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An Invariance Problem for Control Systems with Deterministic Uncertainty

Lech Górniewicz, Paolo Nistri (1996)

Banach Center Publications

This paper deals with a class of nonlinear control systems in R n in presence of deterministic uncertainty. The uncertainty is modelled by a multivalued map F with nonempty, closed, convex values. Given a nonempty closed set K ⊂ R n from a suitable class, which includes the convex sets, we solve the problem of finding a state feedback ū(t,x) in such a way that K is invariant under any system dynamics f. As a system dynamics we consider any continuous selection of the uncertain controlled dynamics F.

An LPV pole-placement approach to friction compensation as an FTC problem

Ron J. Patton, Lejun Chen, Supat Klinkhieo (2012)

International Journal of Applied Mathematics and Computer Science

The concept of combining robust fault estimation within a controller system to achieve active Fault Tolerant Control (FTC) has been the subject of considerable interest in the recent literature. The current study is motivated by the need to develop model-based FTC schemes for systems that have no unique equilibria and are therefore difficult to linearise. Linear Parameter Varying (LPV) strategies are well suited to model-based control and fault estimation for such systems. This contribution involves...

An object-oriented approach to simulating human gait motion based on motion tracking

Martin Tändl, Tobias Stark, Nihat Ercümet Erol, Franz Löer, Andrés Kecskeméthy (2009)

International Journal of Applied Mathematics and Computer Science

Accurate bone motion reconstruction from marker tracking is still an open and challenging issue in biomechanics. Presented in this paper is a novel approach to gait motion reconstruction based on kinematical loops and functional skeleton features extracted from segmented Magnetic Resonance Imaging (MRI) data. The method uses an alternative path for concatenating relative motion starting at the feet and closing at the hip joints. From the evaluation of discrepancies between predicted and geometrically...

An observability estimate for parabolic equations from a measurable set in time and its applications

Kim Dang Phung, Gengsheng Wang (2013)

Journal of the European Mathematical Society

This paper presents a new observability estimate for parabolic equations in Ω × ( 0 , T ) , where Ω is a convex domain. The observation region is restricted over a product set of an open nonempty subset of Ω and a subset of positive measure in ( 0 , T ) . This estimate is derived with the aid of a quantitative unique continuation at one point in time. Applications to the bang-bang property for norm and time optimal control problems are provided.

An observability problem for a class of uncertain-parameter linear dynamic systems

Krzysztof Oprzędkiewicz (2005)

International Journal of Applied Mathematics and Computer Science

An observability problem for a class of linear, uncertain-parameter, time-invariant dynamic SISO systems is discussed. The class of systems under consideration is described by a finite dimensional state-space equation with an interval diagonal state matrix, known control and output matrices and a two-dimensional uncertain parameter space. For the system considered a simple geometric interpretation of the system spectrum can be given. The geometric interpretation of the system spectrum is the base...

An optimal control approach to cancer treatment under immunological activity

Urszula Ledzewicz, Mohammad Naghnaeian, Heinz Schättler (2011)

Applicationes Mathematicae

Mathematical models for cancer treatment that include immunological activity are considered as an optimal control problem with an objective that is motivated by a separatrix of the uncontrolled system. For various growth models on the cancer cells the existence and optimality of singular controls is investigated. For a Gompertzian growth function a synthesis of controls that move the state into the region of attraction of a benign equilibrium point is developed.

An Optimal Control Problem for a Predator-Prey Reaction-Diffusion System

N. C. Apreutesei (2010)

Mathematical Modelling of Natural Phenomena

An optimal control problem is studied for a predator-prey system of PDE, with a logistic growth rate of the prey and a general functional response of the predator. The control function has two components. The purpose is to maximize a mean density of the two species in their habitat. The existence of the optimal solution is analyzed and some necessary optimality conditions are established. The form of the optimal control is found in some particular...

