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A stabilizing controller design for linear systems subject to asymmetric actuator saturation is proposed. Stabilization is achieved by focusing on shifted equilibria selected via the solution of an optimization problem ensuring convergence to the origin of the shifted equilibrium. To enable the computational time required by the optimizer, we impose sampled-data updates of the shifted equilibria and cast our description within a hybrid dynamical systems formulation. Two feedback solutions are given, using exact and inaccurate optimization algorithms, thus establishing interesting trade-offs between continuous-time dynamics and computationally expensive iterative discrete-time parametric optimization schemes. Through numerical examples, estimates of the region of attraction obtained through the method outlined in this paper are compared to other methods in the literature. Additionally, the real-time applicability of the control law is illustrated on numerical examples.

This paper proposes an algorithm that combines Fast Moving Horizon Parameter Estimation and Model Predictive Control subject to an observability constraint designed to ensure a lower bound on the performance of the parameter estimator. Output-feedback stability is proved through input-to-state stability of the state/error system under a small noise and initial error assumption. Numerical experiments have been carried out in the case of Active Simultaneous Localisation and Mapping (SLAM).

Distributionally-robust optimization is often studied for a fixed set of distributions rather than time-varying distributions that can drift significantly over time (which is, for instance, the case in finance and sociology due to underlying expansion of economy and evolution of demographics). This motivates understanding conditions on probability distributions, using the Wasserstein distance, that can be used to model time-varying environments. We can then use these conditions in conjunction with online stochastic optimization to adapt the decisions. We considers an online proximal-gradient method to track the minimizers of expectations of smooth convex functions parameterised by a random variable whose probability distributions continuously evolve over time at a rate similar to that of the rate at which the decision maker acts. We revisit the concepts of estimation and tracking error inspired by systems and control literature and provide bounds for them under strong convexity, Lipschitzness of the gradient, and bounds on the probability distribution drift. Further, noting that computing projections for a general feasible sets might not be amenable to online implementation (due to computational constraints), we propose an exact penalty method. Doing so allows us to relax the uniform boundedness of the gradient and establish dynamic regret bounds for tracking and estimation error. We further introduce a constraint-tightening approach and relate the amount of tightening to the probability of satisfying the constraints.

In this paper, the problem of simultaneous cyber attack and fault detection and isolation (CAFDI) in cyber-physical systems (CPS) is studied. The proposed solution methodology consists of two filters on the plant and the command and control (C\&C) sides of the CPS and an unknown input observer (UIO) based detector on the plant side. Conditions under which the proposed methodology can detect deception attacks, such as covert attacks, zero dynamics attacks, and replay attacks are characterized. An advantage of the proposed methodology is that one does not require a fully secured communication link which implies that the communication link can be compromised by the adversary while it is used to transmit the C\&C side observer estimates. Also, it is assumed that adversaries have access to parameters of the system, filters, and the UIO-based detector, however, they do not have access to all the communication link channels. Conditions under which, using the communication link cyber attacks, the adversary cannot eliminate the impact of actuator and sensor cyber attacks are investigated. To illustrate the capabilities and effectiveness of the proposed CAFDI methodologies, simulation case studies are provided and comparisons with detection methods that are available in the literature are included to demonstrate the advantages and benefits of our proposed solutions.

In this paper, we consider the optimisation of time varying functions by a network of agents with no gradient information. The proposed a novel method to estimate the gradient at each agent's position using only neighbour information. The gradient estimation is coupled with a formation controller, to minimise gradient estimation error and prevent agent collisions. Convergence results for the algorithm are provided for functions which satisfy the Polyak-Lojasiewicz inequality. Simulations and numerical results are provided to support the theoretical results., Comment: 8 pages, 4 figures, accepted in The 2020 Conference on Decisions and Control

We address the problem of maximizing privacy of stochastic dynamical systems whose state information is released through quantized sensor data. In particular, we consider the setting where information about the system state is obtained using noisy sensor measurements. This data is quantized and transmitted to a remote station through a public/unsecured communication network. We aim at keeping the state of the system private; however, because the network is not secure, adversaries might have access to sensor data, which can be used to estimate the system state. To prevent such adversaries from obtaining an accurate state estimate, before transmission, we randomize quantized sensor data using additive random vectors, and send the corrupted data to the remote station instead. We design the joint probability distribution of these additive vectors (over a time window) to minimize the mutual information (our privacy metric) between some linear function of the system state (a desired private output) and the randomized sensor data for a desired level of distortion--how different quantized sensor measurements and distorted data are allowed to be. We pose the problem of synthesizing the joint probability distribution of the additive vectors as a convex program subject to linear constraints. Simulation experiments are presented to illustrate our privacy scheme.

We study the problem of maximizing privacy of data sets by adding random vectors generated via synchronized chaotic oscillators. In particular, we consider the setup where information about data sets, queries, is sent through public (unsecured) communication channels to a remote station. To hide private features (specific entries) within the data set, we corrupt the response to queries by adding random vectors. We send the distorted query (the sum of the requested query and the random vector) through the public channel. The distribution of the additive random vector is designed to minimize the mutual information (our privacy metric) between private entries of the data set and the distorted query. We cast the synthesis of this distribution as a convex program in the probabilities of the additive random vector. Once we have the optimal distribution, we propose an algorithm to generate pseudo-random realizations from this distribution using trajectories of a chaotic oscillator. At the other end of the channel, we have a second chaotic oscillator, which we use to generate realizations from the same distribution. Note that if we obtain the same realizations on both sides of the channel, we can simply subtract the realization from the distorted query to recover the requested query. To generate equal realizations, we need the two chaotic oscillators to be synchronized, i.e., we need them to generate exactly the same trajectories on both sides of the channel synchronously in time. We force the two chaotic oscillators into exponential synchronization using a driving signal. Simulations are presented to illustrate our results., arXiv admin note: text overlap with arXiv:1809.03133 by other authors