Stochastically Resilient Observer Design for a Class of Continuous-Time Nonlinear Systems

This work addresses the design of stochastically resilient or non-fragile continuous-time Luenberger observers for systems with incrementally conic nonlinearities. Such designs maintain the convergence and/or performance when the observer gain is erroneously implemented due possibly to computational errors i.e. round off errors in computing the observer gain or changes in the observer parameters during operation. The error in the observer gain is modeled as a random process and a common linear matrix inequality formulation is presented to address the stochastically resilient observer design problem for a variety of performance criteria. Numerical examples are given to illustrate the theoretical results

Resilient Observer Design for Discrete-Time Nonlinear Systems with General Criteria

A class of discrete-time nonlinear system and measurement equations having incrementally conic nonlinearities and finite energy disturbances is considered. A linear matrix inequality based resilient observer design approach is presented to guarantee the satisfaction of a variety of performance criteria ranging from simple estimation error boundedness to dissipativity in the presence of bounded perturbations on the gain. Some simulation examples are included to illustrate the proposed design methodology

New advances in H∞ control and filtering for nonlinear systems

The main objective of this special issue is to summarise recent advances in H∞ control and filtering for nonlinear systems, including time-delay, hybrid and stochastic systems. The published papers provide new ideas and approaches, clearly indicating the advances made in problem statements, methodologies or applications with respect to the existing results. The special issue also includes papers focusing on advanced and non-traditional methods and presenting considerable novelties in theoretical background or experimental setup. Some papers present applications to newly emerging fields, such as network-based control and estimation

Robust Multi-Criteria Optimal Fuzzy Control of Continuous-Time Nonlinear Systems

This paper presents a novel fuzzy control design of continuous-time nonlinear systems with multiple performance criteria. The purpose behind this work is to improve the traditional fuzzy controller performance to satisfy several performance criteria simultaneously to secure quadratic optimality with inherent stability property together with dissipativity type of disturbance reduction. The Takagi– Sugeno fuzzy model is used in our control system design. By solving the linear matrix inequality at each time step, the control solution can be found to satisfy the mixed performance criteria. The effectiveness of the proposed technique is demonstrated by simulation of the control of the inverted pendulum system

Performance-Robust Dynamic Feedback Control of Lipschitz Nonlinear Systems

This dissertation addresses the dynamic control of nonlinear systems with finite energy noise in the state and measurement equations. Regional eigenvalue assignment (REA) is used to ensure that the state estimate error is driven to zero significantly faster than the state itself. Moreover, the controller is designed for the resulting closed loop system to achieve any one of a set of general performance criteria (GPC). The nonlinear model is assumed to have a Lipschitz nonlinearity both in the state and measurement equations. By using the norm bound of the nonlinearity, the controller is designed to be robust against all nonlinearities satisfying the norm-bound. A Luenberger-type nonlinear observer is used to estimate the system state, which is not directly measurable. The choice of the eigenvalue locations for the linear part of the system is based on the transient response specifications and the separation of the controller dynamics from the observer dynamics. Furthermore, the GPC are incorporated to achieve performance requirements such as H2, H∞, etc. The advantage of using GPC is it allows the designer flexibility in choosing a performance objective to tune the system. The design problem introduced in this dissertation uses various mathematical techniques to derive LMI conditions for the controller and observer design using REA, GPC, and the bounds on the Lipschitz nonlinearities. All work will be demonstrated in both continuous- and discrete-time. Illustrative examples in both time domains are given to demonstrate the proposed design procedure. Multiple numerical approaches are also presented and compared in simulations for ease of use, applicability, and conservatism

Simultaneous State and Unknown Input Set-Valued Observers for Some Classes of Nonlinear Dynamical Systems

In this paper, we propose fixed-order set-valued (in the form of l2-norm hyperballs) observers for some classes of nonlinear bounded-error dynamical systems with unknown input signals that simultaneously find bounded hyperballs of states and unknown inputs that include the true states and inputs. Necessary and sufficient conditions in the form of Linear Matrix Inequalities (LMIs) for the stability (in the sense of quadratic stability) of the proposed observers are derived for ($\mathcal{M},\gamma$)- Quadratically Constrained (($\mathcal{M},\gamma$)-QC) systems, which includes several classes of nonlinear systems: (I) Lipschitz continuous, (II) ($\mathcal{A},\gamma$)-QC* and (III) Linear Parameter-Varying (LPV) systems. This new quadratic constraint property is at least as general as the incremental quadratic constraint property for nonlinear systems and is proven in the paper to embody a broad range of nonlinearities. In addition, we design the optimal $\mathcal{H}_{\infty}$ observer among those that satisfy the quadratic stability conditions and show that the design results in Uniformly Bounded-Input Bounded-State (UBIBS) estimate radii/error dynamics and uniformly bounded sequences of the estimate radii. Furthermore, we provide closed-form upper bound sequences for the estimate radii and sufficient condition for their convergence to steady state. Finally, the effectiveness of the proposed set-valued observers is demonstrated through illustrative examples, where we compare the performance of our observers with some existing observers.Comment: Under review in Automatic

A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Robust and Resilient Control Design and Performance Analysis for Uncertain Systems with Finite Energy Disturbances

This dissertation addresses the problem of robust and resilient control design with additional performance analysis for uncertain systems with finite energy disturbances. The control design is robust and resilient in the sense of maintaining certain performance criteria in the presence of perturbations in both system parameters and feedback gains. The performance analysis evaluates resilience properties of state feedback and dynamic (state estimate) feedback controllers. A resilient and robust state feedback controller is designed using linear matrix inequality (LMI) techniques for the characterization of solutions to the analysis and design problems posed in this work. Uncertainties are allowed in the linear and nonlinear parts of the system model and also in the feedback gain so that the designed controller is robust in addition to being resilient. The design of controllers for various performance criteria including asymptotic stability, H2, Hinf, input strict passivity, output strict passivity and very strict passivity are presented. In addition to the design problem, an approach is presented for performance analysis of the resilience property of perturbed controller and observer gains. The resilience property is defined in terms of both multiplicative and additive perturbations on the gains so that the closed loop eigenvalues do not leave a specified region in the complex plane, such as a vertical strip, disk, sector region, etc. The method presented allows maximum gain perturbation bounds to be obtained based on the designer’s choices of controller eigenvalue region. The LMI technique is used also for the analysis process. Both design and analysis problems are treated using Lyapunov functions. All work is conducted for both continuous- and discrete-time cases. Several illustrative simulation examples are included to show the effectiveness of the proposed design and analysis approaches