ItemStability investigation of non-linrst control systems by the second method of liapunov(Wichita State University, 1967-01) Yang, Philip Wen-TseAn introduction to Liapunov's second method as it applies to autonomous non-linear control system stability with experimental verification is presented in this thesis. Main theorems and definitions of Liapunov's method are treated. Lur'e's method, Szego's method, the variable gradient method and the method of several non-linear elements are presented to generate suitable Liapunov functions for testing the stability of an autonomous non-linear control system, and several examples with experimental verifications are used to illustrate these procedures. The applications of Liapunov's second method to practical engineering problems are still applicable to only certain classes of systems due to the difficulties in generating Liapunov functions. If practical and more generally applicable engineering methods can be devised for generating Liapunov functions, the method may become one of the best tools available for the analysis and design of non-linear systems. ItemSecure message communication via a relay using a secret sharing scheme(Wichita State University, 2023-07) Dodda, Srilekha; Chou, Remi A.Secure message communication between the transmitter and the receiver checks integrity. It involves preserving the message content against unauthorized access. The designed application uses a shamir secret sharing scheme, where a message can be split into shares. And the transmitter distributes each share to the receiver to reconstruct the message through the relays. In this process, the adversary might attack any of the relays to modify the share information and tries to obtain the original message. Where each share is produced by adding additional information to it also providing the identification protocol at the reconstruction phase to ensure the message integrity. At last, the receiver will perform an identification protocol to identify the authentic shares, if the shares are verified as authentic then the receiver will perform a reconstruction protocol to reconstruct the message. ItemElimination of amplify-and-forward relay spoofing signal for global positioning system receiver(Wichita State University, 2023-07) Manne, Jyothi Sri Sai; Kwon, Hyuck M.The Global Positioning System (GPS) provides positioning and timing information for various civil and military devices like the fifth generation (5G) smartphones, aviation systems, autonomous vehicles, drones, and other navigation systems. There have been multiple incident reports that a fake GPS spoofing signal interferes the received GPS signal with a fake pseudo-noise (PN) sequence code and guides a victim’s device to an undesired location. Several solutions have been available on the market against the GPS spoofing threat. The existing methods either need major modifications to current GPS devices, require specific hardware (i.e., high deployment costs), or are not resistant to sophisticated attackers. In this thesis, the GPS spoofing signal is generated by a simple amplify-and-forward (AF) relay near a victim device. The existing anti-spoofing solutions on the market are not effective against this type of an AF relay GPS spoofing signal. In this thesis, a simple method of how to estimate and eliminate the AF relay GPS spoofing signal from the received signal, and obtain an estimate of the true GPS signal. The key steps of the proposed method consist of simple six steps: (1) Take cyclic cross-correlation between the received signal and the available PN sequence used by the GPS; (2) Find the peak correlation position and peak value of the cyclic cross-correlation; (3) Estimate the fake AF relay GPS spoofing signal; (4) Eliminate the fake spoofing signal from the received signal; (5) Take cyclic cross-correlation with the same PN sequence; (6) Estimate the true time delays and the true position. An example is shown to demonstrate these steps and the effectiveness of the proposed method. ItemMulti-user information theoretic security for wireless communication(Wichita State University, 2023-07) Sultana, Rumia; Chou, Remi A.We show that the problem of code construction for multiple access channel (MAC) resolvability can be reduced to the simpler problem of code construction for source resolvability. Specifically, we propose a MAC resolvability code construction which involves a combination of multiple source resolvability codes, used in a black-box manner, and leverages randomness recycling implemented via distributed hashing and block-Markov coding. We consider secret sharing where a dealer wants to share a secret with several participants such that predefined subsets of participants can reconstruct the secret and all other subsets of participants cannot learn any information about the secret. To this end, the dealer and the participants have access to samples of correlated random variables and a one-way (from the dealer to the participants), authenticated, public, and rate-limited communication channel. For this problem, we propose the first constructive and low-complexity coding scheme able to handle arbitrary access structures. Our construction relies on a vector quantization coupled with distribution approximations with polar codes to handle the reliability constraints, followed by universal hashing to handle the security constraints. We stress that our coding scheme does not require symmetry or degradation assumptions on the correlated random variables, and does not need a pre-shared secret among the participants and dealer. Consider a secret sharing model where a dealer shares a secret with several participants through a Gaussian broadcast channel such that predefined subsets of participants can reconstruct the secret and all other subsets of participants cannot learn any information about the secret. Our first contribution is to show that, in the asymptotic blocklength regime, it is optimal to consider coding schemes that rely on two coding layers, namely, a reliability layer and a secrecy layer, where the reliability layer is a channel code for a compound channel without any security constraint. Our second contribution is to design such a two-layer coding scheme at short blocklength. Specifically, we design the reliability layer via an autoencoder, and implement the secrecy layer with hash functions. To evaluate the performance of our coding scheme, we empirically evaluate the probability of error and information leakage, which is defined as the mutual information between the secret and the unauthorized sets of users channel outputs. We empirically evaluate this information leakage via a neural network-based mutual information estimator. Our simulation results demonstrate a precise control of the probability of error and leakage thanks to the two-layer coding design.