An optimal sliding mode congestion controller for connection-oriented communication networks with lossy links

Andrzej Bartoszewicz, Piotr Leśniewski (2014)

International Journal of Applied Mathematics and Computer Science

A new discrete-time sliding-mode congestion controller for connection-oriented networks is proposed. Packet losses which may occur during the transmission process are explicitly taken into account. Two control laws are presented, each obtained by minimizing a different cost functional. The first one concentrates on the output variable, whereas in the second one the whole state vector is considered. Weighting factors for adjusting the influence of the control signal and appropriate (state or output)...

An optimal strong equilibrium solution for cooperative multi-leader-follower Stackelberg Markov chains games

Kristal K. Trejo, Julio B. Clempner, Alexander S. Poznyak (2016)

Kybernetika

This paper presents a novel approach for computing the strong Stackelberg/Nash equilibrium for Markov chains games. For solving the cooperative n -leaders and m -followers Markov game we consider the minimization of the L p - norm that reduces the distance to the utopian point in the Euclidian space. Then, we reduce the optimization problem to find a Pareto optimal solution. We employ a bi-level programming method implemented by the extraproximal optimization approach for computing the strong L p - Stackelberg/Nash...

An optimality system for finite average Markov decision chains under risk-aversion

Alfredo Alanís-Durán, Rolando Cavazos-Cadena (2012)

Kybernetika

This work concerns controlled Markov chains with finite state space and compact action sets. The decision maker is risk-averse with constant risk-sensitivity, and the performance of a control policy is measured by the long-run average cost criterion. Under standard continuity-compactness conditions, it is shown that the (possibly non-constant) optimal value function is characterized by a system of optimality equations which allows to obtain an optimal stationary policy. Also, it is shown that the...

An output controllability problem for semilinear distributed hyperbolic systems

E. Zerrik, R. Larhrissi, H. Bourray (2007)

International Journal of Applied Mathematics and Computer Science

The paper aims at extending the notion of regional controllability developed for linear systems cite to the semilinear hyperbolic case. We begin with an asymptotically linear system and the approach is based on an extension of the Hilbert uniqueness method and Schauder's fixed point theorem. The analytical case is then tackled using generalized inverse techniques and converted to a fixed point problem leading to an algorithm which is successfully implemented numerically and illustrated with examples....

An SFDI observer-based scheme for a general aviation aircraft

Marco Ariola, Massimiliano Mattei, Immacolata Notaro, Federico Corraro, Adolfo Sollazzo (2015)

International Journal of Applied Mathematics and Computer Science

The problem of detecting and isolating sensor faults (sensor fault detection and isolation-SFDI) on a general aviation aircraft, in the presence of external disturbances, is considered. The proposed approach consists of an extended Kalman observer applied to an augmented aircraft plant, where some integrators are added to the output variables subject to faults. The output of the integrators should be ideally zero in the absence of model uncertainties, external disturbances and sensor faults. A threshold-based...

An SQP trust region method for solving the discrete-time linear quadratic control problem

El-Sayed M.E. Mostafa (2012)

International Journal of Applied Mathematics and Computer Science

In this paper, a sequential quadratic programming method combined with a trust region globalization strategy is analyzed and studied for solving a certain nonlinear constrained optimization problem with matrix variables. The optimization problem is derived from the infinite-horizon linear quadratic control problem for discrete-time systems when a complete set of state variables is not available. Moreover, a parametrization approach is introduced that does not require starting a feasible solution...

An unbounded Berge's minimum theorem with applications to discounted Markov decision processes

Raúl Montes-de-Oca, Enrique Lemus-Rodríguez (2012)

Kybernetika

This paper deals with a certain class of unbounded optimization problems. The optimization problems taken into account depend on a parameter. Firstly, there are established conditions which permit to guarantee the continuity with respect to the parameter of the minimum of the optimization problems under consideration, and the upper semicontinuity of the multifunction which applies each parameter into its set of minimizers. Besides, with the additional condition of uniqueness of the minimizer, its...

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