State estimation for linear switched systems with unstable invariant zeros and unknown inputs

International audienceIn this paper the problem of continuous and discrete state estimation for a class of linear switched systems is studied. The class of systems under study can contain non-minimum phase zeros in some of their "operating modes". The conditions for exact reconstruction of the discrete state are given using structural properties of the switched system. The state-space is decomposed into the strongly observable part, the nonstrongly observable part and the unobservable part, to analyze the effect of the unknown inputs. A state observer based on high-order sliding-mode and Luenberger-like observers is proposed. For the case when the exact reconstruction of the state cannot be achieved, the ultimate bounds on the estimation errors are provided. The workability of the proposed method is illustrated by simulations

Stabilization of systems with asynchronous sensors and controllers

We study the stabilization of networked control systems with asynchronous sensors and controllers. Offsets between the sensor and controller clocks are unknown and modeled as parametric uncertainty. First we consider multi-input linear systems and provide a sufficient condition for the existence of linear time-invariant controllers that are capable of stabilizing the closed-loop system for every clock offset in a given range of admissible values. For first-order systems, we next obtain the maximum length of the offset range for which the system can be stabilized by a single controller. Finally, this bound is compared with the offset bounds that would be allowed if we restricted our attention to static output feedback controllers.Comment: 32 pages, 6 figures. This paper was partially presented at the 2015 American Control Conference, July 1-3, 2015, the US

Development of adaptive control methodologies and algorithms for nonlinear dynamic systems based on u-control framework

Inspired by the U-model based control system design (or called U-control system design), this study is mainly divided into three parts. The first one is a U-model based control system for unstable non-minimum phase system. Pulling theorems are proposed to apply zeros pulling filters and poles pulling filters to pass the unstable non-minimum phase characteristics of the plant model/system. The zeros pulling filters and poles pulling filters derive from a customised desired minimum phase plant model. The remaining controller design can be any classic control systems or U-model based control system. The difference between classic control systems and U-model based control system for unstable non-minimum phase will be shown in the case studies.Secondly, the U-model framework is proposed to integrate the direct model reference adaptive control with MIT normalised rules for nonlinear dynamic systems. The U-model based direct model reference adaptive control is defined as an enhanced direct model reference adaptive control expanding the application range from linear system to nonlinear system. The estimated parameter of the nonlinear dynamic system will be placement as the estimated gain of a customised linear virtual plant model with MIT normalised rules. The customised linear virtual plant model is the same form as the reference model. Moreover, the U-model framework is design for the nonlinear dynamic system within the root inversion.Thirdly, similar to the structure of the U-model based direct model reference adaptive control with MIT normalised rules, the U-model based direct model reference adaptive control with Lyapunov algorithms proposes a linear virtual plant model as well, estimated and adapted the particular parameters as the estimated gain which of the nonlinear plant model by Lyapunov algorithms. The root inversion such as Newton-Ralphson algorithm provides the simply and concise method to obtain the inversion of the nonlinear system without the estimated gain. The proposed U-model based direct control system design approach is applied to develop the controller for a nonlinear system to implement the linear adaptive control. The computational experiments are presented to validate the effectiveness and efficiency of the proposed U-model based direct model reference adaptive control approach and stabilise with satisfied performance as applying for the linear plant model

Disturbance Model Identification and Model Free Synthesis of Controllers for Multivariable Systems

In this work, two different problems are addressed. In the first part, the problem of synthesizing a set of stabilizing controllers for unknown multivariable systems using direct data is analyzed. This is a model free approach to control design and uses only the frequency domain data of the system. It is a perfect complement to modern and post modern methods that begin the control design with a system model. A three step method, involving sequential design, search for stability boundaries and stability check is proposed. It is shown through examples that a complete set of stabilizing controllers of the chosen form can be obtained for the class of linear stable multivariable systems. The complexity of the proposed method is invariant with respect to the order of the system and increases with the increase in the number of input channels of the given multivariable system. The second part of the work deals with the problem of identification of model uncertainties and the effect of unwanted exogenous inputs acting on a discrete time multivariable system using its output information. A disturbance model is introduced which accounts for the system model uncertainties and the effect of unwanted exogenous inputs acting on the system. The frequency content of the exogenous signals is assumed to be known. A linear dynamical model of the disturbance is assumed with an input that has the same frequency content as that of the exogenous input signal. The extended model of the system is then subjected to Kalman filtering and the disturbance states estimates are used to obtain a least squares estimate of the disturbance model parameters. The proposed approach is applied to a linear multivariable system perturbed by an exogenous signal of known frequency content and the results obtained depict the efficacy of the proposed approach

Time-Delay Systems

Time delay is very often encountered in various technical systems, such as electric, pneumatic and hydraulic networks, chemical processes, long transmission lines, robotics, etc. The existence of pure time lag, regardless if it is present in the control or/and the state, may cause undesirable system transient response, or even instability. Consequently, the problem of controllability, observability, robustness, optimization, adaptive control, pole placement and particularly stability and robustness stabilization for this class of systems, has been one of the main interests for many scientists and researchers during the last five decades

Security of cyber-physical systems: A control-theoretic perspective

Motivated by the attacks on control systems through the cyber (digital) part, we study how signal attacks injected through actuators and/or sensors affect control system stability and performance. We ask the questions: What are the different types and scenarios of signal attacks? When are the attacks stealthy and unbounded? How to compute the worst stealthy bounded attacks? How to defend against such attacks through controller design? How to identify and estimate signal attacks before significant performance loss happens? We answer the above questions in this thesis using tools from control theory. We show that it is necessary to use a sampled-data framework to accurately assess the vulnerabilities of control systems. In addition, we show that the most lethal attacks are related to the structure of the system (location of zeros and poles, number of inputs and outputs). We show that dual rate control is a powerful tool to defend against these vulnerabilities, and we provide a related controller design. Furthermore, we show that the worst stealthy bounded attacks can be computed by an iterative linear program, and we show how to lessen their effects through iterative controller design. Finally, we study the trade-off between control and estimation of signal attacks and provide several controller designs utilizing the power of dual rate sampling