Sample Complexity of the Robust LQG Regulator with Coprime Factors Uncertainty

This paper addresses the end-to-end sample complexity bound for learning the H2 optimal controller (the Linear Quadratic Gaussian (LQG) problem) with unknown dynamics, for potentially unstable Linear Time Invariant (LTI) systems. The robust LQG synthesis procedure is performed by considering bounded additive model uncertainty on the coprime factors of the plant. The closed-loop identification of the nominal model of the true plant is performed by constructing a Hankel-like matrix from a single time-series of noisy finite length input-output data, using the ordinary least squares algorithm from Sarkar et al. (2020). Next, an H-infinity bound on the estimated model error is provided and the robust controller is designed via convex optimization, much in the spirit of Boczar et al. (2018) and Zheng et al. (2020a), while allowing for bounded additive uncertainty on the coprime factors of the model. Our conclusions are consistent with previous results on learning the LQG and LQR controllers.Comment: Minor Edits on closed loop identification, 30 pages, 2 figures, 3 algorithm

Design of robust controllers for multivariable nonlinear plants

This thesis deals with design techniques for robust non-linear multivariable systems. It describes and discusses some design techniques for such systems. First, one-loop-at-a-time design using the root locus method is considered. The disadvantages of this approach are outlined. Next, some gain-schedulmg controllers are designed for each loop. Then, a multivariable optimization approach is taken. Software to find the frequency domain solution of the two-block weightedmixed- sensitivity problem using the Youla Parameterisation and Smith-McMillan form is developed. This two-variable problem decouples into two single-variable problems, corresponding to optimizing at the input and output of the plant. The fundamental limitations and the trade-offs in design are studied at the input and output of the plant. A11 controllers are tested and implemented on the inverted pendulum-cart apparatus, an unstable single-input two-output system

Optimization methods for deadbeat control design: a state space approach

This thesis addresses the synthesis problem of state deadbeat regulator using state space techniques. Deadbeat control is a linear control strategy in discrete time systems and consists of driving the system from any arbitrary initial state to a desired final state infinite number of time steps. Having described the framework for development of the thesis which is in the form of a lower linear-fractional transformation (LFT), the conditions for internal stability based on the notion of coprime factorization over the set of proper and stable transfer matrices, namely RH, is discussed. This leads to the derivation of the class of all stabilizing linear controllers, which are parameterized affinely in terms of a stable but otherwise free parameter Q, usually known as the Q-parameterization. In this work, the classical Q- parameterization is generalized to deliver a parameterization for the family of deadbeat regulators. Time response characteristics of the deadbeat system are investigated. In particular, the deadbeat regulator design problem in which the system must satisfy time domain specifications and minimize a quadratic (LQG-type) performance criterion is examined. It is shown that the attained parameterization for deadbeat controllers leads to the formulation of the synthesis problem in a quadratic programming framework with Q regarded as the design variable. The equivalent formulation of this objective as a quadratic integral in the frequency domain provides the means for shaping the frequency response characteristics of the system. Using the LMI characterization of the standard H problem, a new scheme for shaping the system frequency response characteristics by minimizing the infinity norm of an appropriate closed-loop transfer function is introduced. As shown, the derived parameterization of deadbeat compensators simplifies considerably the formulation and solution of this problem. The last part of the work described in this thesis is devoted to addressing the synthesis problem of deadbeat regulators in a robust way, when the plant is subject to structured norm-bounded parametric uncertainties. A novel approach which is expressed as an LMI feasibility condition has been proposed and analysed

New Approaches to Smart Grid Security with SCADA Systems

The use of information technology in electric power grid introduces the vulnerability problem looming the future smart grid. The supervisory control and data acquisition (SCADA)is the first defense, which itself is undermined by potential malicious attacks. This dissertation studies two particular security threats facing the smart grid and SCADA systems: the unobservable attack and the replay attack. The former is well known in fault detection of the power grid and has received renewed interest in the past a few years, while the latter is motivated by the Stuxnet worm allegedly used against the nuclear facilities in Iran. For unobservable attacks, this dissertation adopts the dynamic state estimation approach and treats each bus of the power grid as a dynamic agent. A consensus estimation strategy is proposed to estimate the dynamic states of the power grid, based on which unobservable attacks can be effectively detected. Detection of replay attacks is harder. Two different approaches are proposed in this dissertation. The first is the whitening filter approach that converts the detection of the replay attack into an equivalent white noise detection through whitening a feedback signal. However this approach is less effective, if the replay attack does not change much the whiteness of the filtered feedback signal. Hence a second approach termed as spectrum estimation is proposed. It is shown that the spectrum of the feedback signal in presence of the replay attack can be very different from the case when the replay attack is absent. This approach improves the detection results of the former one. Both are illustrated and examined by the simulation studies

Combined system identification and robust control of a gimbal platform

Gimbaled imaging systems require very high performance inertial stabilization loops to achieve clear image acquisition, precise pointing, and tracking performance. Therefore, higher bandwidths become essential to meet recent increased performance demands. However, such systems often posses flexible dynamics around target bandwidth and time delay of gyroscope sensors which put certain limit to achievable bandwidths. For inertial stabilization loops, widely used design techniques have difficulty in achieving large bandwidth and satisfying required robustness simultaneously. Clearly, high performance control design hinges on accurate control-relevant model set. For that reason, combined system identification and robust control method is preferred. In the system identification step, accurate nominal model is obtained, which is suitable for subsequent robust control synthesis. Model validation based uncertainty modeling procedure constructs the robust-control-relevant uncertain model set, which facilitates the high performance controller design. Later, with skewed-mu synthesis, controller is designed which satisfies large bandwidth and robustness requirements. Finally, the experimental results show that significant performance improvement is achieved compared to common manual loop shaping methods. In addition, increased performance demands for new imaging systems are fulfilled