Browsing by Subject "optimal control"

Now showing 1 - 13 of 13

Access status: Open Access ,
Czy sterowanie predykcyjne wymaga dokładnej optymalizacji?
(Wydawnictwa AGH, 2006) Bania, Piotr
A nonlinear predictive control scheme, which does not require an exact solution of optimal control problem is proposed. The proper asumptions are formulated and the stability of the closed loop system is proved. These results are used for analysis of proposed algorithm robustness. Robust stability of the alghorithm is proved in the case of suboptimal solutions of the optimal control problem in the presence of bounded disturbances. Proposed schme is applied to the pendulum-cart nonlinear control system with disturbances.
Access status: Open Access ,
Fractional nonlocal integrodifferential equations of mixed type with time-varying generating operators and optimal control
(Wydawnictwa AGH, 2010) Wang, JinRong; Wei, W.; Yang, YanLong
In this paper, a class of fractional integrodifferential equations of mixed type with time-varying generating operators and nonlocal conditions is considered. Using a contraction mapping principle and Krasnoselskii's fixed point theorem via Gronwall's inequality, the existence and uniqueness of mild solution are given. The existence of optimal pairs of systems governed by fractional integrodifferential equations of mixed type with time-varying generating operators and nonlocal conditions is also presented.
Access status: Open Access ,
Multi-channel virtual-microphone feedback minimum-variance active noise control system
(Wydawnictwa AGH, 2009) Pawełczyk, Marek
Classical active noise control systems are designed to minimise, in a sense, the residual signal at the microphone providing information about acoustic noise and secondary sound interference. The secondary sound operates at the same time on the acoustic noise at other positions including user ears. In the worst case this can result in sound reinforcement at those positions. In many applications placing another microphone directly at the ears is not accepted. It is then justified to make efforts to design a dedicated system. The purpose is to minimise the mean-square value of the noise at the desired location while performing measurements of sound interference results at another location. This can be done by employing the general idea of Vrtual-Microphone Control systems. However, for many active noise control applications the use of a single pair of microphone and loudspeaker does not suffice to obtain satisfactory performance, i.e. generate a zone of quiet of acceptable dimensions. Moreover, for some applications, presence of an obstacle, e.g. the head in an active headrest system, constitutes a barrier for the zone of quiet at one side to propagate to the other side. Therefore, more microphones and loudspeakers are often necessary. In the most general case a coupling between subsequent pairs should be taken into account resulting in a multi-channel system. In previous papers of the author adaptive systems have been designed and analysed. In this paper a fixed parameter multi-channel Virtual-Microphone Control system, optimal in the mean- square sense, is designed. It includes non-minimum phase property of the system channels. Both the case of more inputs than outputs as well as the case of more outputs than inputs are considered. Factorization techniques have been used for the design. The system is verified by successfully controlling noise for the active headrest system.
Access status: Open Access ,
Necessary optimality conditions for predator-prey system with a hunter population
(2010) Apreutesei, Narcisa C.
An optimal control problem is studied for a predator-prey reaction-diffusion system. A hunter population is introduced in the ecosystem and it is interpreted as a control variable. One finds necessary optimality conditions in order that, in the end of a given time interval, the total density of the two populations is maximal.
Access status: Open Access ,
Optimal control of an Infinite Order Hyperbolic System with Multiple Time-Varying Lags
(Wydawnictwa AGH, 2011) Kowalewski, Adam
In this paper an optimal distributed control problem for an infinite order hyperbolic system in which different multiple time-varying lags appear both in the state equation and in the boundary condition is considered. Making use of Lion's scheme (Lions 1971), necessary and sufficient conditions of optimality for the Neumann problem with the quadratic performance functional and constrained control are derived.
Access status: Open Access ,
Problemy sterowania optymalnego zespołem orientowanych ogniw fotowoltaicznych
(Wydawnictwa AGH, 2011) Oprzędkiewicz, Krzysztof; Teneta, Janusz
In the paper problems of optimal control for oriented photovoltaic systems are presented. A structure of hierarchical, two-level control system, control problems and algorithms for plant under consideration are shown. An energy consumption at the process control level should be minimal, because energy used to plant control is produced by the solar system. The supervising and coordina- tion of process control is done with the use of upper level. In the paper a proposition of a cost function describing an energy consumption by the process control level is also presented. This cost function is determined by a number of factors.
