Nonlinear control synthesis by convex optimization

A stability criterion for nonlinear systems, recently derived by the third author, can be viewed as a dual to Lyapunov's second theorem. The criterion is stated in terms of a function which can be interpreted as the stationary density of a substance that is generated all over the state-space and flows along the system trajectories toward the equilibrium. The new criterion has a remarkable convexity property, which in this note is used for controller synthesis via convex optimization. Recent numerical methods for verification of positivity of multivariate polynomials based on sum of squares decompositions are used

A Tractable Fault Detection and Isolation Approach for Nonlinear Systems with Probabilistic Performance

This article presents a novel perspective along with a scalable methodology to design a fault detection and isolation (FDI) filter for high dimensional nonlinear systems. Previous approaches on FDI problems are either confined to linear systems or they are only applicable to low dimensional dynamics with specific structures. In contrast, shifting attention from the system dynamics to the disturbance inputs, we propose a relaxed design perspective to train a linear residual generator given some statistical information about the disturbance patterns. That is, we propose an optimization-based approach to robustify the filter with respect to finitely many signatures of the nonlinearity. We then invoke recent results in randomized optimization to provide theoretical guarantees for the performance of the proposed filer. Finally, motivated by a cyber-physical attack emanating from the vulnerabilities introduced by the interaction between IT infrastructure and power system, we deploy the developed theoretical results to detect such an intrusion before the functionality of the power system is disrupted

Networked gain-scheduled fault diagnosis under control input dropouts without data delivery acknowledgement

This paper investigates the fault diagnosis problem for discrete‐time networked control systems under dropouts in both control and measurement channel with no delivery acknowledgment. We propose to use a proportional integral observer‐based fault diagnoser collocated with the controller. The observer estimates the faults and computes a residual signal whose comparison with a threshold alarms the fault appearance. We employ the expected value of the arriving control input for the open‐loop estimation and the measurement reception scenario for the correction with a jump observer. The jumping gains are scheduled in real time with rational functions depending on a statistic of the difference between the control command being applied in the plant and the one being used in the observer. We design the observer, the residual, and the threshold to maximize the sensitivity under faults while guaranteeing some minimum detectable faults under a predefined false alarm rate. Exploiting sum‐of‐squares decomposition techniques, the design procedure becomes an optimization problem over polynomials

Identification of nonlinear time-varying systems using an online sliding-window and common model structure selection (CMSS) approach with applications to EEG

The identification of nonlinear time-varying systems using linear-in-the-parameter models is investigated. A new efficient Common Model Structure Selection (CMSS) algorithm is proposed to select a common model structure. The main idea and key procedure is: First, generate K 1 data sets (the first K data sets are used for training, and theK 1 th one is used for testing) using an online sliding window method; then detect significant model terms to form a common model structure which fits over all the K training data sets using the new proposed CMSS approach. Finally, estimate and refine the time-varying parameters for the identified common-structured model using a Recursive Least Squares (RLS) parameter estimation method. The new method can effectively detect and adaptively track the transient variation of nonstationary signals. Two examples are presented to illustrate the effectiveness of the new approach including an application to an EEG data set