Nonsmooth optimal regulation and discontinuous stabilization.
Norm estimates for solutions of matrix equations AX-XB=C and X-AXB=C
Let A, B and C be matrices. We consider the matrix equations Y-AYB=C and AX-XB=C. Sharp norm estimates for solutions of these equations are derived. By these estimates a bound for the distance between invariant subspaces of matrices is obtained.
Normalized finite fractional differences: Computational and accuracy breakthroughs
This paper presents a series of new results in finite and infinite-memory modeling of discrete-time fractional differences. The introduced normalized finite fractional difference is shown to properly approximate its fractional difference original, in particular in terms of the steady-state properties. A stability analysis is also presented and a recursive computation algorithm is offered for finite fractional differences. A thorough analysis of computational and accuracy aspects is culminated with...
Note on approximate non-Gaussian filtering with nonlinear observation relation
Note on nonlinear semigroups and free boundary problem for controlled Markov processes
Note on stability estimation in average Markov control processes
We study the stability of average optimal control of general discrete-time Markov processes. Under certain ergodicity and Lipschitz conditions the stability index is bounded by a constant times the Prokhorov distance between distributions of random vectors determinating the “original and the perturbated” control processes.
Note on stability of a control system
Note on stability of a linear homogeneous control system
Note on strong solutions of a stochastic inclusion.
Note on the internal stabilization of stochastic parabolic equations with linearly multiplicative gaussian noise
The parabolic equations driven by linearly multiplicative Gaussian noise are stabilizable in probability by linear feedback controllers with support in a suitably chosen open subset of the domain. This procedure extends to Navier − Stokes equations with multiplicative noise. The exact controllability is also discussed.
Notes on a hierarchical theory of systems and applications
Notes on and robustness tests
An upper bound for the complex structured singular value related to a linear time-invariant system over all frequencies is given. It is in the form of the spectral radius of the -norm matrix of SISO input-output channels of the system when uncertainty blocks are SISO. In the case of MIMO uncertainty blocks the upper bound is the -norm of a special non-negative matrix derived from -norms of SISO channels of the system. The upper bound is fit into the inequality relation between the results of...
Novel fault detection criteria based on linear quadratic control performances
This paper proposes a new approach to designing a relatively simple algorithmic fault detection system that is potentially applicable in embedded diagnostic structures. The method blends the LQ control principle with checking and evaluating unavoidable degradation in the sequence of discrete-time LQ control performance index values due to faults in actuators, sensors or system dynamics. Design conditions are derived, and direct computational forms of the algorithms are given. A simulation example...
Novel optimal recursive filter for state and fault estimation of linear stochastic systems with unknown disturbances
This paper studies recursive optimal filtering as well as robust fault and state estimation for linear stochastic systems with unknown disturbances. It proposes a new recursive optimal filter structure with transformation of the original system. This transformation is based on the singular value decomposition of the direct feedthrough matrix distribution of the fault which is assumed to be of arbitrary rank. The resulting filter is optimal in the sense of the unbiased minimum-variance criteria....
Nový přístup k identifikaci diskrétních dynamických soustav
NTGsim: a graphical user interface and a 3D simulator for nonlinear trajectory generation methodology
Nonlinear Trajectory Generation (NTG), developed by Mark Milam, is a software algorithm used to generate trajectories of constrained nonlinear systems in real-time. The goal of this paper is to present an approach to make NTG more userfriendly. To accomplish this, we have programmed a Graphical User Interface (GUI) in Java, using object oriented design, which wraps the NTG software and allows the user to quickly and efficiently alter the parameters of NTG. This new program, called NTGsim, eliminates...
Null and approximate controllability for weakly blowing up semilinear heat equations
Null controllability and application to data assimilation problem for a linear model of population dynamics
In this paper we study a linear population dynamics model. In this model, the birth process is described by a nonlocal term and the initial distribution is unknown. The aim of this paper is to use a controllability result of the adjoint system for the computation of the density of individuals at some time .
Null controllability of a coupled model in population dynamics
We are concerned with the null controllability of a linear coupled population dynamics system or the so-called prey-predator model with Holling type I functional response of predator wherein both equations are structured in age and space. It is worth mentioning that in our case, the space variable is viewed as the “gene type” of population. The studied system is with two different dispersion coefficients which depend on the gene type variable and degenerate in the boundary. This system will be governed...
Null controllability of a nonlinear diffusion system in reactor dynamics
In this paper, we prove the exact null controllability of certain diffusion system by rewriting it as an equivalent nonlinear parabolic integrodifferential equation with variable coefficients in a bounded interval of with a distributed control acting on a subinterval. We first prove a global null controllability result of an associated linearized integrodifferential equation by establishing a suitable observability estimate for adjoint system with appropriate assumptions on the coefficients. Then...