## Model Based Optimization and Design of Secure Systems

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2013##### Author

Malik, Waseem Ansar

##### Advisor

Martins, Nuno C

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ABSTRACT
Title of dissertation: MODEL BASED OPTIMIZATION
AND DESIGN OF SECURE SYSTEMS
Waseem Ansar Malik, Doctor of Philosophy, 2013
Dissertation directed by: Prof. Nuno C. Martins
Department of Electrical and Computer Engineering
University of Maryland, College Park
Dr. Ananthram Swami
Computational and Information Sciences Directorate
Army Research Laboratory
Control systems are widely used in modern industry and find wide applications in power systems, nuclear and chemical plants, the aerospace industry, robotics, communication devices, and embedded systems. All these systems typically rely on an underlying
computing and networking infrastructure which has considerable security vulnerabilities.
The biggest threat, in this age and time, to modern systems are cyber attacks from adversaries. Recent cyber attacks have practically shut down government websites affecting government operation, undermined financial institutions, and have even infringed on public
privacy. Thus it is extremely important to conduct studies on the design and analysis of secure systems. This work is an effort in this research direction and is mainly focused on incorporating security in the design of modern control systems.
In the first part of this dissertation, we present a linear quadratic optimal control problem subjected to security constraints. We consider an adversary which can make partial noisy measurements of the state. The task of the controller is to generate control sequences such that the adversary is unable to estimate the terminal state. This is done by minimizing a quadratic cost while satisfying security constraints. The resulting optimization problems are shown to be convex and the optimal solution is computed using Lagrangian based techniques. For the case when the terminal state has a discrete distribution the optimal solution is shown to be nonlinear in the terminal state. This is followed by considering the case when the terminal state has a continuous distribution. The resulting infinite dimensional optimization problems are shown to be convex and the optimal solution is proven to be affine in the terminal state.
In the next part of this dissertation, we analyze several team decision problems subjected to security constraints. Specifically, we consider problem formulations where there are two decision makers each controlling a different dynamical system. Each decision maker receives information regarding the respective terminal states that it is required to reach and applies a control sequence accordingly. An adversary makes partial noisy measurements of the states and tries to estimate the respective terminal states. It is shown that the optimal solution is affine in the terminal state when it is identical for both systems. We also consider the general case where the terminal states are correlated. The resulting infinite dimensional optimization problems are shown to convex programs and we prove
that the optimal solution is affine in the information available to the decision makers.
Next, a stochastic receding horizon control problem is considered and analyzed. Specifically, we consider a system with bounded disturbances and hard bounds on the control inputs. Utilizing a suboptimal disturbance feedback scheme, the optimization problem is shown to be convex. The problem of minimizing the empirical mean of the cost function is analyzed. We provide bounds on the disturbance sample size to compute the empirical minimum of the problem. Further, we consider the problem where there are hard computational constraints and complex on-line optimization is not feasible. This is addressed by randomly generating both the control inputs and the additive disturbances. Bounds on sample sizes are provided which guarantee a notion of a probable near minimum.
Model uncertainty is also incorporated into the framework and relevant bounds are provided which guarantee a probable near minimax value. This work finds many applications in miniature devices and miniature robotics.
In the final part of this dissertation, we consider a centralized intrusion detection problem with jointly optimal sensor placement. A team of sensors make measurements regarding the presence of an intruder and report their observations to a decision maker. The decision maker solves a jointly optimal detection and sensor placement problem. For the case when the number of sensors is equal to the number of placement points, we prove that uniform placement of sensors is not strictly optimal. We introduce and utilize
a majorization based partial order for the placement of sensors. For the case when the number of sensors is less than or equal to six, we show that for a fixed local probability of detection (probability of false alarm) increasing the probability of false alarm (probability of detection) results in optimal placements that are higher on a majorization based partial order.

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