Observer design for a class of nonlinear systems combining dissipativity with interconnection and damping assignment

A nonlinear observer design approach is proposed that exploits and combines port-Hamiltonian systems and dissipativity theory. First, a passivity-based observer design using interconnection and damping assignment for time variant state affine systems is presented by applying output injection to the system such that the observer error dynamics takes a port-Hamiltonian structure. The stability of the observer error system is assured by exploiting its passivity properties. Second, this setup is extended to develop an observer design approach for a class of systems with a time varying state affine forward and a nonlinear feedback contribution. For a class of nonlinear systems, the theory of dissipative observers is adapted and combined with the results for the passivity-based observer design using interconnection and damping assignment. The convergence of the compound observer design is determined by a linear matrix inequality. The performance of both observer approaches is analyzed in simulation examples

Observer design for a class of nonlinear systems combining dissipativity with interconnection and damping assignment

A nonlinear observer design approach is proposed that exploits and combines port-Hamiltonian systems and dissipativity theory. First, a passivity-based observer design using interconnection and damping assignment for time variant state affine systems is presented by applying output injection to the system such that the observer error dynamics takes a port-Hamiltonian structure. The stability of the observer error system is assured by exploiting its passivity properties. Second, this setup is extended to develop an observer design approach for a class of systems with a time varying state affine forward and a nonlinear feedback contribution. For a class of nonlinear systems, the theory of dissipative observers is adapted and combined with the results for the passivity-based observer design using interconnection and damping assignment. The convergence of the compound observer design is determined by a linear matrix inequality. The performance of both observer approaches is analyzed in simulation examples

Enhanced Principles in Design of Adaptive Fault Observers

In this chapter, modified techniques for fault estimation in linear dynamic systems are proposed, which give the possibility to simultaneously estimate the system state as well as slowly varying faults. Using the continuous-time adaptive observer form, the considered faults are assumed to be additive, thereby the principles can be applied for a broader class of fault signals. Enhanced algorithms using H∞ approach are provided to verify stability of the observers, giving algorithms with improved performance of fault estimation. Exploiting the procedure for transforming the model with additive faults into an extended form, the proposed technique allows to obtain fault estimates that can be used for fault compensation in the fault tolerant control scheme. Analyzing the ambit of performances given on the mixed H2/H∞ design of the fault tolerant control, the joint design conditions are formulated as a minimization problem subject to convex constraints expressed by a system of linear matrix inequalities. Applied enhanced design conditions increase estimation rapidity also in noise environment and formulate a general framework for fault estimation using augmented or adaptive observer structures and active fault tolerant control in linear dynamic systems

Modeling and Estimation of Biological Plants

Estimating the state of a dynamic system is an essential task for achieving important objectives such as process monitoring, identification, and control. Unlike linear systems, no systematic method exists for the design of observers for nonlinear systems. Although many researchers have devoted their attention to these issues for more than 30 years, there are still many open questions. We envisage that estimation plays a crucial role in biology because of the possibility of creating new avenues for biological studies and for the development of diagnostic, management, and treatment tools. To this end, this thesis aims to address two types of nonlinear estimation techniques, namely, the high-gain observer and the moving-horizon estimator with application to three different biological plants. After recalling basic definitions of stability and observability of dynamical systems and giving a bird's-eye survey of the available state estimation techniques, we are interested in the high-gain observers. These observers may be used when the system dynamics can be expressed in specific a coordinate under the so-called observability canonical form with the possibility to assign the rate of convergence arbitrarily by acting on a single parameter called the high-gain parameter. Despite the evident benefits of this class of observers, their use in real applications is questionable due to some drawbacks: numerical problems, the peaking phenomenon, and high sensitivity to measurement noise. The first part of the thesis aims to enrich the theory of high-gain observers with novel techniques to overcome or attenuate these challenging performance issues that arise when implementing such observers. The validity and applicability of our proposed techniques have been shown firstly on a simple one-gene regulatory network, and secondly on an SI epidemic model. The second part of the thesis studies the problem of state estimation using the moving horizon approach. The main advantage of MHE is that information about the system can be explicitly considered in the form of constraints and hence improve the estimates. In this work, we focus on estimation for nonlinear plants that can be rewritten in the form of quasi-linear parameter-varying systems with bounded unknown parameters. Moving-horizon estimators are proposed to estimate the state of such systems according to two different formulations, i.e., "optimistic" and "pessimistic". In the former case, we perform estimation by minimizing the least-squares moving-horizon cost with respect to both state variables and parameters simultaneously. In the latter, we minimize such a cost with respect to the state variables after picking up the maximum of the parameters. Under suitable assumptions, the stability of the estimation error given by the exponential boundedness is proved in both scenarios. Finally, the validity of our obtained results has been demonstrated through three different examples from biological and biomedical fields, namely, an example of one gene regulatory network, a two-stage SI epidemic model, and Amnioserosa cell's mechanical behavior during Dorsal closure

Learning-based Design of Luenberger Observers for Autonomous Nonlinear Systems

The design of Luenberger observers for nonlinear systems involves state transformation to another coordinate system where the dynamics are asymptotically stable and linear up to output injection. The observer then provides a state estimate in the original coordinates by inverting the transformation map. For general nonlinear systems, however, the main challenge is to find such a transformation and to ensure that it is injective. This paper addresses this challenge by proposing a learning method that employs supervised physics-informed neural networks to approximate both the transformation and its inverse. It is shown that the proposed method exhibits better generalization capabilities than other contemporary methods. Moreover, the observer is shown to be robust under the neural network's approximation error and the system uncertainties