Preventive Secure Control Strategies For Constrained Dynamical Systems

An adversary of a control system is a type of individual who tries to affect the normal operations of the system.The goal of secure control is to maintain normal operations of the control system in the presence of interferences from the adversary.Modern control systems have functionalities such as networking and information processing,thus an adversary could attack the physical system indirectly through the cyber-layer with a certain degree of stealthiness.To guarantee this stealthiness,an adversary first need to obtain data transmitted between sensor,controller and actuator through eavesdropping attacks,in order to have some knowledge about the system dynamics.The purpose of preventive secure control is to prevent effective eavesdropping attacks from the adversary,in an effort to reduce the risk of subsequent attacks.Certain mobile cyber-physical systems are limited in terms of position,velocity and energy supplies,thus can be viewed as a type of constrained dynamical system.For this type of system,an adversary could initiate eavesdropping attacks on the controller to obtain parameters related to the control law.The objective of the adversary is to take control of the system,and thus to exploit the mobility of the system for the personal usage of the adversary.To prevent an adversary from taking over this type of control system,data related to control parameters within the controller also needs to be protected.Therefore,the purpose of preventive secure control for constrained systems is to keep an adversary from taking over the control system.The requirement for this type of control strategy is that the controller input cannot be the system state,the controller output cannot be the control input,and the controller should not contain data related to the control law.The goal is to guarantee stability of the closed-loop system,while guaranteeing that an adversary cannot infer the system state,control input and parameters related to the control law from the knowledge of the controller input and output,as well as internal data of the controller.In the current research on secure control strategies for preventing eavesdropping attacks,the ones based on homomorphic encryption require large computations when performing arithmetics with long integers.The ones based on differential privacy need to add noise to the control input,and if the magnitude of the noise is not chosen properly,system constraints may be violated and stability of the closed-loop system may be affected.The main idea of this thesis when approaching the preventive secure control problem is to reasonably exploit the presence of system constraints and also consider the necessity of performing control calculations at each sampling instant.In the following the main research of this thesis is briefly introduced.A secure control strategy is proposed that is suitable for explicit model predictive control problems.For a class of state and input constrained linear system,utilizing the piecewise affine property of a feedback control law obtained with the robust explicit model predictive control technique,the design of the strategy is based on integer tokens mapping and poly topic affine transforms.This control strategy guarantees semantic security of the state and control information.A secure control strategy is proposed that is suitable for implicit model predictive control problems.The proposed control strategy constructs a Voronoi partition sequence within the system state feasible set,and tokenized polytopic affine transforms have been applied to the Voronoi polytopes in the sequence.This strategy reformulates the original problem into dual optimization problems with a nesting structure,and proposes a method of applying permutations to matrices and vectors of the dual optimization problems,thus altering the order of individual entries of the decision vector.Based on the above methods,this strategy is semantically secure.A polytopic event-triggered robust control strategy based on explicit model predictive control is proposed for a class of state and input constrained linear system.The triggering mechanism employs a contracting polytopic structure,and constructs a terminal polytope to avoid the Zeno-like behavior.Compared with existing results,this mechanism requires less parameters updates,and distance of adjacent triggering instants are not limited by the prediction horizon.The proposed control strategy ensures robust constraint satisfaction and robust stability for the closed-loop system.An event-triggering mechanism is designed for implicit model predictive controllers.This type of controllers generate optimal control values by solving online optimization problems,and the proposed triggering mechanism reduces the number of online optimizations needed to obtain the initial trigger set.Additionally,two methods are designed in this mechanism based on piecewise contracting polytopes for updating the trigger set.In comparison with uniform contraction,both the designed methods generate less frequent trigger set updates.Meanwhile,the proposed event-triggering mechanism creates longer time intervals between adjacent state transmission events.In the following we briefly describe the contributions of this thesis.The conclusion of this thesis provides further descriptions of these results.1.A preventive secure control strategy is proposed based on integer token mappings and poly topic affine transforms.This strategy guarantees the semantic security of system states,control inputs and parameters related to the piecewise affine control law.2.A preventive secure control strategy is proposed based on dual optimization problems with a nested structure.This strategy constructs nested dual problems of the primal optimization problem,thus an adversary cannot infer system states and control inputs by obtaining controller input and output.Further,the adversary cannot cannot infer parameters of the primal problem by solving the dual optimization problems.3.An explicit predictive control strategy is designed based on an event-triggering mechanism with contracting polytopes.The initial trigger set represented as a polytope is designed as well as its method of contraction.The terminal trigger set is constructed to avoid Zeno-like behaviors.The time between adjacent triggerings of state transmission events generated by the triggering mechanism is not limited by the prediction horizon.4.An implicit predictive control strategy is designed based on an event-triggering mechanism with piecewise contracting poly topes.To adapt to the situation that the controller is solving optimization problems online,a method of piecewise polytopic contraction is proposed.In comparison with the contracting method involving all facets of a polytope,the event-triggering mechanism adopting the piecewise contraction method leads to adjacent triggerings of state transmission events with longer time span.By exploiting dynamical system constraints,this thesis constructs polytopes satisfying certain conditions and their affine transforms in the constraint sets.An online optimization problem is converted to nested dual problems.In the design of trigger sets,the method of contracting a single trigger set avoids the need to calculate multiple trigger sets.The set contraction exhibits certain flexibility in that uniform contraction is used in the framework of explicit predictive control,and local contraction is used in the framework of implicit predictive control.These methods exhibits certain theoretical value.The secure control strategies studied in this thesis can ensure information security of the control system within constraints and have no special computation requirements,thus certain value for practical applications can be anticipated in systems such as unmanned aerial vehicles,implantable medical devices and virtual reality headsets.