncertainties are time-varying. We further discuss the practicality of the proposed approaches and provide several numerical examples to illustrate the efficacy of the proposed adaptive control architectures.

Research in adaptive control algorithms for safety-critical applications is primarily motivated by the fact that these algorithms have the capability to suppress the effects of adverse conditions resulting from exogenous disturbances, imperfect dynamical system modelling, degraded modes of operation, and changes in system dynamics. Although government and industry agree on the potential of these algorithms in providing safety and reducing vehicle development costs, a major issue is the inability to achieve a-priori, user-defined performance guarantees with adaptive control algorithms. In this paper, a new model reference adaptive control architecture for uncertain dynamical systems is presented to address disturbance rejection and uncertainty suppression. The proposed framework is predicated on a set-theoretic adaptive controller construction using generalised restricted potential functions.The key feature of this framework allows the system error bound between the state of an uncertain dynamical system and the state of a reference model, which captures a desired closed-loop system performance, to be less than a-priori, user-defined worst-case performance bound, and hence, it has the capability to enforce strict performance guarantees. Examples are provided to demonstrate the efficacy of the proposed set-theoretic model reference adaptive control architecture.

A smooth finite-time distributed control architecture is introduced and analyzed for the cooperative engagement problem. Using a time transformation method as well as Lyapunov stability theory, it is shown that the proposed architecture guarantees finite-time cooperative engagement in that the difference between the positions of each agent and a time-varying target, where this difference represents a dynamic equilibrium point, vanishes in a-priori given, user-defined finite-time. In addition, this finite-time convergence is achieved without dependence on the initial conditions of agents and in the presence of unknown but bounded velocity of the target. Specifically, we first time transformed the proposed smooth finite-time distributed control architecture into an infinite-time (that is, stretched) interval. This time transformation method is then allowed to utilize tools from standard Lyapunov stability theory in that we analyze convergence properties of this architecture and boundedness of local control signals of each agent in this infinite-time interval. While this note focuses on a particular problem in the context of multiagent systems, the proposed time transformation method and the analysis procedure can be used for many other problems, where a-priori given, user-defined finite-time convergence is necessary with smooth control laws.

Finite-time consensus has attracted significant research interest due to its wide applications in multiagent systems. Various results have been developed to enable multiagent systems to complete desired tasks in finite-time. However, most existing results in the literature can only ensure finite-time consensus without considering temporal constraints, where the time used to achieve consensus cannot be preset arbitrarily and is generally determined by the system initial conditions, prohibiting its application in time-sensitive tasks. Motivated to achieve consensus within a desired time frame, user-specified finite-time consensus is developed in the present work for a multiagent system to ensure consensus at a prespecified time instant. The interaction among agents (e.g., communication and information exchange) is modeled as a time-varying graph, where each edge is associated with a time-varying weight representing the time-varying interaction between neighboring agents. Consensus over such time-varying graph is then proven based on a time transformation and is guaranteed to be completed within a prespecified time frame. To demonstrate the developed framework, finite-time rendezvous of a multiagent system is considered as an example application, where agents with limited communication capabilities are desired to meet at a common location at a preset time instant with constraints on preserving global network connectivity. A numerical simulation is provided to demonstrate the efficiency of the developed result.

One of the fundamental problems in model reference adaptive control design is the ability of the controlled system to achieve not only stability but also a user-defined performance in the presence of exogenous disturbances and system uncertainties. To this end, we recently proposed a set-theoretic model reference adaptive control framework, which guarantees the norm of the system error to be less than a user-defined constant performance bound. The contribution of this paper is to generalise the set-theoretic model reference adaptive control framework for enforcing user-defined time-varying performance bounds on the system error, which gives the control designer a flexibility to control the closed-loop system performance as desired on different time intervals (e.g. transient time interval and steady-state time interval). Two adaptive command following control architectures are proposed and their stability and performance properties are rigorously established using system-theoretic methods.