Reliable controller design for nonlinear systems

This paper addresses the reliable H∞ control problems for affine nonlinear systems. Based on the Hamilton-Jacobi inequality approach developed in the H∞ control problems for affine nonlinear systems, a method for the design of reliable nonlinear control systems is presented. The resulting nonlinear control systems are reliable in that they provide guaranteed local asymptotic stability and H∞ performance not only when all control components are operational, but also in case of some component outages within a prespecified subset of control components.published_or_final_versio

Reliable H ∞ control for affine nonlinear systems

This paper addresses the reliable H ∞-control problems for affine nonlinear systems. Based on the Hamilton-Jacobi inequality approach developed in the H ∞-control problems for affine nonlinear systems, a method for the design of reliable nonlinear control systems is presented. The resulting nonlinear control systems are reliable in that they provide guaranteed local asymptotic stability and H ∞ performance not only when all control components are operational, but also in the case of some component outages within a prespecified subset of control components. A numerical example is also given.published_or_final_versio

Control optimization, stabilization and computer algorithms for aircraft applications

Research related to reliable aircraft design is summarized. Topics discussed include systems reliability optimization, failure detection algorithms, analysis of nonlinear filters, design of compensators incorporating time delays, digital compensator design, estimation for systems with echoes, low-order compensator design, descent-phase controller for 4-D navigation, infinite dimensional mathematical programming problems and optimal control problems with constraints, robust compensator design, numerical methods for the Lyapunov equations, and perturbation methods in linear filtering and control

Reliable H∞ control for a class of switched nonlinear systems

Dimirovski, Georgi M. (Dogus Author)This paper focuses on the problem of reliable H∞ control for a class of switched nonlinear systems with actuator failures among a prespecified subset of actuators. In existing works, the reliable H∞ design methods are all based on a basic assumption that the never failed actuators must stabilize the given system. But when actuators suffer ”serious failure”– the never failed actuators can not stabilize the given system, the standard design methods of reliable H∞ control do not work. Based on the switching technique, the problem can be solved by means of switching among subsystems or finite candidate controllers.16th Triennial World Congress of International, Federation of Automatic Control, IFAC 200

A posteriori analysis of discontinuous galerkin schemes for systems of hyperbolic conservation laws

In this work we construct reliable a posteriori estimates for some semi- (spatially) discrete discontinuous Galerkin schemes applied to nonlinear systems of hyperbolic conservation laws. We make use of appropriate reconstructions of the discrete solution together with the relative entropy stability framework, which leads to error control in the case of smooth solutions. The methodology we use is quite general and allows for a posteriori control of discontinuous Galerkin schemes with standard flux choices which appear in the approximation of conservation laws. In addition to the analysis, we conduct some numerical benchmarking to test the robustness of the resultant estimator

Second-Order Fault Tolerant Extended Kalman Filter for Discrete Time Nonlinear Systems

As missing sensor data may severely degrade the overall system performance and stability, reliable state estimation is of great importance in modern data-intensive control, computing, and power systems applications. Aiming at providing a more robust and resilient state estimation technique, this paper presents a novel second-order fault-tolerant extended Kalman filter estimation framework for discrete-time stochastic nonlinear systems under sensor failures, bounded observer-gain perturbation, extraneous noise, and external disturbances condition. The failure mechanism of multiple sensors is assumed to be independent of each other with various malfunction rates. The proposed approach is a locally unbiased, minimum estimation error covariance based nonlinear observer designed for dynamic state estimation under these conditions. It has been successfully applied to a benchmark target-trajectory tracking application. Computer simulation studies have demonstrated that the proposed second-order fault-tolerant extended Kalman filter provides more accurate estimation results, in comparison with traditional first- and second-order extended Kalman filter. Experimental results have demonstrated that the proposed second-order fault-tolerant extended Kalman filter can serve as a powerful alternative to the existing nonlinear estimation approaches

Data-driven modeling and parameter estimation of Nonlinear systems

Nonlinear systems are prevalent in many fields of science and engineering, and understanding their behavior is essential for developing effective control and prediction strategies. In this paper, we present a novel data-driven approach for accurately modeling and estimating parameters of nonlinear systems using trust region optimization. Our method is applied to three classic systems: the Van der Pol oscillator, the Damped oscillator, and the Lorenz system, which have broad applications in various fields, including engineering, physics, and biology. Our results demonstrate that our approach can accurately identify the parameters of these nonlinear systems, providing a reliable characterization of their behavior. We show that the ability to capture the dynamics on the attractor is crucial for these systems, especially in chaotic systems like the Lorenz system. Overall, this article presents a robust data-driven approach for parameter estimation of nonlinear dynamical systems, with promising potential for real-world applications.Comment: 17 pages, 6 figure