Access status: Open Access ,
Projektowanie regulatora worst case dla systemu z niepewnym parametrem z wykorzystaniem teorii gier
(Wydawnictwa AGH, 2009) Ganobis, Michał
W niniejszej pracy przedstawione zostały możliwości wykorzystania teorii gier w sterowaniu systemem z niepewnym parametrem. Przedstawiono metodę bazującą na zasadzie maksimum oraz osiągnięciach rachunku wariacyjnego i gier różniczkowych. Uzyskano trajektorie optymalnego sterowania w pętli otwartej, jak również przebieg maksymalnie niekorzystnego zachowania niepewności parametru. Całość została zilustrowana na przykładzie obiektu fizycznego w postaci wózka o niepewnej masie.
Access status: Open Access ,
Przegląd możliwości sterowania systemem o zmiennym momencie bezwładności typu ball on beam
(Wydawnictwa AGH, 2008) Ganobis, Michał
The purpose of this paper is to present a ball on beam system and a short overview of possibilities of its control. It contains control design methods using mathematical model (LQR), and without it (fuzzy logic controller).
Access status: Open Access ,
Regulator minimalnoenergetyczny dla obiektu II rzędu o niepewnych parametrach
(Wydawnictwa AGH, 2011) Mitkowski, Wojciech; Oprzędkiewicz, Krzysztof
W pracy zaprezentowano przykład syntezy optymalnego regulatora P (proporcjonalnego) dla obiektu II rzędu o niepewnych parametrach, który opisuje dużą klasę rzeczywistych obiektów regulacji (np. serwomechanizmy). Zadaniem regulatora jest przeprowadzenie układu ze stanu początkowego do końcowego z minimalnym zużyciem energii oraz w najkrótszym czasie w obrębie całego obszaru niepewnych parametrów obiektu. Jako funkcje kosztu rozważono: funkcję opisującą »najgorszy przypadek« w całym obszarze niepewnych parametrów oraz funkcję będącą »środkiem ciężkości« funkcji kosztu w całym obszarze niepewnych parametrów obiektu. Syntezę regulatora wykonano metodami symulacyjnymi z użyciem środowiska MATLAB. Wyniki eksperymentów numerycznych pokazują, że zastosowanie obu rozważanych funkcji kosztu daje bardzo zbliżone rezultaty.
Access status: Restricted ,
Sterowanie predykcyjne układem zbiorników z wodą
(Data obrony: 2017-10-23) Jackowski, Dariusz
Wydział Elektrotechniki, Automatyki, Informatyki i Inżynierii Biomedycznej
Access status: Restricted ,
Strategia optymalnego inwestowania z wykorzystaniem sterowania optymalnego
(Data obrony: 2014-07-25) Szabelski, Sebastian
Wydział Matematyki Stosowanej
Access status: Open Access ,
Sufficient conditions for optimality for a mathematical model of drug treatment with pharmacodynamics
(2017) Leszczyński, Maciej; Ratajczyk, Elżbieta; Ledzewicz, Urszula; Schättler, Heinz M.
We consider an optimal control problem for a general mathematical model of drug treatment with a single agent. The control represents the concentration of the agent and its effect (pharmacodynamics) is modelled by a Hill function (i.e., Michaelis-Menten type kinetics). The aim is to minimize a cost functional consisting of a weighted average related to the state of the system (both at the end and during a fixed therapy horizon) and to the total amount of drugs given. The latter is an indirect measure for the side effects of treatment. It is shown that optimal controls are continuous functions of time that change between full or no dose segments with connecting pieces that take values in the interior of the control set. Sufficient conditions for the strong local optimality of an extremal controlled trajectory in terms of the existence of a solution to a piecewise defined Riccati differential equation are given.
Access status: Open Access ,
Warunki normalności zasady maksimum Pontriagina dla zadań z ograniczeniami stanu końcowego
(Wydawnictwa AGH, 2011) Bania, Piotr
A version of Pontryagin's Maximum Principle for optimal control problems with final state and control time constraints is presented. Sufficient conditions for normality of Lagrange multipliers are given. Considerations are illustrated with examples.