Cyber-physical system security, optimal control, and consensus protocols for nonlinear stochastic systems
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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 thesis, 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. Next, we build on this framework to develop an adaptive control algorithm for addressing security for a class of networked vehicles that comprise n human-driven vehicles sharing kinematic data and an autonomous vehicle in the aft of the vehicle formation receiving data from the preceding vehicles by wireless vehicle-to- vehicle communication devices. Speciﬁcally, we develop an adaptive controller for mitigating time-invariant, state-dependent adversarial sensor and actuator attacks while guaranteeing uniform ultimate boundedness of the closed-loop networked system. Next, we propose a novel adaptive control architecture for addressing security and safety in cyber-physical systems subject to exogenous disturbances. Speciﬁcally, we develop an adaptive controller for time-invariant, state-dependent adversarial sensor and actuator at- tacks in the face of stochastic exogenous disturbances modeled as Markov processes. We show that the proposed controller guarantees uniform ultimate boundedness of the closed- loop dynamical system in a mean-square sense. We further discuss the practicality of the proposed approach and apply the proposed framework to the lateral directional dynamics of an aircraft to illustrate the eﬃcacy of the adaptive control architecture. Then, we address networked multiagent systems subject to stochastic exogenous disturbances with compromised sensor and actuators. First, for a class of linear leader-follower multiagent systems, we develop a new structure of the neighborhood synchronization error for the control design protocol of each follower. The proposed control algorithm addresses time-varying multiplicative sensor attacks on the leader state measurements. In addition, the framework addresses time-varying multiplicative actuator attacks on the followers that do not have a communication link with the leader and additive actuator attacks on all fol- lower agents in the network. The proposed adaptive controller guarantees uniform ultimate boundedness of the state tracking error for each agent in a mean-square sense. Next, we extend the approach to develop a distributed robust adaptive control architecture that can foil malicious sensor and actuator attacks in the face of exogenous stochastic disturbances and follower agent model uncertainties. Speciﬁcally, for a class of linear multiagent uncertain systems with an undirected communication graph topology we develop a neighborhood synchronization error for the distributed robust adaptive control protocol design of each follower to account for actuator and sensor attacks on the leader state as well as all of the follower agents in the network. The proposed robust adaptive controller guarantees uniform ultimate boundedness in probability of the state tracking error for each follower agent in a mean-square sense. To show the eﬃcacy of our adaptive control architecture, we provide several numerical illustrative examples involving the lateral directional dynamics of an aircraft group of agents subject to state-dependent atmospheric drag disturbances, sensor and actuator attacks, and follower agent model uncertainties. Finally, the framework is extended to address output feedback architectures for leader-follower multiagent systems with stochastic disturbances and sensor and actuator attacks. We then turn our attention to the development of an energy-based static and dynamic control framework for stochastic port-controlled Hamiltonian systems. In particular, we obtain constructive suﬃcient conditions for stochastic feedback stabilization that provide a shaped energy function for the closed-loop system while preserving a Hamiltonian structure at the closed-loop level. In the dynamic control case, energy shaping is achieved by combining the physical energy of the plant and the emulated energy of the controller. Several numerical examples are presented that demonstrate the eﬃcacy of the proposed passivity-based stochastic control framework. Building on a stochastic optimal control framework, we derive stability margins for optimal and inverse optimal stochastic feedback regulators. Speciﬁcally, gain, sector, and disk margin guarantees are obtained for nonlinear stochastic dynamical systems controlled by nonlinear optimal and inverse optimal Hamilton-Jacobi-Bellman controllers that minimize a nonlinear-nonquadratic performance criterion with cross-weighting terms. Furthermore, using the newly developed notion of stochastic dissipativity we derive a return diﬀerence inequality to provide connections between stochastic dissipativity and optimality of non- linear controllers for stochastic dynamical systems. In particular, using extended Kalman- Yakubovich-Popov conditions characterizing stochastic dissipativity we show that our optimal feedback control law satisﬁes a return diﬀerence inequality predicated on the inﬁnitesimal generator of a controlled Markov diﬀusion process if and only if the controller is stochastically dissipative with respect to a speciﬁc quadratic supply rate. A constructive ﬁnite time stabilizing feedback control law is derived next for stochastic dynamical systems driven by Wiener processes based on the existence of a stochastic control Lyapunov function. In addition, we present necessary and suﬃcient conditions for continuity of such controllers. Moreover, using stochastic control Lyapunov functions, we construct a universal inverse optimal feedback control law for nonlinear stochastic dynamical systems that possesses guaranteed gain and sector margins. Finally, we focus on semistability and ﬁnite time semistability analysis and synthesis of stochastic dynamical systems having a continuum of equilibria. Stochastic semistability is the property whereby the solutions of a stochastic dynamical system almost surely converge to Lyapunov stable in probability equilibrium points determined by the system initial conditions. We extend the theories of semistability and ﬁnite-time semistability for deterministic dynamical systems to develop a rigorous framework for stochastic semistability and stochastic ﬁnite-time semistability. Speciﬁcally, Lyapunov and converse Lyapunov theorems for stochastic semistability are developed for dynamical systems driven by Markov diﬀusion processes. These results are then used to develop a general framework for designing semistable consensus protocols for dynamical networks in the face of stochastic communication uncertainty for achieving multiagent coordination tasks in ﬁnite time. The proposed controller architectures involve the exchange of generalized charge or energy state information between agents guaranteeing that the closed-loop dynamical network is stochastically semistable to an equipartitioned equilibrium representing a state of almost sure consensus consistent with basic thermodynamic principles.
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