Sam Nazari

Positive unknown input observer design for positive linear systems

Positive systems are important class of dynamic systems with impressive properties. The response of such systems to positive initial conditions and positive inputs remain in the nonnegative orthant of the state space. Although positive observers have been designed for positive systems, they are unable to estimate the states when unknown inputs or disturbances are present in the systems. This paper is a first attempt to design positive unknown input observers (PUIO) for positive linear systems. The structural constraints on observer parameters make the design task cumbersome. However, with the aid of a positive stabilization scheme via LMI and by imposing conditions on positivity of the generalized inverse associated with a certain design matrix, we provide a reliable procedure for the design of PUIOs.

Stability radius for extended linearization with system uncertainty

The problem considered is the computation of the stability radius for a class of nonlinear systems which have been brought under extended linearization and are subject to matrix perturbations that are either structured or unstructured. A method to obtain an upper bound for the radius of stability in extended linearization based on overvaluing a comparison system (Metzlerian) is proposed. It is shown that the stability radius around a suitable domain can be obtained by computing the largest singular value of an overvalued matrix that posses special properties.

Robust SDC parameterization for a class of Extended Linearization systems

We consider nonlinear regulation of systems with parametric uncertainty. Under mild conditions, these systems can be brought into a psuedo-linear form known as extended linearization. Under this formulation, conventional linear control synthesis methods can be applied. One popular technique that mimics the LQR method of optimal linear control is referred to as the State-Dependent Riccati Equation (SDRE) approach. SDRE control relies on a non-unique factorization of the system dynamics known as the State Dependent Coefficient (SDC) parameterization. Under system uncertainty, each SDC parameterization will produce its own radius of stability in a region of interest in the state space. In this paper a method to compute the radius of stability in a special class of systems is used to obtain the SDC parameterization which results in the maximum radius of stability for the original nonlinear system in the region of interest. It is shown that the problem of finding the maximum radius of stability from a hyperplane of SDC parameterizations can be reduced to constrained minimization of the spectral norm of a comparison system.

State and unknown input disturbance estimation for positive linear systems

In this paper, we consider the problem of designing a special type of observer to estimate the state and unknown input disturbance for linear time-invariant positive systems. Although positive observers have been designed for positive systems, they are unable to estimate the states when unknown inputs or disturbances are present in the systems. To realize simultaneous estimation of states and unknown inputs, we first design positive unknown input observers (PUIO) for positive linear systems, which is the main contribution of this paper. Then, we provide a procedure to estimate the unknown disturbance. The PUIO design can be performed with the aid of a positive stabilization scheme via LMI. A critical step in the design process is the requirement of imposing a condition on positivity of the generalized inverse of a certain design matrix. We show that this can easily be accomplished with the aid of a unique result, which makes the design of PUIO possible. An alternative LMI with less restrictive assumption is also included to design PUIO. Finally, theoretical results are supported by numerical examples.

Simultaneous state and fault estimation for positive systems

This paper introduces a special type of unknown input observer to estimate the states and faults for linear time invariant positive systems. Both actuator and sensor faults are considered and the solution for each case is provided. Although positive observers have been designed for positive systems, they are unable to estimate the states when unknown inputs (disturbances or faults) are present in the systems. To realize simultaneous estimation of states and unknown inputs, we design a positive unknown input observer (PUIO) for positive linear systems. A critical step in the design process is the requirement of imposing a condition on positivity of the generalized inverse of a certain design matrix. The design can be performed with the aid of a positive stabilization procedure via LMI. We also show that the problem of simultaneous states and sensor faults estimations can be solved by a conversion scheme. By introducing an auxiliary positive system constructed from the output and its augmentation to the original positive system, we convert the sensor fault as an unknown input and employ the PUIO design to the augmented system. Finally, theoretical results are supported by numerical examples.

Robust fault detection for positive systems

In this paper, we consider the problem of robust fault detection for linear time-invariant positive systems. Although positive observers have been designed for positive systems, they are unable to estimate the states when unknown inputs (disturbances or faults) are present in the systems. The first goal of this paper is to show how a positive unknown input observer (PUIO) can be designed for positive systems. The PUIO design can be performed with the aid of a positive stabilization scheme via LMI in which the positivity of the generalized inverse of a certain design matrix is required. Then, we take advantage of PI observer combined with PUIO structure to estimate the faults in positive systems. The main contribution of this paper is to design a PI-based unknown input observer (PIUIO) which is capable of decoupling the unknown input disturbance while estimating the fault. Design procedures with high PI gains are outlined through parametrized eigenvalue assignment and LMI for the case of nonlinear fault. We also demonstrate that the PIUIO with a fading term achieves the same goal with low proportional and integral gains. Finally, illustrative examples are included to support the theoretical results.

Distributed detection filter design for intruder identification

We consider the problem of simultaneously identifying m intruders in a network consisting of n cooperative agents. Our approach consists of identifying attacks through a distributed scheme that uses detection filters. It is shown that the problem of identifying multiple attackers can be formulated as a spectral assignment problem and that the filter gains can be obtained through a carefully constructed linear system of equations. Necessary and sufficient conditions for the existence of the solution to the linear system are provided in terms of the network topology. The approach is highlighted through an illustrative example.